user's manual for program skbrd - lehigh …digital.lib.lehigh.edu/fritz/pdf/400_15.pdf · i i...

I I I I I I I I I I I I I I I I I I I

USER'S MANUAL FOR PROGRAM SKBRD

COMPUTER PROGRAM FOR THE ANALYSIS OF SKEWED ECCENTRICALLY

STIFFENED PLATES AND SKEWED I-BEAM

AND SPREAD BOX-BEAM BRIDGES

by

Ernesto S. deCastro

Celal N. Kostem

Fritz Engineering Laboratory

Department of Civil Engineering

Lehigh University

June 1975

Fritz Engineering Laboratory Report No. 400.15

I I

TABLE OF CONTENTS

I Page

I ABSTRACT

1. INTRODUCTION 1

I 1.1 Structural Idealization 1

1.2 Coordinate System and Sign Convention 3

I 2. INPUT DATA INSTRUCTION 5

I 2.1 Structural Data Specifications 5

2.2 Load Specifications 12

I 2.3 Output Specifications 18

2.4 Load Distribution Information 19

I 3. EXAMPLE PROBLEMS 25

3.1 Ex amp 1 e 4/:1 - Skew I-Beam Bridge 25

I 3.2 Example 4F2 - Skew Box-Beam Bridge 26

I 4. OUTPUT DESCRIPTION 28

4.1 Structure Description 28

I 4.2 Load Description 29

4.3 Vee tor of Displacements 30

I 4.4 Reactions 31

I 4.5 Generalized Force Vector 31

4.6 Stress Resultants 31

I 4. 7 Load Distribution Information 32

5. REFERENCES 34

I 6. FIGURES 35

I 7. TABLES 42

8. LISTING OF PROGRAM SKBRD 50

I I


ABSTRACT

This user's manual describes the input instructions for pro

gram SKBRD. This program performs the finite element analysis of

plates and eccentrically stiffened plates. The plates can be of any

arbitrary shape in plan and may be stiffened with beams or box-beams.

The program is especially suited to the analysis of skew bridges with

!-beams or spread box-beams. When desired, the lateral load distri

bution is performed for a given loading, i.e. the determination of

the loads carried by the individual beams.

/


1, INTRODUCTION

Program SKBRD performs the finite element analysis of

beam-slab structures of arbitrary geometry. The program is specifi

cally written for the analysis of skew bridges with !-beams (Fig. 1)

or spread box-beams (Fig. 2), and subjected to vehicular loads. The

same program can be used in the analysis of general plates and plates

eccentrically stiffened with prismatic beams. the program is based

on the analytical development described in Reference 1. Some of the

Fortran routines, with minor modifications, are from References 2

and 3.

1.1 Structural Idealization

The structural idealization for the I-beam and the box

beam structures are shown in Figs. 1 and 2 respectively. The struc

ture is subdivided into a series of finite elements interconnected at

nodal points. The plane of reference for the whole structure is at

the midplane of the deck slab.

Three basic finite elements are used: (1) quadrilateral

plate element, (2) eccentric beam element, and (3) web element CFig.3).

a) Quadrilateral Plate Element

The plate bending behavior of the element is represented oy

the Q-19 element CRef, 2). The in-plane behavior of the element is

represented by the Q8Dll element CRef. 3). The in-plane and the plate

bending properties are combined in the program to form the basic

-1-

plate element. The element has 4 external nodes, I, J, K, and L in

the counter-clockwise order (fig. 3a). This element is used to model

the deck slab and the top and bottom plate of box-beams. The ele

ment has linear in-plane displacement and cubic transverse displace

ment patterns.

b) Eccentric Beam Element

The in~plane and out of plane behavior of the beam element

is described about an axis on the reference plane (Ref. 1). Thus,

in-plane and bending interaction with the slab can be considered.

The beam element has nodes I and J lying on the reference plane

(Fig. 3c). The eccentricity of the beam is the distance of the cen

troid of the beam cross-section from the reference plane. The beam

element models the I-beam and the diaphragms which can be eccentri

cally attached to the deck slab. The element describes a linear

in-plane displacement and cubic transverse displacement patterns.

c) Web Element

The web element is used only for the beam-slab bridge

superstructure with box-beams. The element represents the in-plane

and out of plane behavior of the webs of the box-beams. The in

plane behavior is approximated by the QUSP12 element (Ref. 3). One

way bending about global X axis is assumed for the out of plane

behavior (Refs. 1 and 3). The element has a cubic displacement

-2-


I I I I I I I I I.

I I I I I I I I I I

pattern in the x~direction and a linear displacement pattern in

the z-direction, The element has 4 nodes I, J, K, and L in the

counter-clockwise order O'ig. 3b). The nodes interconnect the top

and bottom plate elements of the box-beam when one element is used

through the depth of the box-beam.

The material properties of the above elements are specified

in the elasticity matrix as follows

0

0

0 0

where E1 , E2, G12 are the elastic and shear moduli and v12, v21

are the Poisson's ratios in the principal directions. For the beam

element, and in the isotropic case for the plate and web element the

elastic moduli are E1 = E2 = E and Poisson's ratio are v12 = v21 =

v.

1.2 Coordinate System and Sign Convention

The structure must be referred to the global cartesian

x- y- z coordinate system (Fig. 1 and 2). The midplane of the

deck slab must lie of the x ~ y plane. Positive sign convention for

stresses and displacements are shown in Fig. 4.

-3-

The nodes can be numbered in any direction. Care, however,

should be taken such that the bandwidth is minimized (Ref. 1). Only

the x and y coordinates of the nodes are needed. The z-coordinates

of the nodes at the bottom of the web elements are specified in the

web element properties (See Chapter 2, Section 6.c).

Two example problems are illustrated in Figs. 4 and 5.

The general input instructions are detailed in Chapter 2. The input

for the two example problems are worked out in Chapter 3.

-4-



2. INPUT DATA INSTRUCTION

The input data is divided into four parts (1) structural

data specifications (2) load specifications (3) output specification

and (4) load distribution information.

2.1 Structural Data Specifications

The following cards define the title, material and geometry

of the structure.

1. Control Card (A6)

The first card for the structural data deck must be the

START card. The word START must be punched in columns 1-5. The

START card also signifies the beginning of a new problem.

cols.

1-5 START punched in columns 1 to 5.

2. Title Cards (13A6,/13A6)

The cards immediately following the START card are two

cards which contain alpha-numeric information. These two cards may

be used for job description and identification··

cols. 1-78 Job description

cols. 1-78 Job identification

3. Structure Information (6I4, L4, I4)

cols, 1-4 NUMEL total number of elements

-5-

cols, 5-8 NIJ.MNP number of external nodal points

9-12 NlJMBC number of nodes with boundary

conditions

13-16 NMAT number of materials

17-20 NLCS number of load cases

21-24 NBLKL number of equations per block

25-28 QEQ Flag word to indicate if all quad-

rilateral elements and beam ele-

ments are equal: T if true, F if

false (Left justified)

29-32 NBX Number of longitudinal box-beams

CFor spread box~beam analysis only)

4. Material card(s) (14, El0,3, 3Fl0.3, 2El0.3, Fl0.3)

There are NMAT number of cards, one card per different mat-

erial. The material card contains the material constants as follows:

For plate elements;

cols. 1-4 I material number

5-14 E mean modulus of elacticity,

jEl • E21

15-24 RE principal modulus ratio,

El _/ E2

25-34 xu mean Poisson's Ratio

~ 35-44 .XU12 Poisson's Ratio v associated with

shear modulus, E G = 2 (l+v)

-6-



cols, 45-64

65-74

leave blank

Specific weight in force per unit volume

in the +z direction.

In the case of isotopic material, E = E1=E2, RE = 1.0 and

XU == XV12 = v,

For the beam elements

1-4 I material number

5-14 Beam modulus

15-24 must be set equal to 1,0

25-34

35-44 Poisson's ratio for computing shear modulus

45-54

55-74

Effective shear modulus to include shear

distortions in beams.

leave blank

5. Nodal Coordinates (14, 2Fl0.3, 2I4, 2Fl0.3}

The node number and the global x and y coordinates of the

node must be specified for every node point.

1-4 N Node number

5-14 XORD Global x coordinates of node N

15-24 YORD Global y coordinate of node N

The cards must be in numerical sequence starting with N=l.

One card is needed per node. When a sequence of (L-1) node cards is

omitted, the missing nodes and nodal coordinates will automatically be

generated as follows:

xn+k = xn+k-1 + dx

-7-

yn+k = Yn+k-1 + dy

where dx = (Xn+l - X0 )/L, and dy = (yn+l - yn)/L for k = 1,2,3 •••

to L-1. This node card generation is equivalent to specifying equally

spaced node points between the given node cards Nand (N+L),

If mesh generation options are used, the rest of the field

of the node card data must be filled as follows:

cols, 25-28 MOD Module m

29-32 NLIM Limit of generation

33-42 FACX amplification factor fx in

x-direction

43-52 FACY amplification factor fy in

y-direction

where,

xk = x. + fx {X - X. 2

) k ... m """"k-m -K.- m

It should be noted that the node (k-m) and node (k-2m) must be previ-

ously defined before the mesh generation option can be used.

6. Element Information (614, 5F8.3, 214)

There must be one card per element, except when the element

generation option is used. Different sets of information are required

for each type of element.

a) plate elements

-8-



cols. 1-4

5-8

9-12

13-16

17-20

21-24

25-32

33-40

41-48

49-56

57-64

L

NPI

NPJ

NPK

NPL

M

PHI

THI

THJ

THK

THL

Element number

Node point I

Node point J

Node point K

Node point L

Material number

Angle of principal elastic axis

E1 with the global x-axis

Plate thickness at node I

Plate thickness at node J

Plate thickness at node K

Plate thickness at node L

If element cards (N+l) to (N+L-1} are omitted, the missing

cards are generated by increasing the nodal numbers I, J, K, and

L of the preceding element by 1. The generation stops at GN+L)

which is the next element card specified. The material number and

properties of the generated element are set equal to those ~f ele-

ment N. If THI is negative, THJ, THK, and THL are set equal to THI

and need not be specified. If two or more elements have been previ-

ously defined, the element generation option may be used by filling

in columns 65-72 of element N as follows:

cols. 65-68 MOD module m

69-72 NLIM Limit of element generation

The node numbers of the generated elements will be

Ik = Ik + (Ik - Ik 2 ) -m -m - m

-9-

where I means the node I, J, K, or L of the kth element. The element

(k-m) and (k-2m) must be among the elements previously defined.

b) Beam Element (e.g. I, T beams)

cols. 1-4

5-8

9-12

13-16

17-20

21-24

25-32

33-40

41-48

49-56

57-64

L

NPI

NPJ

NPK

NPL

M

THI

THJ

THK

THL

Element number

Node point I

Node point J

Node-point J

Node point I

Material number

leave blank

Beam moment of Inertia

Beam torsional moment of Inertia

Beam eccentricity of centroid with

mid-plane of plate

Beam cross-sectional area

The beam element generation follows exactly the plate gen

eration option.

c) Web element (box-beam only)

cols. 1-4 L Element number

5-8 NPI Node point I

6-12 NPJ Node point J

13-16 NPK Node point K

17-20 NPL Node point L

21 ... 24 M Haterial number

-10-



cols. 25-32

33-40

41-48

49-64

THI

THJ

leave blank

Web element thickness

Web element depth

leave blank

The web element generation follows exactly the plate gen-

eration option.

7. Boundary Condition Data (l4, lX, 5!1, 7F8.2, 4X, 214)

The number of boundary conditions cards must oe equal to

NUMBC except when the boundary condition is used.

cols, 1-4

5

6

7

8

9

10

11-18

N

IBCl

IBC2

IBC3

IBC4

IBC5

ALPHA

Node number with boundary condition

1eave blank

1 if in-plane displacement

u is constrained; otherwise 0.

1 if in-plane displacement

v is constrained; otherwise 0.

1 if transverse displacement

w is constrained; otherwise 0.

1 if rotation about the x-axis

a is constrained; otherwise o. X

1 if rotation about the y-axis ay constrained; otherwise 0,

Angle in degrees, positive counter

clockwise, in the direction of

which u is specified to displace.

-11-

cols. 19-26 BETA

27-70

Angle in degrees, positive

counterclockwise about which

e is specified to rotate. X

leave blank

The boundary condition generation can be used by filling

columns 71 to 78 of Node N such that,

cols. 71-74

75-78

MOD

NLIM

module m

node limit of generation

where the boundry conditions specified for N are also generated for

node (N+n-m), for n = 1, 2, 3 •• ,, up to node (N+n.m). It should

be noted that NLIM = N+n.m.

2.2 Load Specifications

The load specifications consist of the (1) title card (2)

control card (3) concentrated load cards (4) distribution load cards

and (5) truck load cards. Any or all of the above load cards may be

used in combination.

Two types of concentrated loads may be specified according

to the flagwords on the title card : A) Type I where concentrated

loads are applied only at the nodes and B) Type II where concentrated

loads are applied anywhere on the structure. Both types, however,

can consider nodal concentrated load and uniform or varying loads if

specified by the control card.

-12-



1. Title Card (13A6)

The first two words are used as flag words by the program.

The rest of the field is any alphanumerical information which can be

used to identify the load case. The whole title card is printed as

the heading for each load case.

cols. 1-6 HEAD!

7-12 HEAD2

13-74 HEAD3

First flagword used in lateral

load distribution analysis

(See section 2.4)

Second flagword to identify

the load type. Leave blank for

Type I. The word BRIDGE must

be punched in columns 7-12 for

load Type II.

Alphanumeric information

For the second, third or any subsequent load case for the

same problem, the flagword card must precede the title card.

cols. 1-6 CHECK

2. Control Card (!4, 2L4)

Punch SLOADS if the load case

is not the initial load case.

The control card contains the instructions for the number of

concentrated load cards to be read in, and whether to consider uniform

load or dead load of the plate elements.

cols. 1-4 NCLD

-13-

Number of concentrated load

cards

cols. 5-8 DLOAD Punch T to consider gravity load

or the dead load of the plate,

otherwise punch F (left justified)

9-12 GLOAD Punch T to consider uniform dis-

tributed loads, otherwise punch

F (left justified)

3. Concentrated Load Card(s) (14, 5Fl0.3)

The number of concentrated load cards must be equal to NCLD.

If NCLD is zero there are rto concentrated load cards, and this set of

cards is not needed.

4.

cols. 1-4 N

5-14 Rl

15-24 R2

25-34 R3

35-44 R4

45-54 R5

Node number with the applied

concentrated load.

Applied concentrated load F in X

the direction of x.

Applied concentrated load F in y

in the direction of y.

Applied concentrated load F in z

the direction of z.

Applied concentrated moment M X

in the direction of a • X

Applied concentrated moment M y

in the direction of ey.

Distributed Load Cards (14, 4Fl0.3)

Any or all of the elements may have a uniformly distributed

-14-


I I I I I I I I I I I I . I

I I I I I I

load. DLOAD must be punched T for this case (See 3. above). There are

no distributed load cards if DLOAD is punched F, and this set of cards

is not needed.

cols. 1-4

5-14

15-24

25-34

35-44

L

PLI

PLJ

PLK

Pll

Element number with the uni

form load

Distributed load intensity

over node NPI

Distibuted load intensity

over node NPJ

Distributed load over node NPK

Distributed load over node NPL

There must be one distributed load card per element. If dis

tributed load cards for elements (N+l) to (N+L-1) are missing the dis

tributed load for these elements are set equal to those specified for

element N. PLI, PLJ, PLK, and PLL may be set to zero for the elements

without concentrated load which precede the element (N+L) •

Line loads on the structure or the gravity load of the beams

must be reduced to equivalent nodal forces and added to the nodal load

cards in Section 3.

5. Truck Loading Cards

The truck load cards are needed if HEAD2 is equal to BRIDGE.

Otherwise no cards are needed. Three load cases are possible: a) a

group of concentrated loads, b) test vehicle load (Ref.!), and c)

HS20-44 design vehicular load (Ref, 5). When any of the above load

-15-

cases is specified, all the plate elements must be parallelogram in

shape. The skewness of the parellelogram must be defined in degrees 0

from a rectangular shape, i.e., 0 for a rectangular element.

a.) Case A- Group of Concentrated Loads

This case must have at least two cards: the load centroid card

and the individual load card.

Load Centroid Card (A4, 6X, 2FlO,O, IS, FlO.O)

cols. 1-4 TYPES leave blank

11-20 XCEN Global x~coordinate of the cen-

troid of the group of loads

21-30 YCEN Global y-coordinate of the cen-

troid of the group of loads

31-35 NW Number of concentrated loads in

groups

PHI Skew angle in degrees of the

plate elements used.

Individual Load Card(s) (3F8.0)

There are NW cards in this set. One card per concentrated

load is needed.

cols. 1-8 w Load intensity

9-16 xw x-distance of the load from the

centroid of the group

17-24 YW y .. distance of the load from the

centroid of the group

:...16-



b.) Case B - Test Vehicle Load (A4, 6X, 2FlO.O, IS, FlO.O)

, This case needs only the load centroid card. The type of

load is the test vehicle load used in the field tests of highway

bridges (Ref. 1) ,

cols. 1-4

11-20

21-30

31-3S

36-4S

TYPES

XCEN

YCEN

NW

PHI

The word TEST must be punched

in coltmllls 1-4.

Global x-coordinate of the

centroid of the test vehicle

Global y-coordinate of the

centroid of the test vehicle

leave blank

Angle in degrees of the skew

of the element used.

c.) Case C - HS20 Design Vehicle Load (A4, 6X, 2FlO.O, IS, FlO.O)

Only the load centroid card is needed for this type of loading.

cols. 1-4

11-20

21-30

31-3S

36-4S

TYPES

XCEN

YCEN

NW

PHI

-17-

The word HS20 must be punched

in columns 1-4

Global x-coordinate of the

HS20 vehicle

Global y-coordinate of the

centroid of the HS20 vehicle

leave blank

Angle in degrees of the skew

of the elements used.

2.3 Output Specifications

' The output specification deck consists of (1) a control card

and (2) the node card(s) containing the node numbers whose internal

stress resultants are to be printed out.

1. Control Card

cols. 1-4 II

5-8 12

9-12 NSTOR

2. Node Card(s) (2014}

1 must be punched in column 4

if a print of internal nodal

forces is desired;.otherwise

punch 0.

1 must be punched in column 4

if a print of the internal

stresses at the center of the

element is desired; otherwise

punch 0.

The total number of nodes whose

internal stress resultants are

to be computed, averaged and

printed,

If NSTOR is equal to NUMNP, or to the number of nodes of the

whole structure, the node card(s) are not needed. Node numbers for all

the nodes are automatically generated and stress resultants are printed

for all the nodes. Otherwise the following card(s) are needed.

-18-



cols. 1-4 NPSl

5-8 NPS2

'9-12 NPS3

2,4 Load Distribution Information

First node number whose stress

resultant is to be printed

Second node number whose stress

resultant is to be printed out,

and so on,

A load distribution analysis can be carried out only for

beam-slab highway bridges. The beams, either !-beams or box~beams,

must be in· the x-direction, The lateral distribution of the load will

be based on the total composite beam moments at the ~i~ moment

section for I-beam bridges and at the specified section for box-beam

bridges, Composite beam moments at any desired beam node can be

printed out if desired for the !-beam bridges,

The flagword for a lateral load distribution analysis is

TRUCK for I-beam bridges and DISTRI for box-beam bridges. The correct

flagword must be punched in columns 1-6 of the title card in the load

specifications (Section 2.2). If any word other than TRUCK or DISTRI

is punched in these. columns, a lateral load distribution analysis will

not be performed.

a.) If the flagword is TRUqJ.· , i,e., I-beam bridges, the fol._..

lowing cards are needed:

1, Beam Card (214)

cols. 1-4 NB Number of longitudinal beams

-19-

cols. 5-9 NND

2. Beam Node Card(s) (2014)

Number of beam nodes where

composite moment value is

desired

This card specifies the starting element number of each

longitudinal beam. This card(s) is needed to identify beam

elements to individual longitudinal beams. Once the initial

beam element number of a longitudinal beam is defined, the

other beam elements of the same beam are determined through

the beam linkage.

cols. 1-4

5-8

9-12

IBEAMl

IBEAM2

IBEAM3

First beam element number of

the first longitudinal beam

First beam element number·of

the second longitudinal beam

and so on up to NB

3, Effective Width Card(s) (10F8.0)

These widths are used in the computation of the maximum

beam moments. The location of maximum moment for each beam

is selected by the computer program. The width must be spe

cified for each longitudinal beam,

cols. 1-8 BMXl

9-16 BMX2

=20-

Effective width for the first

longitudinal beam

Efective width for the second

longitudinal beam



cols. 17.-24 BMX2 and so on up to NB

4. Specified Beam Node Card(s) (2014)

If NND is specified not equal to zero, the following

card(s) must follow:

cols. 1-4

5-8

9-12

NBNl

NBN2

NBN3

Any node number of the

beam where a print of the

composite number is des

ired

same as above NBNl

and so on until NND

5, Specified Beam Effective Width Cards (10F8,0)

The effective width corresponding to the specified beam

nodes must be punched follows:

cols. 1-8

9-16

17-24

EWl

EW2

EW3

Effective width for the

beam node NBNl


beam node NBN2

and so on up to NND

b.) If the flagword is DISTRI, i.~., bo~beam bridges, the

following sets of cards are needed (one set for each longitudinal box

beam). Each set contains the node numbers and the contributing width

of the box-beam section where the beam moment for load distribution

analysis is to be computed. The procedure is applicable only for

-21-

one web element through the depth of a box .. beam.

1. Deck Node Cards (2014)

This deck card contains the nodes at the deck elements

of the box-beam section.

cols, 1-4 NTPl

5-8 NTP2

9-12 NTP2

First node number of the

deck element of the box-

beam section

Second node number

Third node number and so on.

2, Deck Element Effective Width (10F8.0)

This card specifies the width at each node which is to

be taken as the effective width in integrating the nodal

internal forces,

cols. 1-8 WTPl

9-16 WTP2

17-24 WTP3

Effective width for the first

deck node of the beam


second deck node of the beam

and so on.

3, Bottom Node Cards (20!4) •

This card contains the bottom nodes of the box-beam.

cols. 1-4

5-8

First bottom node

Second bottom node

-22-



cols, 9-12 Third bottom node (tf two or more plates

model the bottom plate of the box-beam),

and so on.

4, Bottom Node Effective Width Card (10F8.0)

This card specifies the width which is considered to be

the effective width at each bottom node in the integration

of the modal internal forces.

cols. 1-8 WTBl

WTB2

5. Web Node Cards (20!4)


first bottom node


second bottom node, and

so on.

This card contains the top and bottom nodes for the

two web elements of the box-beam at the section.

cols, 1-4 NTWl Node number at the top of

the first weo

5-8 NTW2 Node nmnber at the bottom

of the first web

9-12 NTW2 Node number at the top of

the second web

13-16 NTW3 Node number at the bottom

of the second web

-23-

6. Web Depth Card (10F8.0)

The full depth of the web is specified for the four

nodes in this card. The program computes the effective

portion of the webs contributing to the top or bottom

nodes.

cols. 1-8

9-16

WTWl

WTW2

-24-

Web depth from midplane of

the deck slab to the mid

plane of the bottom plate.

same as above, and so on

up to WTIJ4.



3. EXAMPLE PROBLEMS

A complete set of data is given for each example. A set

of data contains header description to idenify the several parts of

the deck with input instruction in Chapter 2.

3.1 Example #1 - Skew I-Beam Bridge

The first example is a 45 degree skew bridge with 4 pre-

stressed concrete !-beams. The structure is 28 ft. wide and 64 ft.

long. The beams are spaced at 8 ft. The structure is idealized

into parellelogram plate elements and eccentric beam elements (Fig 5).

Two plate elements are specified between the beam and 6 elements are

used along the span. Smaller elements are used near the skew midspan

of the structure (Ref. 1).

The properties of the deck slab are assumed as follows

(Ref. 6).

Plate thickness

Mean Modulus E

Principal Modulus Ratio E1/E2

Mean Poisson's Ratio

Poisson's ratio associated with shear modulus

Specific weight , (for dead loa~

computation)

-25-

7.5 in. uniform throughout

3500 ksi

0.4444

0.15

0.15

o.oo

The properties of the beam element are assumed as

follows (Ref. 6).

Modulus of Elasticity

Poisson's Ratio

Effective Shear Modulus (to include shear distortion)

Moment of Inertia

Torsional Moment of Inertia

Beam Eccentricity

Beam Cross-Sectional Area

3. 2 ·Example ·112 · • · Skew · Box• Beam ·.Bridge

4500, ksi

·o.oo

140065.0 in4

25127.7 in4

29.82 in.

2 642.0 in.

0 The second example is a 30 skew bridge with 3 pre-

stressed concrete spread bo~beams. The structure is 28 ft.

wide and 71 ft.- 6 in. long. The bo~beams are spaced 10 ft.-

2 1/2 ins. on centers. The PennDOT 48/48 prestressed concrete

box-beam is used (Ref. 7). The deck slab and the top and bottom

plate of the box-beams are idealized by parallelogram elements.

The webs of the box-beams are idealized by rectangular web

elements (Figo 6). One plate element is specified between the

box-beams and 6 elements are used along the span. Smaller

elements are employed near the skew midspan. The thickness of

the top plate of the beam beams is incorporated to the thickness

of the deck element on the box beam (Ref. 1). The properties

of the deck slab are specified as follows:

-26-


I I I I I I I I I I I I I

the deck

I I I I I I

Plate thickness:

M~an Modulus

Pirncipal Modulus Ratio


Poisson's Ratio associated with shear modulus

Specific Weight

7.5 inches throughout except

over the bearas_ wh'er.e ... the.

4000 ksi

1.0

0.15

0.15

0.0

The properties of the web elements are assumed as follows:

Thickness

Mean Modulus of Elasticity

Principal Modulus Ratio


Poisson's Ratio associated with shear modulus

Specific Weight

5.0 ins.

4000 ksi.

1.0

.15

.15

o.o

The properties of the bottom plate element are the same as

element except that the thickness is. 5. 0 ins.

-27-

The printed output of the program gives the following

information.

4.1 Structure·nescription

The full description of the structure geometry and

material properties are printed out. The information includes

both the echo print of the provided input and the generated

data.

Title

The two title cards in the structural data input are

printed out.

The echo print of the control parameters such as

number of element, number of nodes, number of boundary condi-

tions, number of load cases, specified number of equations per

block, etc. is provided.

Material Property·Taoles

The properties for each individual material specified

are listed.

Structure Geometry

All the node numbers with their x and y coordinates are

printed out.

-28-



· 'Element·Artay

The element number, nodal points and element properties

are printed.out.

Bourtdary·cortditions

The nodes with the boundary condition, including the

specified direction of inplane displacement and out of plane

rotation, are listed. In this version, specified displacements

if any, are ignored by the program.

4.2 Load Description

The load description part of the output consists of

the following.

· Title Card

The specified title for the given load card is printed.

Control Parameters

The control parameters such as the number of nodal

force cards, and flags for distributed or gravity loads are

echo printed.

· Concentrated Load

The node number and the corresponding nodal forces

for each degree of freedom at the specified nodes are listed,

if any.

-29-

Distributed Load

The element number and the load intensity at the nodes are

printed out, if any.

Truck Load

The information printed out for this type of loading con-

sists of the following:

a. The load case number, the load type, x and y coordinates

of the load centroid and the skew angle of the support.

b~ The wheel load intensity, the local x and y coordinates

of the wheel from the load centroid.

c. The element on which the wheel load is located, the

global x and y coordinate of the wheel load, and the

statically equivalent forces in the wheel load as app-

lied to the nodes of the element.

The information in b and c are given for each wheel load.

Global Force Vector

This portion of the output contains the sum at the nodes of

all the applied loads. The loads are FX, FY, FX, which are the app-

lied loads in the global x, y and z direction; and, MX and MY which

are the applied moments in the 6x and 6y direction, respectively.

4.3 Vector of Displacements

The vector of unknown displacements contains the u, v, w,

6 and 9 displacements and rotations at each node. These X y

-30-



displacements are printed out in two ways: (a) in the direction of

the skew axis when the boundaries are specified to displace and ro

tate about the skew axes, and (b) in the direction of the global

axes. When no boundary transformations are specified, (a) and (b)

are the same.

4.4 Reactions

The reaction at the nodes are printed out in the skew axes

when boundary transformations are specified. Otherwise, reactions

in the global axes are printed.

4.5 Generalized Force Vector

The generalized force vector or simply the product of the

global stiffness matrix and the vector of displacements are printed

out in the global coordinate system.

4.6 Stress Resultants

An echo print of the nodes where stress resultants are de

sired is given. Two types of stress resultants are printed out: (a)

stress resultant at the center of the element, and, (b) stress re

sultant at teh nodes. The stress resultant at the nodes is the aver

age of the node stresses of the plate elements meeting at that parti

cular node. For the beam elements only the stress resultant at the

nodes is printed. The stress resultants are defined as follows:

NXX, NYY, NXY internal forces per unit length inte

grated over the thickness t.

-31-

MXX~ MYY, MXY

Nl, N2, Nl2

Ml, M2, M12

internal bending moment and twist per

unit length

Principal internal forces.

Principal internal moments

Stress Resultants at Center of the Plate and Web Elements

The stress resultants at the center of the plate and web

elements contain the internal forces NXX, NYY, NXY, MX, MY and MXY.

These forces are integrated over the thickness of plate. These for

ces are also printed out in terms of the principal stress resultants

Nl, N2, Ml, M2, and M12.

Stress Resultants at the Nodes

The stress resultants at the nodes contain the NXX, NYY,

NXY, MXX, MYY, MXY internal forces and moments at the specified nodes.

The nodal stresses of all the elements at the nodes and its average

are listed for each node. Based on the averaged nodal stresses, the

computed principal stresses Nl, N2, Nl2, Ml, M2, and M12 are printed

out.

4.7 Load Distribution Information

The load distribution information contains the moment of the

composite I-beam or box beam section.

I-Beams

The averaged nodal moment of the beams at a common node are

printed out. The effective plate moments and the composite moments

-32-



at the maximum section are printed separately. Based on the composite

moment of each beam, and the total moment at the maximum moment sec

tion, the moment percentage carried by each beam are listed. The

composite moments at nodes specified in the input are printed out

thereafter.

Box-Beams

For each box-beam section, the following information is

printed: (a) in-plane and moments integrated over the effective width

of the deck slab for box-beam section, (b) in-plane forces and mom

ent integrated over the width of the bottom plate element of the box

section, and (c) in-plane forces, moments and effective width of the

web elements for the box-beam section. The forces and moments are

summed about the bottom plate and the composite box-beam moment is

printed. Based on the composite moment at the specified beam sec

tions, the composite moment and the moment percentages of the beams

are printed out.

-33-

5. REFERENCES

1. deCastro, E. S. and Kostem, c. N. LOAD DISTRIBUTION IN SKEWED I-BEAMS AND SPREAD BOX-BEAM BRIDGES, Fritz Engineering Laboratory Report No. 400.19, Lehigh University, Bethlehem, Pennsylvania, July 1975.

2. Felippa, c. A. ANALYSIS OF THIN AND MODERATELY THICK PLATES IN BENDING, Computer Programming Series PB-LCCT, Department of Civil Engineering, University of California, Berkeley, October 1967.

3. William, K. J. and Scordelis, S. C. COMPUTER PROGRAM FOR CELLULAR STRUCTURES OF ARBITRARY PLAN GEOMETRY, SESM Report 70-10, Department of Civil Engineering, University of California, Berkeley, 1969.

4. Zienkiewicz, 0. C. and Cheung, Y. K. FINITE ELEMENT METHOD IN STRUCTURAL AND CONTINUUM MECHANICS, McGraw-Hill, New York, 1967.

· 5.· .American Association of State Highway and Transportation Officials STANDARD SPECIFICATIONS FOR HIGHWAY BRIDGES, 11th Edition, 1973; and INTERIM SPECIFICATIONS-BRIDGES, 1974; Washington, D. C.

6. Zellin, M. A., Kostem, C. N. and VanHorn, D. A. LOAD DISTRIBUTION IN PRESTRESSED CONCRETE I-BEAM BRIDGES, Fritz Engineering taboratory Report No. 387.2, Lehigh University, Bethlehem, Pennsylvania, January 1975.

7. Pennsylvania Department of Transportation STANDARDS FOR BRIDGE DESIGN, BD-201 Bureau of Design, Commonwealth of Pennsylvania, June 1973.

-34-


I I I I I I I I I 6. FIGURES

I I I I I I I I I -35-

I

I ~ ~ I

Fig. 1 Finite Element Discretization of an I-Beam Bridge

-------------------

-------------------

I ·w -...1 I

Fig. 2 Finite Element Discretization of a Spread Box-Beam Bridge ·

I I

y I I I I

X I J I

a) Quadrilateral Element

I I J I X

I h

I I L IK I I

z b) Web Element

I I

X

I /

y/ 1 I c) Beam Element

I z

Fig. 3 Finite Elements

I -38-

I

I I I I I I I I I

.I I I· I I I I I I I

y

,

/ My

b) Bending Stress Resultants

Fig. 4 Element Stresses

-39-

I .j::'-0 I

I

I y z

•

( )

0

Fig. 5 Example No. 1

63 Node Points (only on top)

48 Plate Elements

24 Beam Elements

- - - - - - - - -· - - - - - - - - - -

-------------------7

z

Fig. 6 Example No. 2

/

• 98 Node At Top 8 Bottom

() 60 Top E Bottom Plate Elements

0 36 Web Elements

96 Total No. of Elements


7. TABLES

Table 1: Input For Program SKBRD For Example No. 1

Table 2: Input For Program SKBRD For Example No. 2

-42-


TA8LF 1

••• Q, ~TDUCTURAL ~ATA SPECIFIC~TION ••• ••• 1. ~ONTRQL CARD CA~I ••• 1234567R901~3455?39~123~5S7~9012345673901234567A901234~67S9012345&789012J~567~90

SHRT

••• ? TITLF CA~DS t1~A5/1~Anl ••• 1234567~911234557~qOt?~L5~7A9012345573901?3L5~7A9012l4567A9012345678901234567890 EXAMPLF N0.1.- ?~ ~l. WinE 8DIDGf 4 r~AMS 45 ~E~~EE SKEW I-qEAM BRIDGE 3EAM ~IZE 24/45 ~ PT, ~PAGING h4 FT. SPAN

••• ,~. STRI.If::TIJRE INFO~MATIQN CF,It.,L4,!41 ••• 12345S78Q0123~S~7AYOt?~~567~90121456739012345f7Rg012345h7~901234567~90123456739n

12 s~ 1~ ? t~QF

••• 1f. "AT~RIAL CAfHlC"' ti4.3E1r1.~,3Ft0.3,2E10.3,F10.31 ••• t~J4557~QOl234567~9~123456799D1234567~9D1231,557~9nt?34557~9n12345S7A90123456789n

1 ,15nE+04 .444 .1so .150 2 .450F+04 t.oon .ooo .tso

••• 5. NJnAL ~OORDINATES ti4.2Ft0,3,?!4.2FlO.ll ••• 1214567~9012345S7~90t?3456799012345579901234S57A9n1?34567R9012345678901234567~9n

1 • 0 0 • !) I) .

3 3')6.00 4 3'11+.00 5 412.00 7 7')'1.0!) 8 25.00

10 :~u.oo

11 h19.00 12 i+H.0\1 14 79~.0Q

15 73.0:) 17 vg. on u 457.00 19 4'\S.on 21 .'1 !•1. 0 Q

57 .n8. nn c;;g Sq4.00 50 Pz.oa 61 ?•;o.oo 63 1106.00

.....

• on • (l 'l • '1'1 • no

25.0'1 25. 00 . ., s. 1 ~ 21. (] (] ??,O'J ~~.nn

7 ~. 110 7 L 0~

7 ~.on 7J.fll)

3 ~ '3. ~ '1 ·n ~. oo :1.) ~.a,

3~~.on

3 .l '1. 011

7 56

.... ••• PLATE ~LEMENT~ ••• 12 455789~12345~7jgntz3~5~7~go1234567~9012345G7Q901234557'190123455799D1234557890

1 1 2 g ~ 1 .oo -8.0 6 6 7 14 t< 1 .on -~.n

7 ~ q 16 t~ t .oo ~.n

13 1s 1~ 2~ z~ 1 .on 3.o 19 2? 21 10 ;>q t .oo 9.0 41 ~0 ?t 58 S7 1 .00 -R,n 4'1 53 ~s 6~ E? 1 .nn -'l.o

-43-

'I. n ~. 0 13. 0

8. 0 0 'I. on fl, 0'1

8.00 s.on a. o o 42

••• f3F!\'~ "L"t·lENTS ••• 12345S7e90123456 7 dqntz1~5~7qgot234S~759012J4567Bqo1234557~9~1234567890123456789"

4g 8 ~ g ~ ? .0014005~.0 2~127.7 29.82 642.00 0 0 55 22 21 23 2? 2 .00140C~5.0 25127.7 29.82 642.00 0 ~

61 36 37 37 1~ ? .00140065.0 25127.7 29.82 642.00 6 72

••• 7. qOUNOA1Y CONniTION nATA !T4,6X,7F~.0,4X,2I41 ••• 1234~678901234567d901234567Rq~12345678901234567~gryt234567B9012145578901234567R9ry

1 11100 7 57 7 n110J 7 63

3. L0u1 SPECIFICATION ••• ..,... 1. TITLE r.ARDI131\F,J ••• 1234567~9Jt?345~7~40t2145S?Sg0123~567A901234~67Aqnt234567~gry1234567~901234567R90

TPUCK q~I1G~ VfYTClE AT ~InSPANLOAn CASE 1 PHI 45.0

••• ~. r.ONT~nL f.ll.on IT4,2L'•l ••• t234567~gnt234567~q112l45~7~~01234S67dq012345678qOl2145S789~1234557A901234567S9n

OF F .... ~. roucK LJAO caRncs> • •• ••• LOA~ C~NT?OTO CARG !D4,6X,?"lO.O,I5,FlO.OI ••• t214567sgot23455?3got23~S67dqot2345678qot234567qqot?3456789D1234567Sgot2l4567890

HS-:>0 !t:3.00.

... ,. ...... •u 1. r.r:JNT'~OL CDr~'l I 3! 4 I ••• 1234557°9012345S7~901?34;67~~a12~45S7~gnt-:J3h567~931?345S7~9012345~7A9G1234567890

1 1 6~

•..,. • ? • t~ J 0 !=" C 'I R 11 ( S I I ? 1 I If) • • •

12J45678901?J45576901?3~567R~01?345f7R901?345S7~q~t2345~789n12345678901234567R90 4 q

.... .. .. ••• t. '3cA'1 NYJE CARC'ISI !?OI4l ••• 1234567~g012345SfRgQ12345~?oqQ12J45~ 7 Rg012345S7A901?34567~q012345~78901234567890

<.g 55 61 0 7

••... 2. [i'F[f.TIVE WI(JTLi r,niFl!SI !10FR.Ol ••• 1234567~9D12J4567~J1t21~567sqD12J45673aD1234567qgot?345~78grytz34567~got2l4~67A90

7J.oo g6.no qs.no 71.oo

••• 3. S°F•'":IFI"n :l"At·' 'ILJOE r..~~n(<;) 120!41 ••• 1234567~9n12345673gn1?145G7~901?345f7Aqnt?3!t567AOOl2345S73g01234567Rg0123456789"

10 24 3~ S? 1? ?~ hq 54

....... '•· ~OFCJFit::n :!'::AI' CFFE:CTIVC t>J!nTH cncr)(SI (10F8.0) .... 12345~7°9n1234567dgQ12145S731~12~45G7~9n12345S7AgG12345678901?145S78901?34567~9n

73.00 lS.O~ 16.nQ 7~.~0 7~.JO qs.O" g&.OO 7 3.00

-44-


I I I I I I 1-I I I I I I I I I I I I

n• · E. ·:>U'JSFO'IFNT LOADltlG FL AGWORD CA~f'l . ••• 12345&78gQ123~567~gntz34567Aq~1234~678901234567A90123456789012345678901234567890.

SLOAOS

••• F. scroND LOAD SPECIFICATIO~S, OUTPUT SPFGIFIGATIONS ETC. ••• 1234567891123~567~90t2~4567~q01234S678gQ1234~67Agn1234567890123456789012J4567890 TRUCK B"'If):;E IJE'-iiCLE AT rHfJSPANLOAO CASE 2 PHI 45.0

OF F HS?O 601.00 ?t7.00 6 45.00

1 1 53 4 A

49 5? f)t 67 73.00 16. 0 0 '.l"1. 0 0 n. DO

10 24 B 52 1? 21': 40 54 7 3. no '16. I) (1 q'). 0 0 71.1)!) 71. 0 !1 a 6. OlJ 0

"· 0 0 7 J. 00

•H G. fF.R'-~t'II\TION OF ?UN FLAGW0°'l CA~I'1 ••• t234567~g01~345S7B90t2145~7Ag~1234t~7A901~345678gry1?34567A9n1z34567A901234~67A90 :>TOPF

TA~LE 2

........

••• t. CONTROL CAPil !A61 ••• 1234567qq~1?345~7d9012345&78301?34567A901234567A91Jt234567891J12!45678g01234567890

SHRT

••• z. TITLE c~ons <t3ft~/t3A6J ••• 1Zl45S7~g~1?345~7Jg~1?~~5~7~9~123~5~7~qot?34S6789ntz34567890123456789D12345678go

~WAMPLf N1.~- ~<EW S~RFA~ ~JX-~E~M ~~IUGF 1 8EQ~~ ~5 O~GREE SKEW 1 aEAMS!43/4~J 7t 'T. ~ INS. SPAN ?~ F-. n !~. wt~E

••• 3. STRIJCi'.NE INFO~M~.TTO~l !ST''•L'•,I4l .:.,..,. 1234567P9G12J4567~1012145G7A101?345678901?J~SS7A901?J456789012345678901214567890

96 9A 12 1 ~ tlSF 3

• .._ ~ • ~1 !\ T ' •'< I A l C A? n < ')I ! I !. , 3 E: 1 n • 3 ,3 F 1 0 • 3 , 2 F U • J , F 1 0. 1 I ~ • • 12345678gn12345S7~Yryt2l4S~7~9D1234567R9n1?34~67ggot234567A9012l45578901234567A90

1 .45GF+04 t.lnl .15J .150 2 .451~+04 t.nn~ .1so .tsn S .45!1HfJ~ 1.DO'l .1?0 .150

••• ~. NO~DL ~JOP~IN~T'~ !I4.2F1~.3.?I4,?F10.31 ••• 12345678901~345~?J901~l45G7~q012Jit5~7~q01234;S?~oot?J456789012345S7A9G1234557ggo

1 .on .n.n 3 3~1.oo .aQ 4 5 7 !l

10 11 12

4? ':1. 7 r:; 4::,'\.?J a:;;7.5il

13. 8S 40?.80:, 4 1+ 2. h 1 482.3'1

• 0 1

• 0 0 • [J (l

4.00 4.0n 4. 0 0 4. p

-45-

••• NOOnL COORDINATES (CONT.l ••• 1234567R901234~67~901?345678901234567R901234567R9012345678901234567690123456789D

14 671.35 24.00 15 13.86 21+.00 17 402.66 ?4. 00 16 442.51 24.00 19 '+82.36 24.00 21 671.35 24.00 22 H. 58 sr.on 24 427.6~ S?'.OO 25 467.43 57.00 26 507.18 67.00 28 8 g~=,. 18 1')7.0() 29 H.68 n7.on 31 427.611 67.00 32 467.43 'l7.00 B 507.16 57.00 35 8'36.18 67.00 36 %.511 146.c:;o 38 473.58 145.50 39 513.33 146.?0 40. 553.08 11>!). c;o 42 942.08 1 46. 5fl 43 ~4.5~ 14S.50 45 473.58 146.511 46 513.33 146.50 47 551.0'\ 146.50 49 942.08 145.50 50 109.41 139.50 52 4'B.41 189.~()

53 538.16 1119.50 54 577.91 1'19."0 56 966.91 B9.r:;n 57 109.41 Bg.c;o 59 4g6.41 1'1'3.50 60 538.16 189.50 51 577.91 189.c;n 5.3 966.91 189.50 64 1513.31 2og.oo 66 544.31 26q.Q() 67 5114.06 ?.IS1. ()!1

nB 623.81 ?6q.nn 70 1012.81 269.00 71 155.31 25'!.00 73 544.31 2fl'l.OO 74 584.05 2nq.oo 75 623.111 26'!.00 77 1012.81 25'!.00 78 1:30.13 312.00 60 56q.1J 312.00 61 6()8.88 H2. on 82 648.63 312. 1, 84 1 0 H. 53 312.00 65 130.13 .312.00 87 56'! .13 312.1)0 68 61)6.83 312.00 69 548.53 312'.00 91 1037.63 31:?.0fl

-46-

I I I I I I I I I I I I I I I I I


••• NOOAL GOORDIN/\ TICS !CO~IT. l ••• t2~4567BQOt234567d901234567~1D1234567gso1234567~90t2345&7gsot2345&7g9nt23456789o

sz t~J.sg ~3~.oo

94 ~~?.99 ~•s.oa

95 6?2.74 3~S.OO 96 662.41 11S,OO ~~ 10~1.4g ~1~.08

...... s . ....... ••• DFC~ "LcMfNTS ••• t2345673qJt2J4567~gOt234567~101?345678901?34567A?Ot234567A9012345678901234567'190

1 1 ? g ~ 1 .0000 -7.5000 7 g 11 zq 1 .nooo-1o.5ooo

11 zq JO 37 36 t .uoon -?.sooa 19 3S 3~ 5~ 57 t .ooon-to.soou 25 57 s~ 65 ~~ 1 .nona -7.5ooo 31 64 o5 ~5 R~ t ,Jn00-10.5000 37 'I'' HS 91 12 .noon -7.sooo 3d o,;·, q7 94 03 1 .nnoa -7.~oon .noon .ooon .oono 1 42

••• 20TTOM PLATF EL~ME~TS """'"" t234567A901234567~g~12145G7~101234~57q9Q1?34567Sg01234567A901234567R9012145670.90

43 1s 1; 21 22 ? .oono -s.oooo 49 4~ 44 51 5~ 2 .OnQO -5.0000 ss 11 1~ 10 ?R z .noon -s.oaoo s& 12 71 so 7q ? .o~oo -s.noon .oooo .ooon .oooo 1 60

~~~ W~J ELF~ENTS ••• 1234567~9Q123~5678g01?14S~73l01234567~901?345S7AgQ1234567B90123456789D12J4567890

61 s ~ ts t~ 1 .oooo s.~onn 4g.2soo .onoo ~oooo

57 2? ~~ 2~ z~ ~0oon s."aoo 4g.zsoo .oooo .oooo 73 3& t7 44 41 ~ .1noo s.oooo 4q,zsoo .oooo .oooo 79 s7 s~ 51 so 1 .o~oo s.oaon 49.2~oo .oooo .oooo R 5 6'' r) 5 7 2 7 1 > , 0 '1 0 0 3 • 0 J fJ 0 '-t g, 2 S 0 0 , 0 0 0 0 • 0 !l 0 0 g 1 g? ~ ·'l .., 1 1 o 1 • n., o o 5 • ~ fJ n 11 '• 9 • z s a o • no n '1 • o o o o ~2 Rb 37 so 70 .nno~ s.qooo 49.?son .oooo .anon t g~

,. • • ~ • S tl U t.! 0 ~ •{ v (' 0 '! 0 I T I 0 ~-: 0 l\ T 1\ ! I 4 , 5 Y , 7 F e. 0 , 4 X, 2 I 4 l • • • 12l4567qg11?345G73an123~567~qn1234557840t2J4SS7~9012l45;789012345S78901234567890

15 11110 0 0 43 1111 '1 0 0 71 1111'] 0 a 22 1111 a 0 !)

50 1 t 1 1 ') 0 0 78 1111J {) n 21 0111"' 0 0 4'3 01111 0 0 77 0111!1 0 0 28 011 try a 0 50 o 111 n 0 ')

34 01111 0 0

-47-

..... 1· LOAD SPECIFICATION • •• n• 1. TITL!C CAROI131\6l ••• 123456789012345678qG123456789012345678g01234567890123456789012345678901234567890 OISTRIBRIOGE VFHtCLE AT HlOSPANLOAO CASE 1 PHI 30.0

••• 2. CONTROL CARD 1!4,?l4l ••• 12345678901234~6789012l4567890123456789012345678901234567890123456789012J4567890

OF F .... ~. TPUCK LOA~ CARDISl ... .... ••• LOAD CENTROID CARD IA4,6X,2F10.0,I5,F10.0l ••• 123456789~1234567~90121456789012345678901234567890123456789012345678901234567890 FULL 525.74 168.00 12 30.00

••• INDIVIDUAL LOAD CA~O!Sl (1F8.01 ••• 12345678901234567~901~345~78901234567~901234~67890123456789012345678901214567890

.....

4.00 -202.64 -?4.00 16.00 -14.64 -?4.00 16.00 1J3.16 -24.00 16.00 133.36 -96.00 16.00 -34.64 -96.00 4.00 -202.64 -q6.00

16.00 -133.~6 96.00 16.00 34.64 95.00 4.00 202.64 96.00 4.00 202.64 24.00

16.00 34.64 24.00 16.00 -133.36 24.00

C. OUT~UT SPEr.IFICATIONS ...... •n 1. CONTROL CARD CH4l ••• 1234567~9~12345678901?345678901?345678901~345678901?3456789012345678901234567890

1 1. 9'3

.... D. LOAD OISTRI3UTION IN~ORMATTON • ••

..... LONGITUDINAL BOX-BEA~ 1 ..... ••• t. OEC~ NO~E CARD 120!41 ••• 12345678901234567i90123456789012345678901234S67890123456789Q12345&789012~456789~

4 11 32 0 0 0

..,... 2. n~CK EL':MF.:NT fFF"ECTIVE WinTH 110F'3.0l ..,..... 123456789J123455789Q1?34567890123456789012345678901234567890123455789012345&7890

12.00 33.50 s1.2s .oo .oo .o~

.... 3. ICHH'OM NODE CARD 12fl !4 l ••• 12345678901234567~901234567Rqn1?345678gQ1234S6789~1234567890123456789012345&7890

18 25 0

••• 4. 30TTOM ~ODE EFFEGTIVF WIDTH !AF10.0l ••• 12345678901234567~9n1234567qg012345f7~901234567Aq01234567A90123456789012l4567A90

21.so 21.50 .on -48-


I I I I I I I I

I I

t

I I I I I I

••• 5. W~B NODE CARD (20I4l ••• 123456789012345678901~3~5678901234567890123456789012345678901234567890123\567890

11 18 32 25

••• ~. WEB DEPTH CAPO (10F8.0) ••• 123456789012345678901234567~901234567R901234567890123456789012345678901234567890

49.25 49.25 49.25 49.25

••• LONGITUDINAL 30X-9EAM ?. ••• 1234567890123456789012345678901234;6789012345~7890123456789012345678901214567890

39 60 0 0 0 0 61.25 61.25 .o~ .oo .oo .oo

46 53 0 21.50 21.50 .on

39 46 60 53 49.25 49.25 4q.z5 49.25

••• LONGITUDINAL 30X-9EAM J ••• 123456789012J456789012J456789012345678901234567R901234567890123456789012J4567890

67 88 95 0 0 0 . 61.25 ~3.50 12.00 .oo .oo .on

74 81 0 21.50 21.50 .oo

67 74 88 81 49.25 49.25 49.25 49.25

••• E. TERMINATION OF RUN FLAGW0PD CAqn ••• 123456789012345&7890123456189012345678901234567890123456789012345678901234567890 STOPF

-49-

I I I I I I I I 8. LISTING OF PROGRAM SKBRD

I I I I I I I I I I -50-

I

I I I

I I I I I I I I I I I I I I I

c

c c c c c c c c c c c c c c c c c c c c c c c

c

c

c

c

c c c

OvERLAY (PLATE,O,OI

PROGRAM SKBROCINPUT,TAPES=INPUT,OUTPUT,TAPE&=OUJPUT,JUH1=100,TAPE1 1=JUM1,JUH2=100,TAPE2=JUM2,JUM3=100,TAPEJ=JUMJ,JUH~=100,TAPE~=JUH'' 2JUH7=100,TAPE7=JUH7,JUH8=100,TAPE8=JUH8,D.TA=100,TAPE77=DATAl

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FINITE ELEMENT PROGRAM FOR THE ANALYSIS OF ELASTIC, ISOTROPIC OR ORTHOTROPIC ECCENTRICALLY STIFFENED PLATES OF ARBITRARY PLAN GEOMETRY.

THEORY AND NUMERICAL COMPARISONS ARE PRESENTED IN t LOAD DISTRIBUTION IN SKEWED I-BEAH AND SPREAD BOX-dEAH BRIOGEStt BY E. S. DE CASTRO ANO C. N. KOSTEM, FRITZ ENGINEERING LABORATORY REPORT NO. 400.19, LEHIGH UNIVERSITY BETHLEHEM, PA. JULY 1975.

THIS PROGRAM HAKES USE OF ROUTINES AND MODIFIED VERSIONS OF ROUTINES FROM THE FOLLOWING REFERENCES: 111 PB-LCCT ANAlYSIS OF THIN AND ~ODERATELY THICK PLATES USING LIN~AR CURVATURE COMPATIBLE TRIANGULAR FINITE ELEMENTS BY C.A. FELIPPA, UNIVERSITY OF CALIFORNIA COMPUTER PROGRAMMING SERIES AND 121 COMPUTER PROGRAM FOR CELLULAR STRUCTURES OF ARBITRARY PLAN GEOMETRY, BY K.J. WILLIAM AND A.G. SCORDELIS, SESM REPORT 70-10, UNivERSITY OF CALIFORNIA,19~9

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • COMMON ICBOO/ JUH1,JUM2,JUM3,JUH4,IN,IO COMMON ICB01/ ~UMEL,NUMNP,NUMBC,NMAT,NLCS,NN,MH,NPSEGM COMMON /C302/ NUM3LK,NaLKL,IBANOW,NEQBC COM~ON /SOLV/ NA1,LWIDTH,NFREf,NAS,LA~A,ISEGM,JUM5,JUM&,JUM7,JUM6

COMMON /PLTS/ NTOTP,NBP,NGPH COHMON /NTRUN/ NRUN COMMON /C~03/ MAXEL,HAXNP 9 HAXP0 9 MAXMT CO~MON /TITLE/ TITELl101 COMMON /HEAD/ HEAD11131,HEAD21131,QEQ COMMON /STEvE/ NW,XLBR . COMMON /Wf3/ NWEB,NTP,NTd COMMON /NF3/ Nd,NND,NSN COHMO~ /CARDS/ OATA,OATA1,0ATA2 COMMON /LOGIC/ DLOAO,GLOAD

DIMENSION TIMI121

INTEGER OATA,QATA1,0ATA2

LOGICAL QEQ LOGICAL D~OAO,GLOAD

DECLARATION OF FILE NU~BER AND SCRATCH TAPES

IN=5 IO=o JUM1=1 JUM2=2

-51-

1 2 3

' 5 6 7 8 9

10 11 12 13 1~

15 16 17 16 19 20 21 22 23 24 25 2& 27 28 29 30 31 32 33 J\ 35 36 37 38 ~9

40 41 42 43 44 45 46 47 48 49 so 51 52 53 5~

55 s& 57 58

c c c c c c c c c c c c c

c c c

c c c

c c c

110

120

130

JUI13=3 JUI14~4 JUI17:t7 JUHS=IS DATA=77 REWIND JUH7 REWIND JUI18

THE CONTENTS OF THE FILES ARE AS FOLLOWWSI

JU111 JU112 JU113 JU114

JUI17 JUI18 DATA

STRUCTURE GEOMETRY ELEMENT PROPERTIES ELEMENT STIFFNESS MATRICES COMBINED ELEMENT CIN-PLANE AND OUT-OF-PLANE STIFFNESS MATRICES) GLOBAL DISPLACEMENT ~ECTOR, SCRATCH FILE GLOBAL STIFFNESS MATRIX LOAD DISTRIBUTION OUTPUT FILE

WRITE (10,2001 READ CIN,210t CHECK IF lCHECK.EQ.5HSTOPF) GO TO 190 IF lCHECK.EQ.5HSTARTI GO TO i2D IF lCHECK.EQ.SHPLOTSJ GO TO 160 IF lCHEGK.EQ.6HSLOAOSI GO TO 130 IF lCHECK.EQ.&HSNOOESI GO TO 140 GO TO 110

PRINT J08 TITLE AND DESCRIPTION

READ liN,230) TITEL WRITE CI0,2401 TITEL NRUN=1 NA=1 NB=O

INPUT STRUCTURE DATA, LOADING, AND GENERATE PROPERTIES

CONTINUE CALL SECOND lTIMl1)) CALL O~ERLAY l5HPLATE,1,01 CALL SECOND !TIM 12) I IF lN~UN.GT.il GO TO 150

FORMATION OF GLOBAL STIFFNESS MATRIX

CALL SECOND lTIMC3JJ CALL OVERLAY (5HPLATE,2,0l CALL SECOND lTI11(4))

c C ASSEMBLE LOADING AND FORCE VECTOR c

CALL SECOND CTI11l5J) CALL O~ERLAY l5HPLATE,l,OI CALL SECOND CTIMC611

c C FORMATION OF SUBSEQUENT LOADING AND FORCE VECTOR

-52-

I

59 I 60 61 I 62 63 64 65

I 66 67 68 69

I 70 71 72 73 74 I 75 76 77 78 I 79 80 81 82 I 83 84 85 86

I 87 88 89 90

I 91 92 93 9ft 95 I 96 97 93 99 I 100

101 102 103 I 10ft 105 106 107

I 108 109 110 111

I 112 113 114 115 116 I

I I I


c

c

IF INRUN.EQ.11 GO TO 150 140 CALL SECOND ITIH 151 I

CALL OVERLAY I&HPLTL0$,1,01 CALL SECONO ITIHI61l

150 CONTINUE

C SOLUTION OF SIMULTANEOUS EQUATIONS AND ~RINT OF REACTIONS c

c

CALL SECOND ITIM I 71 I CALL OVERLAY 15HPLATE,4 9 0) CALL SECOND CTIMC811

C OUT~UT OF NODAL DISPLACEMENTS, NOFAL FO~CES, AND INTERNAL FORCES c

c

CALL SECO~O CTIH<<H I CALL OVERlAY (5HPLATE,S,OI CALL SECONO CTIHI10tl IF IHEAD2111.NE.&HTRUCK I GO TO 170 READ IIN,2201 NB,NNO,NSN

1&0 CONTINUE

C LATtRAL LOAD DISTRI8UTION ANALYSIS c

c

CALL SECOND CTHtl11lt CALL OVERLAY 15HPLATE,6 7 01 CALL SECOND (TIHI121)

C PRINT EXECUTION TIME OF EACH OVERLAY c

c c

170·CONTINUE WRITE I IO ,2501 IF INRUN.GT.11 NA=4 DO 180 I=NA, 6 J=2•t K=J-1 TIHIIJ=TIHIJI-TIHIKI

18 0 WRITE ti 0, 2 6 0 I I , T I t1 ( I I NRUN=NIWNH

. GO TO 110 190 STOP

200 FORMAT 11H1,11111,24X,39H• • • • • • • • • • • • • • • • • • • •,1 124X,39H• •,124X,39H• 2 PROGRAM SKBRO •,t21tX,39H• BY 3 •,124X,39H• E.S. DE CASTRO AND C.N. KOSTEM •,124X,J9 4H• LEHIGH UNIVERSITY •,124X,39H• 5 1975 •,124X,39H• 6 •,124X,39H• • • • • • • • • • • • • • • • • • • •,IIIII)

210 FORMAT ( A&l 220 FORMAT 120I41 230 FORMAT 110A6) 240 FORMAT 11H1,1110X,10A81 250 FORMAT (//125H TIHE USED PER LINK ,1111 260 FORMAT I&H LINK,I3,F10.3/I

END

-53-

117 118 119 120 121 122 123 124 125 12& 127 128 129 130 131 132 133 134 135 13& 137 138 139 140 141 142 143 144 145 11t6 147 11t8 149 150 151 152 151 154 155 15& 157 158 15q 160 1&1 162 163 164 165 166 167 168 169 170 171 172 173-

I I

OVERLAY CPLATE,t,Ot FT1 C FT1

PROGRA" FORTi FT1

1 I 2 3

C FT1 4 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FT1 C FT1 C THIS PROGRAM READS IN CONTROL INFORMATION AND RESETS THE FIELD FT1

5 I 6 7

C LENGTH FOR A DYNAMIC STORAGE ALLOCATION OF ELEMENT AND COORDINATE FT1 8 C ARRAY OESC~IPTIONS AND PROPERTIES FT1 C FT1 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FT1

9 I 10 11

C FT1 12 COMMON /C600/ JUH1,JUM2,JUM3,JUM4,IN,IO FT1 COMMON /C801/ NUHEl,NU~NP,NUHBC,NMAT,NLCS,NN,HH,NPSEGH FT1 COMMON /CB02/ NUHBLK,NBLKL,IBANQW,NEQBC FT1

13

I 14 15

COMMON /CB03' HAXEL,HAXNP,MAXPO,MAXMT FT1 16 COMMON /TITLE/ TITELC101 FT1 COMMON /HEAD/ HEAD1C131,HEA02C131,QEQ FT1 COMMON /NTRUN/ NRUN FT1

17

I 18 19

COMMON INFB/ NBX,NND,NSN FT1 20 COMMON AC11 FT1

C FT1 LOGICAL QEQ FT1

C FT1

21 22 I 23 24

C IFLAG=1 WILL STOP THE PROGRAM WHEN THE FOLLOWING LIMITS TO THE FT1 25 C NUMBER OF ELEMENTS, NODAL POINTS, NODAL POINT DIFFERENCE, AND FT1 C MATERIALS ARE EXCEEOED FT1 C FT1

2& I 27 28

IFLAG=D FT1 29 MAXEL=400 FTt MAXNP=4SO FT1 HAXP0=22 FT1

30 I 31 32

HAXMT=30 FT1 33 C FT1 C READ AND PRINT OF CONTROL INFORMATION AND MATERIAL PROPERTIES FT1 C FT1

34

I 35 3&

REWIND JUM1 FT1 37 REWIND JUH2 FT1 REWIND JUM3 FT1 REWIND JUH4 FT1

38

I 39 40

IF CNRUN.GT.1l GO TO 20 FT1 lt1 READ CIN,&OI HEA01 FT1 READ CIN,701 NUMEL,NUMNP,NUMBC,NMAT,NLCS,NBLKL,QEQ,NBX,NNO,NSN FT1 NUHBLK=CS•NUHNP+NBLKL-11/NBLKL FT1

42

I 43 ....

NPSEGM=NBLKL/5 FT1 45 WRITE CI0,1301 HEA01 FT1 WRITE CI0,801 NUMEL,NUMNP,NUMBC,NMAT,NLCS,NBLKL,NUMBLK,QEQ FT1 WRITE CI0,9DI NBX FT1 NN=S•NUMNP FT1

46 47 I 48 lt9

IF CNUMEL.LE.MAXELI GO TO 10 FT1 50 WRITE CI0,100t FT1

10 IF CNUMNP.LE.HAXNPI GO TO 20 FT1 WRITE <I0,110) FT1

51 I 52 53

IFLAG=1 FT1 Sit 20 CONTINUE FT1

NLCS=NRUN FT1 -54-

. 55

I 5&

I I I


c c c c

c

c

c

c

c

c

c

c c c

c

c

N1 TO N21 AKE THE LOCAL ADDRESSES IN SEQUENCE OF THE DIMENSIONED VARIABLES

N1=1 N2=N1+NHAT N3=N2+NHAT N4=N3+NI'1AT N5=N4+NMAT N6=N5+NMAT N7=N6+NMAT N8=N7tNI1AT N9=N8+1t•NUHEL N10=N9+NUHNP N11=N10+NUMNP N12=N11 tNUI1EL N13=N12+1t•NUMEL N11t=N13+NUHEL N15=N11t+NUHEL N16=N15+ft•NUHEL N17=N16+NUMNP N18=N17+2•NUHNP N19=N18+5•NUI1NP N20=N19+NUHNP N21=N20+5•NUHNP NLOC=LOCFCAIN1ll NRFL=NLOC+N21 WRITE ( IO ,120 l NRFL, NRFL NRFL=I1AXOCNRFL,35000Bl

CALL REQMEH CNRFLl

IF CNRUN.GT.1l GO TO JO

FT1 FT1 FT1 FT1 FT1 FT1 FT1 FTt FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FTl FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1 FT1

CALL SETUP IACN1l,ACN2l,ACN3l,ACNiti,ACNSl,ACN&l,ACN7l,ACN8t,ACN9l,FT1 1 A ( N 1 0 l , A C N 11) , A I N 12 l , A ( N 1 3 l , A C N 1 4 l , A ( N 1 5 l , A ( N 16 I , A ( N 17) , A C N 1 8 ) t A ( NFT 1 2191,NUMEL,NUMNP,NMATI FT1

FT1 30 CONTINUE FT1

FT1 CALL LOAD CAIN71,ACN1tl,ACN12l,ACN141,ACN15t,ACN1&l,A(N20l,NUHEL,NFT1

1UMNP,NMATl FT1

IF CNRUN. GT .1l GO TO 40 FT1 FT1 FT1

CALL STORE CAIN11,AIN21,ACN3t,ACN41,ACN5l,ACN6t,AIN7l,ACN8t,ACN9t,FT1 1ACN10I,ACN11l,ACN12J,A(N131,ACN14t,ACN15l,A(N1&t,AlN17),ACN18l,A(NFT1 219t,ACN20l,NU~EL,NUMNP,NHATl FT1

CONSIDER TRUCK LOADING IF SPECIFIED

IF CHEA02C2l.EQ.6HBRIDGEl GO TO 40 GO TO 50

ItO CONTINUE

CALL LDTRK1 CACN8l,ACN9t,A!N10l,ACN20t,NUMNP,NUHELl

50 CONTINUE -55-

FT1 FT1 FT1 FT1 FT! FTl FT1 FT1 FT1 FTl

57 58 59 60 61 62 63 61t &5 66 67 68 69 70 71 72 73 Tit 75 76 77 18 79 80 81 82 83 8ft 85 86 87 88 89 90 91 92 93 94 95

'96 97 98 99

100 101 102 103 10ft 105 106 11)7 108 109 110 111 112 113 114

c c

c c c c c c c c c c c c c c c c c c c c c c c c c c

c

c

FT1 FTl

60 FORMAT (13Aol FT1 70 FORMAT C6I~tl4,li4J FT1 80 FORMAT C1H0,/36H NUM8ER OF ELEMENTS ••••••• oi6/36H NUMBER FTt

!OF EXTERNAL NODES ••• • .I6/36H NUMBER OF BOUNDARY CONDITIONS .FTt 2 •• I&/36H NUMBER OF MATERIALS •••••••• I6/36H NUMBER OF LOAFT1 30 CASES ••••••• I6//36H SPECIFIED NUMBER OF E~UATIONS/BLOCKIFT1 46/36H NUHBER OF BLOCKS I61/36H FLAG (J IF ALL QUFT1 SAOS ARE EQUAU •• L&J FT1

90 FORMAT (/J&H NUMBER OF SPREAD BOXES • • l&,f/1 FT1 100 FORMAT (JOHOHAX. NO. OF ELEMENTS EXCEEDEDI FT1 110 FORMAT C34HOHAX. NO. OF NODAL POINTS EXCEEDED) FT1 120 FORMAT C/SX,•FIELD LENGTH•,t5X,010,• IN OCTAL•,/5X,I10,• IN OECFT1

1IMAL•,tt FT1 130 FORMAT (1H0,1346//I FT1

END FT1

SUBROUTINE LDTRK1 CNP,XORD,YORO,R,IP,IEI LOT LOT

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LOT

THIS ROUTINE WILL SEARCH FOR THE ELEMENT LOADED BY THE CONCENTRATED LOAD AND COMPUTE A STATICALLY EQUI~ALENT FORCE VECTOR AT THE NODES OF THE ELEMENT

LOT LOT LOT LOT LOT

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LOT

INPUT X Ul Y III X(51 ,YC51 p F (II

OFCII

P III

OUTPUT

F I II

ORDINATE OF THE QUADRILATERAL NODE POINTS !=1,4 IN COUNTERCLOCKWISE ORFER ORDINATE OF CONCENTRATED LOAD P MAGNITUDE OF CONCENTRATED LOAD !=1,12 CONCENTRATED FORCE VECTOR AT THE NODES INITIALIZED TO ZERO !=13,19 INTERNAL FORCE VECTOR I=1,5 DISTRIBUTED LAT~R LOAD ON ELEMENT INCLUDING INTERNAL NODE POINT PLATE THICKNES AT EXTERNAL AND INTERNAL NODE

!=1,12 STATICALLY EQUIVALENT FORCE VECTOR AT EXTERNAL NODES

THE

LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT LOT

COM~ON

COMMON

LOT /CBOO/ JUH1,JUM2,JUM3,JUM4,IN,IO LOT /PLBOG/ X(51,Yf51,CHC3,3J,P(5J,8MC3,5t,CVC3,5t,SC19,19t,Fl1LOT

19) COMMON COMMON CO HMO~

/STnE/ NW, XLBR /NTRUN/ NRUN /TITLE/ TITELC10t

LOT LOT LOT LOT LOT

DIMENSION NPCIE,4t, XOROCIPI, YORDCIPI, RCS,IPt, WC36l, XW(JoJ, YWLOT 1(3&1, NPTC5t, CSC2,21 LOT

DATA CW(Il,I=1,81/2•to.Oi~•s.,z•5./

-56-

- LOT LOT

115 116 117 118 119 120 121 122 123 12 .. 125 126 127 128 129 130 131-

1 2 3 4 5 0 1 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 2 .. 25 26 27 28 29 30 31 32 33 3 .. 35 36 37 38



c

c

DATA IVWII) ,I=1,81/-36.,36. ,-37.5,37.5,-37.5 1 37.5 1 -39. ,39.1 DATA IXWC!) ,I=1, 81/2•-160., 2•85. ,2•85., 2•241./

REWIND 7 READ 17t R READ IINt2ftOJ TYPES,XCEN,YCEN,NW,PHI IF ITYPES.EQ.~HTESTI NW=8 IF ITYPES.EQ.~HHS20t NW=& WRITE II0,250t NRUN,TYPES,XCEN,YCEN,NW,~HI

PHI1=90.-PHI PHI=PHI/57.295775 PHI1=PHI1/57.295775 IF ITYPES.EQ.ftHTESTI GO TO 30 IF ITYPES.EQ.ftHHS20t GO TO 20 DO 10 N=1 ,NW

10 READ IIN,2&0l WINl 1 XWI~J,VWINt 20 W11l=16.0

wczl=t&.o Wl31=16.0 wc4t=t&.o W(51=1t.O Wl&l=ft.O xwiu=-112.0 XW(21=-112.0 XWC31=56.0 XWI4l=5&.0 XWI51=224.0 XWtol=224.0 YWtil=-36.0 Y~Hlt=-3&.0

YWISI=-3&.0 YWI21=3o.O YWI4;=3o.O vwc51=J&.o

30 WRITE 110,2701 00 40 N=1 1 NW

40 WRITE U0,280J N,~UNl ,XWCNI ,YWINI WRITE U0,2001

C EXTERNAL LOOP FOR ALL CONC. LOAD OF THE GROUP c

c

DO 180 N=t,NW XC=XCEN+XWINI YC=YCENH'WINJ XP=W INJ

C THE FOLLOWING ROUTINE IS A STATICALLY EQUIVALENT NODAL FORCE C ~ECTOR COMPUTATION BAESO ON A STATIC CONDENSATION PROCEDURE c

SN=SINCPHII CN=COSIPHU REWIND 2 DO SO NL=1,IE READ 121 X,Y,CM,CS,P,NEN,NPT LOEL=NL IF IY14J.LT.YCI GO TO 50 XS=IYC-YC211 4 SN/CN XB=X12J+XS

-57-

LOT 39 LOT ·ItO LOT ~1 LOT 42 LOT 43 LOT ltlt LOT ~5 LOT lt6 LOT ~7 LOT ~8 LOT 49 LOT 50 LOT 51 LOT 52 LOT 53 LOT Sit LOT 55 LOT 56 LOT 57 LOT 58 LOT 59 LOT 60 LOT 61 LOT 52 LOT 63 LOT 54 LOT :&5 LOT 66 LOT 67 LOT 68 LOT 69 LOT 70 LOT 71 LOT 72 LOT 73 LOT 74 LOT 75 LOT 75 LOT 77 LOT 78 LOT 79 LOT 80 LOT· 81 LOT 82 LOT 83 LOT 84 LOT 85 LOT· 86 LOT B7 LOT 88 LOT 89 LOT 90 LOT 91 LOT 92 LOT 93 LOT 94 LOT 95 LOT 95

I I

XA=X CU +XS LOT 97

I IF CXC.GE.XA.ANO.XC.LE.XBI GO TO 60 LOT 98 so CONTINUE LOT 99

WRITE U0,210l N, XP, XC,"tC LOT 100 GO TO 180 LOT 101

I 60 WRITE UO ,2201 LOEL LOT 102 c LOT 103 c COMPUTE PARALLELOGRAM OIHENSIONS 2A AND 2B LOT 10lt c LOT 105

SN=SINCPHill LOT 106 I CN=COS(I»HU I LOT 107 IF CCN.EQ.O.I GO TO 70 LOT 108 TAN=SNICN LOT 109 GO TO 80 LOT 110 I 70 CONTINUE LOT 111 TAN=1.0E+30 LOT 112

80 CONTINUE LOT 113 A=O.S•CXC2)-X(1)) LOT 114 I B=O.S•CYC4t-Yilti/SN LOT 115

c LOT 116 c DETERMINE DISTANCES BASED ON CENTER OF ELEMENT LOT 117 c LOT 118

I XS=XC-XI51 LOT 119 Y5=YC-Y(5) LOT 120

c LOT 121 c TRANSFORM TO SKEW COORDINATES LOT 122

I c LOT 123 XNU= C XS-YS/TAN t LOT 12ft XI=CY51SNI LOT 125

c LOT 126

I c DETERMINE MINIMUM DISTANCES FROM ANY NOOE LOT 127 c LOT 128

XX1=(XNU-Al/A LOT 129 XX2= CXNU +At I A LOT 1JO YY1= CXI-Bt/B LOT 131 I YY2=CXI+i:U/B LOT 132 XY11=XX1"'YY1 LOT 133 XY22=XX2•YY2 LOT 131t XX12=XX1"'XX2 LOT 135 I YY12=YY1• YY2 LOT 136 XY12=XXt "'YY2 LOT 137 XY21=XX2•YU LOT 138 XX=AHIN1C-XX1,XX21 LOT 139 I YY=AMIN1C-YY1,YY21 LOT 140 IF CXX.LT •• 1.0R.YY.LT •• 1l GO TO 90 LOT 11t1 GO TO 120 LOT 142

90 CONTINUE LOT 143

I FCU=8.•XY11 LOT 144 FC41=-8.•XY21 LOT 145 F (71 =8• •XY22 LOT 146 F(10)=-8.•XY12 LOT 11t7

I C=4.•B•YY12 LOT 148 D=tt.•A•XX12 LOT 149 F(2t=-XY11•C LOT 150 FC5l=XY21•C LOT 151 F(8)=XYZ2•C LOT 152 I F' 111 =-xu2•c LOT 153 F(JI=XY11•0 LOT 154

-58- I I I

I I I F1Eii=XY21•0 LOT 155

FI9J=-XY22•0 LOT 156 F 1121 =-xu2•o LOT 157

c LOT 158

I c TRA NSFORHS TO GLOBAL FORCE \lECTOR LOT 15q c LOT 160

CN=-CN LOT 161 DO 100 1=2,11,3 LOT 162

I J=I•1 LOT 1&3 FIJI=FCJI•FIII•CN LOT 1&1t

100 FUI =FUI•SN LOT 1&5 DO 110 1=1, 12 LOT 166

I 110 FCII=X~•F<It/32. LOT 1&7

GO TO 150 LOT 168 c LOT 169 c CONDENSATE INTERNAL NOuE WITH A~PLIED LOAD AS FORCE \lECTOR LOT 170 c LOT 171

I 120 CONTINUE LOT 172 DO 130 J=1, 19 LOT 173

130 F<JJ=O. LOT 17ft DO 11t0 1=1,3 LOT 175

I DO 140 J=1,5 LOT 176 litO BMU.Jl=O. LOT 117

F 1131 =XfJ LOT 176 X15J=XC LOT 179

I YI51=YC LOT i.60 c LOT 181

CALL SSnATE ,,., LOT 182 c LOT 163

I 150 CONTINUE LOT 164

J1=NPTUI LOT 185 J2=NPTC21 LOT 186 J3=NPT131 LOT 187

I Jlt=NPT!Itl LOT 1'88 00 1&0 J=1.3 LOT 189 JJ=J+2 LOT 190 K=J LOT 191 RCJJ,J1J=RIJJ,J1J+FIKI LOT 192

I K=J+J LOT 193 RIJJ,J21=RCJJ,J21+FIKl LOT 194 K=JH> LOT 195 RIJJ,J31=RIJJ,J31+FIKI LOT 196

I K=J+9 LOT 197 RCJJ,J~I=RIJJ,Jitl+FIKI LOT 198

1&0 CONTINUE LOT 199 c LOT 200

I c PRINT ELEMENT NODAL FORCES LOT 201 c LOT 202

WRITE (!0,2901 LOT 203 DO 170 J=1,1t LOT 20ft

I JJ=NPTCJI LOT 205 NF=J•J-2 LOT 206 NL=NF•2 LOT 207

170 WRITE 110,3001 JJ,(FCKI,K=NF,NLI LOT 208 180 CONTINUE LOT 209

I c LOT 210 c P~INT GLOaAL FORCE \lECTOR LOT 211 c LOT 212

I -59-

I I

WRITE UO,l10t LOT 213 WRITE U0,2301 LOT 211t 00 190 J=1,IP LDT-215 WRITE (10,3201 J, fRCI.JJ ,1=1,51 LOT 2l6

190 CONTINUE LOT 217 REWIND 7 LOT 218 WRITE C71 R LQT,219 IF fTITEL CU .EQ.5HCHECKJ STOP 1 LOT 220 RETURN LOT 221

C LOT 222 C LOT ,223

c c c c c c c c c

c

c

c c

200 FORMAT CI5X,•ELEMENT NODAL FORCES•,!) LOT 221t 210 FORHAT CISX,•OIAGNOSTICS •• WHEEL NO.•,IS,SX,•IS OFF THE BRIDGE•,ISXLDT 225

!,•WHEEL LOA0 ••••••••••••• •,6X,F10.2,15X,•GLOBAL X-COORDINATE •,FLDT 226 ZH;.&,/SX,•GLOBAL Y-COORDINATE •,F16.6,/Il LOT 227

220 FORMAT f5X,•ELEHENT LOADED N=•,ISJ LOT 228 230 FORMAT (/6X,•NOOE•,5X,•Fx•,t&X,•FY•,1&X,•Fz•,t&X,•Hx•,t6X,•HY•,tl LOT 229 240 FORMAT CA4,&X,2F1D.O,I5,F10.0) LOT 230 250 FORMAT f//5X,•LOAO CASE NUMBER =•,5X,I5,15X,•LOAO TYPLOT 231

1E =•,&X,Ait,ISX,•X-COORDINATE OF LOAD CENTROID LOT 232 2=•,Ft0.2,/5X,•Y-COORDINATE OF LOAD CENTROID =•,Ft0.2,15X,•NUHBER OLDT 233 3F LOADS IN GROUP =•,5X,I5,15X,•SKEW ANGLE OF SUP~ORT LDT 234 4=•,F10.2,/II LDT 235

260 FORMAT C1DF6.0J LOT 236 270 FORMAT C/5X,•WHEEL•,tOX,•LOAO •,5X,•X-DISTANCE•,5X,•Y-BISTANCLOT 237

tE•tl LOT 236 280 FORMAT C1DX,I5,JCF1D.l,5XJI LOT 239 290 FORMAT C6X,•NOOE•,17X,•Fz•,13X,•Hx•,t3X,•HY•I LOT 240 300 FORMAT C5X,I5,5X,3C5X,F10.31J LOT 241 310 FORMAT C/5X,•GLOBAL FORCE VECTOR•,/1 LOT 242 320 FORMAT C5X,I5,5CE16.5,2XIJ LOT 243

END LOT 244-

SUBROUTINE SSPLATE CNTRIJ SSP 1 SSP 2

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SSP 3 SSP It

THIS SUBROUTINE ASSEMBLES THE STIFFNESS MATRIX AND CONSISTENT SSP 5 ELEMENT LOAD VECTOR OF EITHER A QUADRILATERAL FORMED BY FOUR SSP 6 LCCT-11CNTRI=41 OR A SINGLE LCCT-9 TRIANGLECNTRI=1J SSP 7

SSP 8 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SSP 9

SSP 10 COHHON /PLSTR/ XAC4t,YAC41,CSC6t,SPDC12,1Zt,R1C1Zt,ESIGC5,3t SSP 11 COHHON IPLBOG/ XC5J ,VC51,CMC3,31 ,PC5J,Bt1C3,51,CVC3,5t,SU9,191,FUSSP' 12

191 SSP 13 COHHON /TRIAG/ 8(3J,A(3J,CMTC3,3t,THIKC31,PTC31,STC12,12l,FTC121 SSP 14

SSP 15 OIHENSION LOCC17,4t, IPERHC41, NCCJI SS~ 16

SSP 17 DATA 1PERHIZ,3,4,11,LOC/1,Z,3,4,5,&,13,14,15,17,16,20,21,24 1 25,26,SSP 18

129,4,5,&,7,8,9,13,14,15,18,17,21,22,24,2&,27,29,7,8,9,10,11,12,13,SSP 19 214,15,19,18,22,23,2\,27,28,29,10,11,12,1,2,3,13,14,15,1&,19,23,20,SSP' 20 324,28,25,291 SSP 21

SSP 22 NBF PLATE BENDING DEGREES OF FREEDOM SSP 23

-60-



c c c c c c c c c

c c c

c

c c c c

c c c c

11 FOR SLCCT-11 9 FOR SLCCT09

NEF EXTERNAL DEGREES OF FREEDOM 12 FOR QUADRILATERAL CJ•NPI 9 FOR TRIANGLE

NIF INTERNAL DEGREES OF FREEDOM 7 INTERNAL NODES FOR A QUADRILATERAL D INTERNAL DOF FOR A TRIANGLE

NBF=11 NEF=12 NIF=7 NDF=N9F NTF=NEF+NIF NCCJI=NBF-o DO 10 I=1,373

10 SCI,U=O.

DETERMINE INTRINSIC DIMENSIONS OF ELEMENT OR SUBELEHENT

DO 30 N:t,NTRI M=IPERMCNI NC ( 1t =N NCC21=11 L=NCC31 AIU=XCLI-XCHI A(21 =XCNI-X(LI Al31 =XCMI-XCNI BUI=VCMI-YCU B121=YILI-Y(NI BIJI=YCNI-YIMI DO 20 I=t,J L=NC III THIK CI I =f» ILl DO 20 J=1,3

20 CMTII,JJ=CM!I,Jl

CALL SSLCCT CNBF I

INSERT CONTRIBUTION OF TRIANGULAR STIFFNESS LCCT-11 INTO QUADRILATERAL STIFFNESS

FTC 111 =-FTC 11l DO 30 I=t,NDF K=LOCII,NI FCKI=FIKI+FTUI STCI,111=-STCI,111 STC11,II=-STC11,II DO 30 J=1,I L=LOCCJ,NI C=SCK,Lit-STCI,JI SCK,U=C

30 SCL,KI=C

STATIC CONDENSATION OF 7 INTERNAL OEGQEES OF FREEDOM FOR A QUAORILATERAL ELEMENT

00 ltD H=t,NIF

-61-

SSP 21t SSP 25 SSP 2& SSP 27 SSP 28 SSf» 29 SSP 30 SSP 31 SSP 32 SSP 33 SSI» 34 SSP 35 SSfl 3& SSP J7 SSP 38 SSP 39 SSfl 40 SSP 41 SSP lt2 SSP 43 SSP 44 SSfl 45 SSP 46 SSP 47 SSP lt8 SSP 49 SSP 50 SSP 51 SSP' 52 SSP 53 SSP 54 SSP 55 SSf» 56 SSP 57 SSP 58 SSP 59 SSP 60 SSP 61 SSP 62 SSP ' 63 SSP 64 SSP 1)5

SSP il6 SSP 67 SSf» &8 SSP 69 SSP 70 SSP 71 SSP 72 SSP 73 SSP 74 SSP 75 SSI» 76 SSP 11 SSP 76 SSP 79 SSI' 110 SSP 81

c c c c c c c c c c

c

c

c

c c c

\0

L=NTF-H SSP 82 N=L+1 SSP 83 PIVOT=S(N,NJ SSP 8-FN=F(NI SSP 85 FCNI=FN/PIVOT SSP 86 DO 40 I=1,L SSP 87 C=S U, NJ /PIVOT SSP 88 SU,NI=C SSP 89 F ( U =F C U -C•FN SSP 90 DO 40 J:I,L SSP 91 SCI,JI=S«I,JJ-C•S(N,JI SSP 92 SCJ,U=SU,J) SSP 93 RETURN SSP 94 END SSP 95-

SUBROUTINE SSLCCT CNBFI SSL 1 SSL 2

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SSL 3 SSL 4

STIFFNESS SUBROUTINE FOR COMPATIBLE TRIANGULAR PLATE ELEMENT SSL 5 WITH tNBFt BENDING D.F. lNBF=12,11 1 10 9 9) -RIGHT-HAND SYSTEM- SSL 6 ORTHOTROPIC ELASTIC MATERIAL, LINEARLY VARYING THICKNESS AND SSL 1 OPTIONAL INCLUSION OF TRANSVERSE SHEAR (6 INTERNAL O.F.I SSL 8

SSL 9 • • • • • • • • • ~ • • • • • • • • • • • • • • • • • • • • • • • SSL 10

SSL 11 COMMON ITRIAGI BC31,AC3t,C~TC3,3t,THIKCll,PT(3),STC12,12l,FTC12l SSL 12

SSL 13 DIMENSION PC21,121, HC2U, UC2U, QCJ,&I, HTC31, IPERHCJ), TXC3) 1 SSL 14

1TY CJt, NKNC4,3), NSNC\,3) SSL 15 SSL 1&

EQUIVALENCE CCI111tCMTUIJ, CCM12,CHH21), CCH13,CHTC3U, CCH22,CHTSSL 17 11511, CCH23,CMTC6tl, CCH33,CHH911 SSL 18

SSL 19 DATA IPERMI2,3,11,NKN/2,5,3,6,8,2,9,3,5,8,&,9/,NSN/2,3t5t6t3t1t&t4SSL 20

1,1,2t4t51 SSL 21 SSL 22

INITIALIZATION SSL 23 SSL 2ft

NOF=NBF SSL 25 AREA=A(31•BC21-AC21•BC3t SSL 26 TO=CTHIKC1J+THIK(2J+THIKC3)1/3. SSL 27 F AC=To•• 3•AREA/ S&ft. SSL 28 DO 10 1=1,3 SSL 29 J=IPERHCil SSL 30 K=IPERMCJ) SSL 31 X=ACit••2+BCit••z SSL 32 Ulii=-CACII•ACJI+9Cit•~(J))/X SSL 33 X=SQRTC XI SSL 3ft HTfiJ=4.0•AREA/X SSL 35 TYUI=-o.s•BUI/X SSL 3& TXCIJ=O.S•ACII/X SSL 37 A1=ACIIIAREA SSL 38 A2=ACJI/AREA SSL 39 B1=BIIJ/AREA SSL 40 B2=B(J)/AREA SSL ft1

-62-

I


I I I act.r•=at•at SSL lt2

Q<2,Il=A1•A1 SSL lt3 QC3,U=2.•A1•B1 SSL ,. .. Q(1,I+3l=2.~B1•B2 SSL 45

I Q(2,I+3t=2.•A1•A2 SSL It& QC3,I+3J=2.•<A1•82+A2•~1) SSL 47

10 CONTINUE SSL lt8 DO 20 1=1,3 SSL .. q J=IPERI'I(H SSL 50

I K=IPERM(Jl SSL 51 II=J•I SSL 52 JJ=J•J SSL 53 KK=J•K SSL 54

I A1=A<U SSL 55 A2=A(JI SSL 5& Al=AIKl SSL 57 Bt=BIU SSL 58

I B2=B IJ) SSL sq B3=B1Kl SSL 60 Ul=U IH SSL 61 U2=UIJl SSL 62

I U3=U!Kl SSL 63 W1=1.-Ut SSL 64 W2=1.-U2 SSL 65 W3=1.-U3 SSL &6

I BtD=z.•at SSL 67 B2D=2.•92 SSL &8 BJD=z.•sJ SSL ()q A10=2.•At SSL 70 A2D=2.•Az SSL 71

I A3D=Z.•A3 SSL 72 C21=61-B3•U3 SSL 73 czz=-B1o+az•w2+93~U3 SSL 74 C31=A1-A3•U3 SSL 75

I C32=-A1D+A2•W2+A3•U3 SSL 76 C51=BJ•W3-32 SSL 77 C52=820-B3•WJ-B1•U1 ss:.. 78 C61=A3•w3-A2 SSL 79

I C62=A20-A3•w3-A1•U1 SSI. 80 C81=B3-B2D-B2•U2 SSL 81 C82= a to- a 3+ s1• w1 SSL 82 C91=A3-A2D-A2•U2 SSL 83

I C92= A10-A 3+ A 1•1o11 SSL 84 FT<II-21=0. SSL 85 Fi(II-1l=O. SSL 86 FTCIU=O. SSL 87 FTC10l=O. SSL 88

I FT (1 U =0. SSL 89 FTct2t=o. SSL 90 DO 20 N=ltl SSL 91 L=6•<I-1l+N SSL 92

I Q11=Q(N,Il SSL 93 Q22=Q(N,JI SSL 94 Q33=QIN,KI SSL 95 Q12=Q(N, I+ll SSL 96

I Q23:Q(N,J+31 SSL 97 Q31=QCN 1 K+31 SSL 98 Q23H=Q23-fl33 SSL 99

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I I I

I I

Q3133=QJ1-Q33 SSL 100 P(L,II-21=&.•C-Q11+W2•Q33+UJ•Q23331 SSL 101 I P<L,II-1t:C21~Q23+C22•Q33-BJD•Q12+B2D~Q31 SSL 102 P<L,IIl=C31•Q23+CJ2•Q33-A3D•Q12+A2D•QJ1 SSL 103 P<L,JJ-21=&.•CQ22+W3•Q23J3l SSL 104 PCL,JJ-11=C51•Q2333+81D~Q22 SSL. 105

I P(L,JJI=C&1•Q2333+A3D~Q22 SSL 106 P<L,KK-21=&.•cl.+U2t•QJJ SSL 107 PCL,KK-1J=C81•Q33 SSL 108 Ptl, KK. =C91•QJ3 SSL 109

I P<L,I+91=0. SSL 110 PtL,J+9l=HTCJI~Q33 SSL 111 PCL,K+91=HTCKJ•Q2333 SSL 112 P<L+J,II-2J=&.•(Q11+UJ•QJ1331 SSL 113 PCL+3,II-1J=C21•Q3133-B3D•Q11 SSL 114 I PCL+3,IIl=C31•Q3133-A30•Q11 SSL 115 P(L+J,JJ-21:&.•C-Q22+U1•Q33+W3•Q3133J SSL 11& P(L+3,JJ-1J=C51•Q31+C52•QJl+B3D•Q12-B1D•Q2J SSL 117 PCL+J,JJl=C&1•QJ1+C62•Q3J+AJO•Q12-A1D•Q2J SSL 118 I P(L+J,KK-21=&.•C1.+W11•QJJ SSL 119 PCL+J,KK-11=C82•QJJ SSL 120 P<L+3,KKI=C9~QJJ SSL 121 P(L+J,I+9t=HTCIJ•OJ3 SSL 122

I fJ(L+J,J+91=0. SSL 123 P(l+3,K+9J=HT<Kt•Q3133 SSL 124 P<N+18,II-2J=2.•<Q11+UJ~Q12+W2•~J11 SSL 125 PCN+18,KK-1J=((81D-a2Dt•QJJ+C82•Q23+C81•QJ1J/3. SSL 126

I PCN+18,KKJ=C<A10-A2Dt•Q33+C92•Q23+C91•Q31113. SSL 127 20 P(N+18,K+91=HT<Kt•Q1213. SSL 128

c SSL 129 c STATIC CONDENSATION OF MIDSIDE NODE SSL 130 c SSL 131 I NK=12-NBF SSL. 132

IF <NK.LE.OI GO TO 40 SSL 133 DO 30 N=1,NK SSL 134 K=13-N SSL 135 I DO JO L=1,4 SSL 136 J=NKN<L,NI SSL 137 IF <L.LE.21 C=TX<K-91 SSL 138 IF CL.GT .21 C=TY<K-91 SSL 139

I FT<JI=FTCJI+C•FT<KI SSL 140 00 30 I=1,21 SSL Hi

30 PCI,JI=P(I,JI+C•P<I,KI SSL 142 c SSL 143

I c FORMATION OF MOMENT VECTOR U <ZU SSL 144 G SSL 145

40 DO 80 J=t,NOF SSL 146 00 SO L=1,3 SSL 147

I KK=L+18 SSL 148 II=L-6 SSL 149 Pl=PCKK,JI SSL 150 H(KIO=O. SSL 151 DO SO N=1,3 SSL 152 I II=II+o SSL 153 JJ=II+3 SSL 154 P1=PCII,JI SSL 155 P2=P(JJ,Jl SSL 156

I SUM=P1+P2+P3 SSL 157

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I I I


T1=SUM+P1 SSL 153 T2=SUIHfl2 SSL 159 T3=SUH+fl3 SSL 1&0 HI II I =T1 SSL 161 H(JJI=T2 SSL 1&2 HIKKI=THHIKKI SSL 1&3

50 CONTINUE SSL 16ft DO 50 N=1,19,J SSL 165 UINI=CM11•H(NI+CM12•H(N+1l+CM13•HIN+2l SSL 1&& UIN+11=CM12•HINI+CM22•HIN+11+CH23•HCN+21 SSL 167

EiO UIN+2l=CH1J•HINI+CH23 4 HIN+11+CH33 4 H(N+21 SSL 168 c SSL 169 c FORMATION OF STIFFNESS MATRIX SSL 170 c SSL 171

00 80 I=1,J SSL 172 X=O. SSL 173 DO 70 N=1,21 SSL 174

70 X=X+UINI•P(N,!I SSL 175 STU,JI=X•FAC SSL 17&

80 SHJ,H=STU,JI SSL 177 RET~RN SSL 178 ENO SSL 179-

SUBROUTINE SETUP tE1,E2,XU,G12,G13,G23~RHO,NP.XORD,YORD,~AT,THIK,ESET 1 1AXGLE,NEP,OF,~TAG,ROT,SDIS,COUNT,NMEL,NHNP,NMTI SET 2

C SET J C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SET ~ C SET 5 C THIS SUBROUTINE INPUTS OR GENER~TES ST~UCTURE DATA SET 6 C SET 7 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SET 6 C SET 9

CO~MON /CBOO/ JUM1,JUM2,JUM3,JU~4,IN,IO SET 10 COMMON /Co01/ NUMEL,NUMNP,NUMBC,NM~T,NLCS,NN,MM,NPSEGM SET 11 COMMON /CB02/ NUMBLK,NSLKL,I6ANOW,NEQ3C SET 12 COMMON /C903/ MAXEL,MAXNP,MAXPD,MAXMT SET 13 COH!10N /HEAD/ HEA01 I 131, HEAD2 ( 131 ,QEQ SET 14 COMMON /STEVE/ NW,XL8R SET 15

C SET 16 IJIMENSION E11NHTI, E21NHTI, XUINMTI, G121NMTI, G23CNHT), G131NMH,SET 17

1 RHOINMTI, NPINMEL,41, MATINMELI, THIKINHEL,41, EAXGLEINMEU, NEPISET 18 2NMELI, UFINMEL,41, XOROINMNPI, YOROINMNPI, NTAGINMNPI, ROTINHNP,21SET 19 3, S!)!SINHNP,:il, COUNTlNHNPI, NPTI41, SPOISI, THI41, I3CI51 SET 20

C SET 21 LOGICAL QEQ,FLAT,NOG SET 22

C SET 23 WRITE 1!0,3801 SET 2~ 00 10 N=1,NMAT SET 25 READ IIN,J901 I,E,RE,XUIII,XU12,G131II,G23(!1 ,RHOIII SET 26 WRITE 1!0,4001 I,E,RE,XU(!I,XU12,G131II,G23(!1,RHO(!I SET 27 E11II=E 4 SQRTIREI SET 28 E21Il=E11II/RE SET 29

10 G121Il=0.54 E/11.+XU121 SET 30 C SET 31 C READ OR GENERATE AND PRINT NOO~L POINT COORDINATES SET 32 C SET 33

-65-

c

WRITE CIO,ft10l L=O

20 READ liN,ft20) N,XORDCNl,YORDCNt,HOD,NLIH,FACX,FACY L1=L+1 IF (N-L1) 90,70,30

30 IF IL.LE.OJ GO TO 80 OIIJ=N-L OX=IXORDCNt-XORDlLJtiDIV OY=IYOROCNJ-YORDlLJl/OIIJ DO ftO L=L1,N XOROCLJ=XORD(L-1l•OX

40 YOR0(LJ=YORD(L-1J•OY GO TO 70

50 L1=N•1 WRITE CI0,430J HOO,NLIH IF (FACX.LE.O.J FACX=1• IF CFACY.LE.O. t FACY=1.

60 N=N•1 Nt=N-HOD N2=N1-MOD IF CN1.LE.O.OR.N2•LE.Ot GO TO 100 XORDCNJ=XORD<N1t•FACX•CXORDCN1t-XORD<N2tt YORO<NI=YOROIN1t•FACY•<YORDCN11-YOROCN21J IF (N.LT.NLIHI GO TO 60 HOD=O

70 L=N WRITE (10,4401 tK,X.ORDfKl ,YOROCKt ,K=L1,NJ IF IHOO.GT.OI GO TO 50 IF (N-NUMNPI 20,120,110

80 WRITE JI0,\501 GO TO 370

90 WRITE ti0,4601 N GO TO 370

100 WRITE CI0,4701 GO TO 370

110 WRITE CI0,4801 N,NUHNP GO TO 370

C READ OR GENERATE AND PRINT ElfHENT PROPERTIES c

120 WRITE (I0,5001 N=1

130 READ IIN,620) L,NPT,H,PHI,TH,MOD,NLIH NOG=. TRUE. IF (L-NI 280,140,160

140 IF CH.LE. Ot M=1 FLAT=THf11.LT.O. NEN=4 IF INPH U .EQ. NPTI4tJ NEN=3 IF (NPTI2t.EQ.NPTI3ll NEN=2 00 1SO 1=1,4 THICK=TH (I)

IF IFLATl THICK=ABSfTH(1t) THIKfN,It=THICK

150 NP(N,Il=NPT!Il T4=THIK(N,41 IF (T4.LE.O •• ANO.NEN.€Q.4l NEN=5 GO TO 200

-66-

SET 3't SET 35 SET 36 SET 37 SET 38 SET 39 SET ItO SET 41 SET 42 SET 43 SET 44 SET 45 SET ft6 SET 47 SET 48 SET 49 SET 50 SET 51 SET 52 SET 53 SET 54 SET 55 SET 56 SET 57 SET 58 SET 59 SET· 60 SET 61 SE.T 62 SET 63 SET 64 SET 65 SET o& SET 67 SET &8 SET 69 SET 70 SET 71 SET 72 SET 73 SET 74 SET 75 SET 76 SET 77 SET 78 SET 79 SET 80 SET 81 SET 82 SET 83 SET 84 SET 85 SET 86 SET 87 SET 88 SET 89 SET 90 SET 91

I I I I I I I I I I I I I I I I I I


c

160 IF CN.LEoU GO TO 270 DO 170 I=1,1t THIKCN,II=THIKCN-1,11

170 NPCN 9 II=NPCN-1,II+1 GO TO 200

180 IF INOGI WRITE CI0,43DI HOQ,NLI11 NOG=.FALSEo N1=N-110D N2=N1-110D IF CN1.LE.O.OR.N2.LE.OI GO TO 100 DO 190 I=1, It THIKCN,II=2.•THIKCN1,II-THIKCNZ,II

190 NPCN,I1=2•NPIN1,II-NPCN2 9 II 200 MATINI=f1

EAXGLECNI =PHI NEPINI=NEN IF INEN.EQ.51 GO TO 240 IF INEN-31 230,220,210

210 WRITE CI0,5101 N,CNPCN,Ut!=1,41 ,H,PHI,(THIKCN,II,I=1,1tl GO TO 250

220 WRITE II0,520) N.CNPIN,I•ti=1,31,H,PHitiTHIKCN,I),l=1,31 GO TO 250

230 WRITE CI0,5301 N, INPCN,II tl=1t21 ,11, CTHIK!Ntii ,I=1,1tl GO TO 250

2lt0 WRITE CI0,4901 N, INPCN,Ut!=1,41 ,M,PHI,(fHIKCN,It,I=1,3t 250 N1=N

N=Nt-1 IF IL-NI 2&0,140,160

260 L=N IF CMOD.GT.O.AN~oN1.LT.NLIMl GO TO 180 IF CN1-NUMELI 130,300,290

270 WRITE CI0,5lt01 GO TO 370

280 WRITE CI0,5501 L GO TO 37G

290 WRITE (!0,5601 N1,NUMEL GO TO 370

C READ AND PRINT OF DISPLACEMENT BOUNDARY CONDITIONS c

300 L=O DO J10 N=1, NUHNP NTAGINI=O ROTIN,U=O.O ROT IN,2 I =D. 0 COUNTINI=O. DO 310 I=1,5

310 SOISIN,II=O. WRITE CI0,57DI

320 READ CIN,5801 N,IBC,ALPHA,SETA,SPO,HOO,NLIH GO TO 340

330 N=Nt-MOO 340 L=Lt-1

WRITE 110,5901 N,ISC,ALPHA,dETA,SPIJ NTAGCNJ=1&•IBCC5l+8•IBG141t-4•I9G(31+2•IBCI2Jt-1•IBC11l ROTCN,1t=ALPHA/57.295775 ROTIN,21=6ETAI57.295775 DO 350 K=1,5

-67-

SET 92 SET 93 SET 94 SET 95 SET 96 SET 97 SET 98 SET 9CJ SET 100 SET 101 SET 102 SET 103 SET 104 SET 105 SET 106 SET 107 SET 108 SET 109 SET 110 SET 111 SET 112 SET 113 SET 114 SET 115 SET 116 SET 117 SET 118 SET 119 SET 120 SET 121 SET 122 SET 123 SET 124 SET 125 SET 12& SET 127 SET 128 SET 129 SET 130 SET 131 SET 132 SET 133 SET 134 SET 135 SET 136 SET 137 SET 138 SET 139 SET 140 SET 141 SET 142 SET 143 SET 144 SET 145 SET lit& SET 147 SET 148 SET 149

SDISlN,KI=SPDlKI SET 350 CONTINUE SET

IF (MOO.GT.O.AND.N.LT.NLIHJ GO TO 330 SET IF fl.LT.NUI1BCI GO TO 320 SET

C SET C CHECK BAND WIDTH AND ELEMENT NUMBERING FOR STIFFNESS ASSEMBLY SET C SET

NPO=O SET IFLAG=O SET DO 3&0 N=1,NUHEL SET NEN=NEP(Nl SET IF CNEN.EQ.5J NEN=4 SET DO 3&0 I=1,NEN SET K=NPCN,II SET COUNT C Kl =COUNT C K I •1· SET DO 3&0 J=1,I SET L=IABSCNPCN,JJ-Kt SET IF CNPO.LT.U NPO=L SET IF CL.LE.MAXPDI GO TO 3&0 SET WRITE CIO,&OOI N SET IFLAG=1 SET

J&O CONTINUE SET HH=5•CNP0+11 SET IBANDW=MH SET WRITE CI0,&10l HH SET IF CIFLAG.NE.OI GO TO 370 SET XLeR=XORDI7J-XORDC1l SET RETURN . SET

370 STOP SET C SET C SET

360 FORMAT C/24HOMATERIAL PROPERTY TABLE//6H HAT N0.,7X,6HMEAN E,10X,5SET 1HE1/E2,7X,7HHEAN NU,9X,5HNUG12,9X,3HG13,11X,3HG23,6X,11HSPEC.WEIGHSET 2TII SET

390 FORMAT II4,E10.3,3F10.3,2E10.3,F10.JI SET 400 FORMAT C1HO,I7,1PE14.4,0P3F14.4,1P2E14o4tOPF14.4/) SET 410 FORMAT l/24HONODAL POINT COORDINATES//6H POINT,10X5HX-ORD,11X5HY-OSET

1RD/1Xl SET 420 FORMAT ([4,2F10.3~2I4,2Fl0o3J SET 430 FORMAT f22HOGENERATION WITH HOD =I3,3X,6HNLI~ =I4J SET 440 FORMAT CI&,2F1&.&1 SET 450 FORMAT (J1HOFIRST NODAL POINT CARD MISSINGJ SET 4&0 FORMAT C2&HCOORDINATE CARD FOR NODE =I4,1&H NOT IN SEQUENCEJ SET 470 FORMAT C40HINSUFFICENT INFORMATION TO GENERATE HESHI SET 460 FORMAT C12HONOOE NUMBERt4,22H EXCEEDS GIVEN NUHNP =I41 SET 490 FORMAT CSH ~Ed I4,3X,4I5,I9,F20.4,5X,3F14.41 SET 500 FORMAT (14H1ELEMENT ARRAY//6H ELEMENT9X,14HEXTERNAL NODES,5X,6HMATSET

1ERIAL,7X,12HELASTIC AXES,1&X,40HPLATE THICKNESS, WEB, OR BEA" PROPSET 2ERTIES/1&X,1&HI J K l,7X,3HN0.,9X,12HANGLE lX1,XI,JX,•TI SET lOR IY 0~ Tl TJ OR JT OR H1 TK OR ECC OR HZ TL OR XSEC•I1Xl SET

510 FORMAT CSH QUAOI4,3X,4I5,I9,F20.4,5X,4F14.41 SET 520 FORMAT ISH TRIGI4,3X,JI5,I14,F20.4,5X,3F14.4) SET 530 FORMAT f5H BEAMI4,3X,2I5,!19,25X,1P4E14.41 SET 540 FORMAT (27HOFIRST ELEMENT CARO MISSING! SET 550 FORMAT C17HOELEMENT CA~D NO.I4,1&H NOT IN SEQUENCEI SET 560 FORMAT 112HOELEMENT NO.I4,22H EXCEEDS GIVEN NUMEL =I4l SET 570 FORMAT (42H1BOUNOARY CONDITIONS (1=RESTRA[NED,O=FREEI//&H POINT,9XSET

1,7H3C TAGS,15X,5HANGLE,3&X,23HSPECIFIED DIS~LACEHENTS/11X,10HU VSET

-68-

I I

150 151

I 152 153 154 155 15& I 157 156 159 160 I 1&1 1&2 1&3 !&It

I 1&5 166 1&7 1&8

I 1&9 170 171 172 173 I 174 175 176 177 I 176 179 180 181

I 182 163 16 .. 185

I 16& 167 188 189 190 I 191 192 193 194 I 195 196 197 198 I 199 200 201 202

I 203 204 205 206

I 207

I I I


c c c c c c

c

c

c

c

2 W ,10H O-X 0-Y ,2X,5HALPHA,6X,4HBETA,8X,1HU,13X,3H V ,12X,3H 3 ,12X,3HO-X,12X,3HO-Y,/1XI

560 FORMAT 1IIt,1X,5I1,7F8.2 1 4X 9 2I41 590 FORMAT CI6,2X,5I4,2F10.4,5F15.8l 600 FORMAT C48HOMAX. NODAL POINT DIFFERENCE EXCEEDED, ELEMENT =I~I 610 FORMAT (/1lHOBAND WIDTH =IItl 620 FORMAT 16I4,5F8.3,2I41

END

WSET 2011 SET 209 SET 210 SET 211 SET 212 SET 213 SET 2.llt SET 215-

SUBROUTINE STORE IE1,E2,XU,G12,G13,G23,RHO,NP,XORO,YORO,~AT,THIK,ESTO

1AXGLE,NEP,OF,NTAG,ROT,SOIS,COUNT,R,NMELtN"NP,NMTI STO STO

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • STO

THIS SUBROUTINE STORES ALL ELEMENT PRPERTIES ON TAPE STO STO

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • STO

COMMO~ /CiOO/ JUM1,JUM2,JUM3,JUH4,IN,IO COMMON /C301/ ~UMEL,NUHNP,NUHBC,NHAT,NLCS,NN,MH,NPSEGM

STO STO STO STO

DIMENSIOt-1 EUNMf), E21NMT), XU(NHT), G12lNMTI, G23lNt1;f), G131NHH,STO 1 RHOINHTI, NPINHEL,41t HATINMELI, THIKlNHEL,~I, EAXGLElNHELI, NEPCSTO 2NMELI, OFINMEL,41, XOROlNHNPI, YOROINHNPI, NTAGCNHNPl, ROTCNMNP,21STO 3, SUISCNHNP,SI, CO.UNTl~MNPI, Rl5,Nt1NPl, XCSI, YC5), CMlJ,JI, CSC2,STO '+21, THI5l, NPTl51, SNA(Itlt CNAIItl, NTG(Itl, 50(5 9 41, SFCS,Itl, Pl51 STO

DO 60 N=1,NUMEL NEN=NEP(NI M=M~TINI DO 10 I=1,4

10 THCII=THIKIN,II DO 40 I=1,4 K=NPIN,II NPTIIl=K XIII=XOROit<l Y I U =YORO IKI PI I l =OF ( N, I l CNAIII=1. SNAIII=O. PHI=ROTCKI IF IPHII 20,30 9 20

20 CNAIII=COSCPHil SNA I I l =SINIPHI I

30 NTGIII=NT~G<Kl DO ItO J=1,5 SDIJ,Il=SDISIK,JI

'+0 SFIJ,II=RIJ,KI/COUNTIKI NPTCSI=NUHNP+N X<51=o.zs•cxc1l+XI21+X<JI+X<411 YI51=0.25•CYC11+YI21+YI31+YI411 THC51=0.25•1TrlC11+THI21+THC31+THI'+Il P(51=0.25•(PC1l+PI21+P13l+P(4)1 EAG=EAXGLEINI

CALL FOR!'IC <E1 U11 .E2(HJ ,XU(MI ,G121MI,G1~(HI ,G231HI,EAG,CM,CS)

-69-

STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO STO

1 2 3 4 5 6 1 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 itO 41 42 43 44 45 46 47

I I

IF CNEN.EQ.2) CMC1,1)=EUH) STO 48 DO 50 1=1,9 STJ 49

50 CHCI,ti=CHCI,1t STO 50 &0 WRITE CJUH21 X,Y,CH,CS,TH,NEN,NPT,H,EAG,SNA,CNA,NTG,SD,SF STO 51

IF lNLCS.EQ.11 WRITE CJUHtl NP,HAT,THIK,EAXGLE,NEP,XORD,YORD,NTAG,STO 52 I

1ROT,SDIS,COUNT,OF STO 53 WRITE (JUH11 RHO,HAT,THIK,NEP,NTAG STO 54 RETURN STJ 55 END STO 5&- I SUB~OUTINE FORMC CE1,E2,XU,G12,G1J,G2J,ANG,CM,CS) FRC 1 I

C FRt: 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FRC 3 C FRC 4 C THIS SUBROUTINE COMPUTES THE STRESS-STRAIN COEFFICIENTS FRC 5 I C IN THE GLOBAL X-Y-Z SYSTEM FOR A Z-CYliNDRICALLY ORTHOTROPIC FRC 6 C MATERIAL DEFINED BY CONSTANTS REFERRED TO THE PRINCIPAL MATERIAL FRC 7 C AXES X1-X2-Z FRC 8 C FRC 9 I C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FRC 10 C FRC 11

DIMENSION CMC3,3), CSC2,2) FRC 12 C FRC 13

C=t. FRC 14 I S=O. FRC 15 IF lANG) 10,20,10 FRC 16

10 PHI=ANG/57.2957795 FRC 17 S=SINlPHII FRC 18 I C=COSCPHII FRC 19

20 C2=C•C FRC 20 SC=S•C FRC 21 S2=S•S FRC 22 I C4=C2•C2 FRC 23 S2C2=S2•C2 FRC 2' S4=S2•S2 FRC 25 XUH=1.-xu••2 FRC 26 I C11=E1/XUH FRC 27 C22=E2/XUH FRC 28 C12=SQiH CEt•E2) •XU/XUH FRC 29 Z=C12+2.•Gt2 FRC 30 RZ1=C11-Z FRC 31

I RZ2=Z-C22 FRC 32 RZ=CRZ1-RZ21•S2C2 FRC 33 ZS2C2=2.•Z•S2C2 FRC 34 CMC1,11=C11 4 C4+C22•S4+ZS2C2 FRC 35 I CHC2,2t=C22•C4+Ct1•S4+ZS2C2 FRC 36 CMC1,21=C12+RZ FRC 37 CMC3,Jt=G12+RZ FRC 38 CMC1,3)=CRZt•C2+RZ2•SZI•SC FRC 39 I CHC2,3J=CRZ2•C2+RZ1•S2t•sc FRC 40 CMC2,11=CHC1,21 FRC 41 CMC3,1J=CMC1,31 FRC 42 CMC3,21=CMC2,JI FRC 43 I CSH,U=G13 4 C2+G23 4 S2 FRC 4ft CSC2,21=G13•S2+G23•C2 FRC 45 CSC1,21=CG13-G2JI•SC FRC 46

-70- I I I I


CSC2,U=CSI1,21 RETURN END

FRC 47 FRC 48 FRC 4q-

SUaROUTINE LOAD (RHO,MAT,THIK,NEP,OF,NTAG,R,NMEL,NHNP,NHTI LOA 1 C LOA 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LOA 3 C LOA It C THIS SU3RO~TINE INPUTS CONCENTRATED NODAL LOADS, GRAVITY AND LOA S C DISTRIBUTED LATERAL LOADS LOA 6 C LOA 7 C • • • • • • • • • • • + • • • • • • • • • • • • • • • • • • • • • LOA 8 C LOA 9

COMMON /C300/ JUH1,JUH2,JUM3,JUM4,IN,IO LOA 10 COMMON /C301/ NUHEL,NUMNP,NUHBC,NHAT,NLCS,NN,MH,NPSEGM LOA 11 COMMON /HEAD/ HF.A01(131,HEAQ2(1li,QEQ LOA 12 COMMON /SOLV/ NA1,LWIOTH,NFREE,NAS,LAHA,ISEGH,JUHS,JUM&,JUH7,JUM6 LOA 13 COHHON /PLTS/ NTOTP,N9P,NGPH LOA 14 COMMON /NTRUN/ NRUN LOA 15

C LOA 16 C DISTRIBUTED UNIFOqH LOAD OR GRAVITY LOADS MUST BE THE FIRST LOAD LOA 17 C CASE LOA 18 C LOA 19

DIMENSION RHO (NMEll, MAT INMEU, T HIK (NHEL, 41, NEP(NHELI, OF ( NHEL, 4LOA 20 11, NTAGINMNfJ), RCS,NHNPI, TH(Itl, PL(ftl LOA 21

C LOA 22 LOGICAL QEQ,GLOAO,OLOAD LOA 23

C LOA 2ft NHT=NMAT LOA 25 IF (NRUN.EQ.U GO TO 10 LOA 26 REWIND JU~7 LOA 27 REWIND JUH1 LOA 28 READ (JUM11 LOA zq READ (JUM1l (~HOUI ,I=1,NMATl ,MAT,THIK,NEP,NTAG LOA 30

10 CONTINUE LOA 31 DO 20 1=1,5 LOA 32 DO 20 J=1,NMNP LOA 33

20 RCI,JI=O. LOA 34 READ CIN,2101 HEA02,NCLD,OLOAO,GLOAO LOA 35 WRITE (!0,2201 NLCS,HEAD2,NCLO,OLOAO,GLOAD LOA 36 DO 30 N=l,NUMEL LOA 37 00 30 1=1,4 LOA 38

30 OF<N,II=O. LOA 39 DO 40 N=l,NN LOA 40

40 R (NI =0. 0 LOA lt1 C LOA 42 C INPUT OF CONCENTRATED LOADS LOA 43 C LOA 44

IF INCLO.LE.OI GO TO 60 LOA 45 WRITE (!0,2301 LOA 46

C LOA 47 C READ APPLIED CONCENTRATED FORCES AT THE NODES LOA 48 C LOA 4q

DO 50 N=1,NCLO LOA 50 READ (!N,2601 L,R(1,Ll ,R(2,LI ,R(3,Ll ,R(4,LI ,R(5,LI LOA 51

50 WRITE: (10,2401 L,~(1,LI,R!2,U,RC3,LI,RCit,LI,R(5,LI LOA 52

-71-

C LOA 53 C INPUT OF DISTRIBUTED LATERAL LOADS LOA 54 C LOA 55

60 IF I .NOT • DLOADl GO TO 140 LOA 5& WRITE (I0,2501 LOA 57 N=1 LOA 58

70 READ UN,2&01 LtPL LOA 59 IF !N-ll 80,80,100 LOA &0

80 DO 90 I=1,4 LOA &1 90 DF!N,II=PL!Il LOA &2

GO TO 120 LOA 63 100 DO 110 I=1t4 LOA 64 110 uF(N,IJ=QF(N-1,IJ LOA 65 120 NEN=NEP!Nt LOA 66

WRITE !I0,2401 N,(DF!N,II ,I=1,NENI LOA 67 N=N+1 LOA 68 IF !N-U 100,80,130 LOA 69

130 L=N LOA 70 IF !N+1.LT.NUMELI GO TO 70 LOA 11

C LOA 72 C ADO GRAVITV LOAD TO DISTRIBUTED LATERAL LOAD LOA 73 C LOA 74

1'+0 IF !.NOT.GLOA!Jl GO TO 180 LOA 75 WRITE !I0,2501 LOA 16 DO 170 N=1,4UMEL LOA 77 NEN=NEP !N l LOA 78 M=HAT!NI LOA 79 DO 150 I=1,4 LOA 80

150 TH!II=THIK!N,Il LOA 81 DO 160 I=1,4 LOA 82 IF !NEN.NE.2J DF!N,IJ=OF!N,Il+RHOIMJ•TH!Il LOA 83

1&0 IF !NEN.EQ.2l OF!N,Il=OF!N,Il+RHO!Hl•TH!41 LOA 84 WRITE U0,240t NdOF!N,Il ,I=1,NENI LOA 85

170 CONTINUE LOA 86 C LOA 87 C IF DEGREE OF FREEDOM IS RESTRAINED, CORRESPONDING SPECIFIED LOA 68 C FORCE IS HADE 0. LOA 89 C LOA 90

180 DO 200 N=1,NUMNP LOA 91 L=NTAG(N) LOA 92 IF IL.EQ.OI GO TO 200 LOA 93

C LOA 94 C MOO IS INTRINSIC FUNCTION WHICH COMPUTES!L~TRUNC!L/21•21 LOA 95 C LOA 96

DO 190 K=1,5 LOA 97 IF !MOO!L,2l.NE.Dl RIK,NI=O. LO~ 98

190 L=L/2 LOA 99 200 CONTINUE LOA 100

WRITE !71 R LOA 101 RETURN LOA 102

C LOA 103 C LOA 1il4

210 FORMAT !13A6/I4,2L41 LOA 105 220 FORMAT (14H1LOAO CASE NO.I4//1X,13A6///40H NO. OF NODAL FORCE CARDLOA 106

1S • • • • .I6/ftOH FLAG !T TO INPUT DISTRIBUTED LOADI •• L6/4LOA 107 20H FLAG !T TO CONSIDER GRAVITY LOAOJ ••• L6//J LOA 108

230 FORMAT !26H1CONCENTRATEO NODAL FORCES/ISH POINT,7X,7HU-FORCE,5X,LOA 109 17Hv-FORCE,6X,7HW-FORCE,6X,6HX-MOMENT,6X,8HY-MOMENTf1X) LOA 110

-72-



2'+0 FORMAT ti8,5F1'+.51 250 FORMAT (26H1DISTRIBUTED LATERAL LOADSI/8H

1J,12X,2HPK,12X,2HPL/1XI 260 FORMAT (I~,5F10.31

ENO

LOA 111 ELEMENT,10X,2HPI,12X,2HPLOA 112

LOA 113 LOA 114 LOA 115-

OVERLAY !PLTLOS,l,OI FTA 1 C FU 2

PROGRAM FORTA FTA 3 C FTA It C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •FTA 5 C FTA 6 C THIS PROGRAM KESETS THE FIELD LENGTH FOR DYNAMIC STORAGE ALLOCAT- FTA 1 C ION OF THE LOAD VECTOR FTA 8 C FTA q C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •FTA 10 C FTA 11

COMMON /HEAD/ HEAD1(131,HEAD21131,QEQ FTA 12 COMMON /C901/ NUMEL,NUMNP,NUMBC,NHAT,NLCS,NN,HH,NPSEGH FTA 13 COMMON ICBOO/ JUM1,JUH2,JUM3,JUM't,IN,IO FTA 1~ COMMON /SOLV/ NA1,LWIOTH,NFREE,NA5,LAHA,ISEGM,JUH5,JUH6,JUH7tJUH8 FTA 15 COMMON INTRUN/ NRUN FTA 16 COMMON A(11 FTA 17

C FTA 18 NUHEL4=4•NUMEL FTA 19 NUHNP5=5•NUMNP FTA 20 N1=1 FTA 21 N2=N1~~HAT FTA 22 N3=N2tNU~EL FTA 23 N4=N3•NUHEL4 FTA 24 N5=N4tNUHEL FTA 25 N6=N5~NUHEL4 FTA 26 N7=N6tNUHNP FTA 27 N6=N7tNUMNP5 FTA 26 NLOC=LOCF!AIN111 FTA 2q NRFL=NLOC~N8 FTA 30 NRFL=MAXO!NRFL,JSOOODI FTA 31 WRITE (I0 7 101 NRFL,NRFL FTA 32

C FTA 33 CALL REQHEH !NRFLI FTA 34

C FTA 35 CALL SLOAD !AIN11,A(N21,AIN31,A!N41,AIN51,A!N6),A(N71,NUHEL,NUHNPIFTA 36

C FTA 37 C FTA 36

c c c c c

10 FORMAT !/5X,•FIELD LENGTH•,t5X,010, 4 IN OCTAL•,t5X,I10,• IN OEFTA 39 1CIMAL•,IJ FTA 40

END FTA 41-

SUBROUTINE SLOAO IRHO,MATtTHIK,NEP,DF,NTAG,R,NHEL,NMNPI SLO SLO

• • + • • • 4 • • • • • • • • • • • • • • • • • • • • • • • • • • SLO SLO

THIS SU3ROUTINE INPUTS CONCENTRAT£0 NODAL LOADS, GRAVITY AND SLO DISTRIBUTED LATERAL LOADS SLO

-73-

1 2 3 It 5 6

I I

C SLO 7 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SLO 8 C SLO q

COMMON /C300/ JUM1,JUM2,JUM3,JUM4,IN,IO SLO 10 COMMON /Cd01/ NUMEL,NUMNP,NUMBC,NMAT,NLCS,NN,MM,NPSEGM SLO 11

I COMMON /HEAD/ HEAD11131,HEA02113l,QEO SLO 12 COMMON /SOLV/ NA1,LWIOTH,NFREE,NA5,LAMA,ISEGM,JUM5,JUM6,JUM7,JUM8 SLO 13 COMMON /NTRUN/ NRUN SLO 14 COMMON /LOGIC/ OLOA0 1 GLOAO SLO 15 I

C SLO 1& DIMENSION RHOINMELI, MATINMELI, THIKINMEL,41, NEPINMELI, DFINMEL,4SLO 17

U, NTAGHlMNPI, RIS,NMNPI, THI41, PL141 SLO 18 C SLO 19 I

LOGICAL QEQ,GLOAD,DLOAO SLO 20 C SLO 21

IF I NRUN. EQ.11 GO TO 10 SLO 22 REWIND JUM1 SLO 23 I READ IJUM11 SLO 2ft READ IJUHU I~HOIII ,I=1,NMATI ,MAT,THIK,NEP,NTAG SLO 25

10 CONTI~UE SLO 26 NLCS=NRUN SLO 27 I READ IIN,240J HEA02,NCLO,OLOAD,GLOAD SLO 28 WRITE II0,1901 NlCS,HEA02,NCLD,OLOAO,GLOAD SLO 29 DO 20 N=1,NUMEL SLO 30 DO 20 1=1,4 SLO 31

20 OFIN,Il=O. SLO 32 I 00 30 N=1,NA1 SLO 33

30 RINI=O.O SLO 34 C SLO 35 C INPUT OF CONCENTRATED LOADS SLO 3& I C SLO 37

IF INCLO.L£.01 GO TO 50 SLO 38 WRITE II0,2001 SLO 39

C SLO 40 I C READ APPLIED CONCENTRATED FORCES AT THE NODES SLO ~1 C SLO 42

DO 40 N=1,NCLD SLO 43 REA n I I ~ , 21 0 l L , R 11 , Ll , R I 2 , U , R I 3 , U , R P+ , ll , R I 5, Ll S L 0 44 I

4 0 w KITE II 0, 2 2 0 l L , R 11 , U , R I 2 , L I , ~ I 3, L I , >U It, L I , R I 5, U SL 0 4 5

C SLO 46 C INPUT OF DISTRIBUTED LATERAL LOADS SLO 47 C SLO 48

50 IF I.NOT.DLOAOI GO TO 160 SLO 49 I

WRITE II0,230l SLO 50 N::1 SLO 51

60 READ IIN.Z10l L,PL SLO 52 IF IN-ll 70,70,90 SLO 53 I

70 DO 80 1=1,~ SLO 5~ dO OFIN,Il=PLIIl SLO 55

GO TO 110 SLO 56 90 DO !OJ I=1,4 SLO 57 I

100 DFIN,Il=DFCN-1,11 SLO 58 110 NEN=NEPINI SLO 59

WRITE (!0,2201 N, IOFIN,II .I=1,NENI SLO 60 N=N+1 SLO 61 I IF !N-L l 90,70,120 SLO 62

120 L=N SLO 63 IF IN•1.LT.NUt1Ell GO TO 60 SLO 64 I

-74-

I I I


C SLO C AOD GRAVITY LOAO TO DISTRIBUTED LATERAL LOAD SLO C SLO

IF I.NOT.GLOADl GO TO 1&0 SLO DO 150 N=1,NUMEL SLO NEN=NEPINl SLO M=HATINl SLO 00 130 I=1,4 SLO

130 THIII=THIKIN,Il SLO DO 140 I=1,4 SLO IF INEN.NE.21 OFCN,Il=DFCN,II+RHOI~l"'THIIl SLO

140 IF INEN.EQ.2l OFCN,Il=OF(N,Il+RHOIMI"'TH14l SLO 150 CONTINUE SLO

C SLO C IF DEGREE OF F~EEDOM IS RESTRAINED, CORRESPONDING SPE~IFIEO SLO C FORCE IS MAuE O. SLO C SLO

1o0 DO 180 N=1,NUMNP SLO L=NTAGI~l SLO IF ( L. E Q. 0 I GO T 0 18 0 SL 0

C SLO C MOD IS INTRINSIC FUNCTION WHICH COMPUTESCL-TRUNCCL/21•2) SLO C SLO

00 170 K=1,5 SLO IF IMODIL,2l.NE.Ol ~(K,Nl=O. SLO

170 L=L/2 SLO 180 CONTINUE SLO

REWIND JUM7 SLO REWIND JUM7 SLO REWIND JUHT SLO WRITE (7l R SLO RETURN SLO

C SLO C SLO

c

c c c c c c c

1q0 FORMAT 114H1LOAD CASE ~O.I4//1X,13A6///40H NO. OF ~OOAL FORCE CARDSLO 1S ••••• Io/40H FlAG IT TO INPUT DISTRIBUTED LOAD I •• L&14SLO 20H FLAG CT TO CONSIDER GRAVITY LOADI ••• L&//1 SLO

200 FORMAT 12&H1CONCENTRATEO NODAL FORCES//8H POINT,7X,7HU-FORCE,&X,SLO 17HV-FO~CE,&X,7HW-FORCE,&X,8HX-HOMENT,6X,8HY-HOHENTI1Xl SLO

210 FORMAT II4,5F10.Jl SLO 220 FORMAT I I8,3F1ft. 51 SLO 230 FORMAT C2&H1DISTRI8UTED LATERAL LOADS//8H ELEMENT,10X,2HPI,12X,2HPSLO

1J,12X,2H~K,12X 9 2HPL/1Xl SLO 240 FORMAT 113A5/14,2l41 SLO

END SLO

OIIER.LAY IPLATE,2,0l FT2 FT2

PROGRAM FORT2 FT2 FT2 .,. .. .,. . • • • . .. .,. • .,. . .. .,. .. .. . • • • .. .. .. . .. .. .. . .. • • • FT2 FT2

THIS PROGRAM SETS THE FIELD LENGTH FOR GENERATION AND STORAGE FT2 OF INOIIIIDUAL ELEMENT STIFFNESS MATRICES FT2

FT2 .. .. . .. . . . . . .. . • • • • .. .. . .. . . .. . .. .. .. . • • • . ... • FT2

-75-

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 66 87 88 89 qo q1 92 q3 94 qs 96 q7 qs qq

100 101 102 .103 10ft 105 106 107 108 109-

1 2 3 4 5 6 7 8 9

10

c

c

c

c

c

c

c c

c c c c c c c

' Fl2 COHHON COMMON COHMON COMMON COHHON COMMON

N1=1

/CBDO/ JUH1,JUH2,JUMJ,JUM4,IN,IO /CB01/ NUHEL,NUMNP,NUMBC,NHAT,NLCS,NN,HM,NPSEGM /SOLV/ NA1,LWIDTH,NFREE,NA5,LAMA,ISEGH,JUM5,JUH&,JUH7,JUH8 /PLTS/ NTOTP,NBP,NGPH /NTRUN/ NRUN A 111

N2=N1+1t•NUHEL N3=N2+NUMEL N4=N3+4•NUMEL N5=Nit+NUMEL N6=N5+NUiftEL N?=NG+NUHNP N8=N7+NUMNP N9=N8+NUHNP N10=Nq+z•NUHNP N11=N10 +5•NUHNP N12= N11 +NUMNP N1J=N12+1t•NUHEL N14=N13+5•NUMNP NLOC=LOCF lA I 111 NRFL=NLOC+N14+1 NRFL=MAXOINRFL,35000BI

CALL REQMEM INRFLI

WRITE II0,10J NRFL,NRFL

FTZ FTZ FTZ FTZ FTZ FTZ FT2 FTZ FTZ FTZ FT2 FT2 FT2 FTZ FT2 FT2 FTZ FT2 FT2 FT2 FT2 FT2 FTZ FTZ FTZ FTZ FT2 FT2 FT2

CALL FO!U1K IAINU,AIN2J,AIN31 ,AINitl ,AIN5t,AIN61,AIN7J,A(N81,AIN9J ,FT2 1AIN10l,AIN11l,AIN121 ,AIN131 tNUMEL,NUMNP,NMATI FTZ

REWIND JUM7 WRITE IJUM71 IAIII,I=N13,N1~1

10 FORMAT 1/SX,•FIELO LENGTH•,/5X,010,• 1CIMAL•,II

END

FTZ FTZ FTZ FTZ FTZ

IN OEFTZ FTZ FT2

FRIC • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FRIC

FRIC THIS SUdROuiiNE FORMS THE ELEMENT ~TIFFNESS MATRICES FRK

FRIC • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • FRK

FRIC COMMON /CBOO/ JUM1,JUH2,JUHJ,JUM4,IN,IO FRK COMMON /C801/ NUMEL,NUHNP,NUHBC,NMAT,NLCS,NN,MH,NPSEGH FRK COMMON /PLSTR/ XAI41 ,YAI4l ,OSiol ,SPDI12,121 ,R.11121 ,ESIGI5,:JJ FRK COMMON /PLBDG/ XXI51,YY15I,OHI3,31,PP15l,BMI3,5J,CIJI3,51,SPiH19,19FRK

1l,VAI191 FRK COMMON /SOLIJ/ NA1,LWIOTH,NF~EE,NA5,LAMA,ISEGM,JU"5,JUMo,JUM7,JUH8 FRK COMMON /PLTS/ NTOTP,NaP,NGPH FRK COMMON /NTRUN/ NRUN FRK

-76-

11 12 13 14 15 16 17 ta 19 20 21 22 23 2ft 25 26 27 28 29 30 31 32 33 34 35 36 37 38

. 39 40 41 42 43 44 45 46 '+1 48 49 50-

1 2 3 4 s 5 1 8 9

10 11 12 13 14 15

I I I I I I I I I I I I I I I 1 .. , I I I


COMMON /HEAD/ HEAD1(13t,HEA021131 1 QEQ FRK 16 COHMON /WEB/ NWEB,NTP,NTB FRK 17

C FRK 18 DIMENSION Xl51, Yl51, CMC3,3t, CS!2,21, THKCSI, NPT15lt SNAIItt, CNFRK 1q

1A(Itt, NTG!41, SOC5,41, SFI5,41, XTI~I, YTC~t, IPE(~t, STCZO,ZOI, SFRK 20 2tH(1g,1g), 5(20,201, XOI41, Y0!4t, NPINMEL,41, MAHNHELI, THIK(NHEFRK 21 3L,4t, EAXGLf.(NMELt, NE~14MELI, OFINMEL,41t XOROINHNPI, YORD(NHNPI,FRK 22 4 NTAGCNHNPI, ROT!NHNP,21, SDISINHNP,51, COUNTCNMNPI, R(5,NMNPI, IIAFRK 23 5T 1121 FRK 24

C FRK 25 LOGICAL QEQ FRK 26

C FRK 27 DATA IPE/2,3,4,1/ FRK 28

C FRK 29 NMAT=NMT FRK 30 REWIND JUM1 FRK 31 REWIND JUM7 FRK 32 READ (JUH7l R FRK 33 READ (JUH1l NP,MAT,THIK,EAXGLE,NEP,XORO,VORD,NTAG,ROT,SOIS,GOUNT,OFRK 34

iF FRK 35 C FRK 36 C DETERMINATION OF ELEMENT STIFFNESSES FRK 37 C FRK 38

REWIND JUM2 FRK 39 DO 10 1=1,4 FRK 40 XTIII=O.O FRK 41

10 YT!Il=O.O FRK 42 NWE8=0 FRK ft3 DO 350 N=t,NUMEL FRK 4~ ITYPG=O FRK 45 ITYPM=O FRK 46 NTRI =It FRK 47 READ (JUH21 X,Y,CM,CS,THK,NEN,NPT,M,EAG,SNA,CNA,NTG,SO,SF FRK 48 IF INEN.EQ.Jl NTRI=1 FRK 49 IF INEN.EQ.SI THK151=THKI11 FRK 50 00 20 1=1,3 FRK 51 DO 20 J=t,3 FRK 52

20 OMII,JI=CM!I,JI FRK 53 DSI11=CM(1,1l FRK 54 DSI21=:M(2 9 21 FRK 55 DSI3l=CMIJ,31 FRK 56 DSI41=CM(1,21 FRK 57 OSI5t=CM(1,31 FRK 58 DS(oi=CH(2,31 FRK 59 DO 30 !=1,6 FRK 60

30 DSCII=THK151•DSIII FRK 61 DO 40 1=1,5 FRK 62 XX!Il=X!ll FRK 63 YY!II=YIII FRK G4

40 PPIIt=THKIIJ FRK o5 DO 50 1=1,4 FRK 66 L=NPTIII FR'< 67 XA(II=XORDILt FRK 58 YA(Il=YORDILI FRK 69 8M(1 9 li=OF(N,ll FRK 70

50 CONTINUE FRK 71 a~(1,5t=0.2~•(dM!1,11+3M(1,21+3MI1,31+BM(1,411 FRK 72

C FRK 73

-77-

I I

C IF ELEMENT IS THE SAME AS THE PREVIOUS ELEMENT, THE STIFFNESS FRK 7~ C IS NOT RECOMPUTED. THE STIFFNESS OF THE PREVIOUS ELEMENT IS IN FRK 75 C TEMPORARY STORAGE ST, AND SBT FRK 7& C FRK 77 I

DO oO !=1,~ FR( 76 J=IPECII FRK 79 XDCII=XX(Jl-XXCII FRK 60 YOCII=YY(JI-YYCII FRK 81 I OIF=XDCII-XTCII FRK 82 IF (ABSCOIFI.GT.t.E-&1 ITYPG=1 FRK 83 OIF=YD<Il-YT<II FRK 84 IF CABS COIF I.GT .1.E-6l ITYPG=1 FRK 85 XTCil=XDCil FRK 86

I 60 YTCII=YD(II FRK 87

IF <N.EQ.11 GO TO 70 FRK 88 N1=N-1 FRK 89 T5=0.25•CTH!KCN1,1l+THIKIN1,21+JHIK(N1 7 3l+T~IKIN1,~ll FRK 90 I IF <T5.NE.THK<5J l ITYPG=1 FRK 91 IF CM.NE.MATCN-111 ITYPH=1 FRK 92 IF CQEQ.ANO.ITYPM.EQ.OI GO TO 300 FRK 93 IF IITYPG.EQ.O.AND.ITYPM.EQ.OI GO TO 300 FRK 94 I

70 CONTINUE FRK 95 C FRK '3& C AS 1 GOES FROM 1-4, J WILL PERMUTE TO 2,3,4,1 FRK '37 C ITYPG OR ITYPM OF 1 MEANS AT LEAST ONE DIMENSION OF THE PREVIOUS FRK 98 I C ELEMENT IS NOT EQUAL TO THE CORRESPONDING OH1ENSION OF THE CURRENTFRK 99 C ELEMENT. THE OIEME~SIONS OF THE CURRENT ELEMENT ST STORED IN FRK 100 C XTC41, AND YTC'+I. FRK 101 C FRK 102 I

IF INEN.NE.SI GO TO 190 FRK 103 IF CHEAD1Ul.NE.5HDEBUGI GO TO 90 FRK 104 WRITE (!0,3601 FRK 105 DO 80 I=1,4 FRK 106

80 WRITE (!0,3701 NPTCIJ,XUJ,YCIJ FRK 107 I WRITE liO,JdOI ((CM(I,JJ,I=1,3l,J=1,31 FRK 106 WRITE li0,3':101 lOSlii ,I=1,&l FRK 109

90 CONTINUE FRK 110 OX=XC2l-X(11 FRK 111 I OY=YC21-Y(1l FRK 112 xLz=ox•ox•ov•ov FRK 113 XL=SQRTCXL21 FRK 114 SI=OY/XL FRK 115 I CO=OX/XL FRK 116 XAC11=0.0 FRK 117 XA(41=0.0 FRK 116 YA(1l=O.O FRK 119 I YAC21=0.0 FRK 120 00 100 I=1,2 FRK 121 K=I+1 FRK 122 J=I+2 FRK 123 XA(KI=XL FRK 12~

I YAIJI=THKl2l FRK 125 PPIII=THKC11 FRK 12&

100 PP(JI=THKC11 FRK 127 DO 110 1=1,4 FR~ 126 I XX<II=XAtii FRK 129

110 YYCil=YACil FRK 130 IF (HEAJ1Ul.NE.5HOEBUGI GO TO 130 FRK 131 I

-78-

I I I


c

c

c

c

c

c

c

c

c c

WRITE IIO,ItOOI DO 120 1=1,4

120 WRITE U0,4101 NPTIIJ,XAIIt,YACII,PPIIt 130 CONTINUE

CALL QUSP12 13J

DO 140 1=1,3 DO 11+0 J=1,J

140 DMII,JJ=DHII,JJ•THK15t••3/12.0

CALL SONEW

CALL WEa IS,SI,COJ

IF IHEAD111 I .NE.5HDEBUGI GO TO 270 NWE!3=NWEIH1 IF INWEB.GT.21 GO TO 270 WRITE UO,It30l DO 150 1=1, 10

150 WRITE IIO,It20l ISII,JI,J=1,101 WRITE II0,430l DO 160 I=1, 10

160 WRITE II0,420l ISII,JI,J=11,201 WRITE II0,430l DO 170 I=11,20

170 WRITE II0,4201 ISII,JI,J=1,10l WRITE 110,4301 DO 180 I=11,20

180 WRITE (10,420) ISII,JI.J=11 9 2fd GO TO 270

1 '30 CONTINUE IF I NF.N-31 200,210,210

200 CALL SBEAM 1St

GO TO 270

210 CALL Ql\011 121

C IF ELEMENT IS A TRIANGLE, THE STIFF~E~S OF THE FOURTH NODE C DEGENERATES TO THE FIRST NODE c

c

c

IF INEN.NE.31 GO TO 250 DO 220 I=1.8 SPD11,11=SPOI1,11•SPOI7,II

220 SPOII,21=SPOII,21+SPDII,Al DO 230 1=1,8 SPDI1,11~SPOI1,11•SPDI7,Il

230 SPOI2,11=3POI2,IJ+SPOI8,11 DO 240 1=1, 8 DO 240 J=1,2 SPDII,J+61=0.0

240 SPOIJ+6,1l=O.O

250 CALL SPLATE INTRII

-79-

FRK 132 FRK 133 FRK 134 FRK 135 FRK 136 FRK 137 FRK 138 FRK 139 FRK 140 FRK 141 FRK 142 FRK 143 FRK 144 FRK 145 FRK 146 FRK 147 FRK 1'+8 FRK 14'3 FRK 150 FRK 151 FRK 152 FRK 153 FRK 15 .. FR( 155 FRK 15& FRK 157 FRK 158 FRK .15'3 FRK 160 FRK 161 FRK 162 FRK 163 FRK 164 FRK 165 FRK 166 FRK 167 FRK 168 FRK 16'3 FRK 170 FRK 171 FRK 172 FRK 173 FRK 174 FRK 175 FRK 176 FRK 177 FRK 178 FRK 17'3 FRK 180 FRK 181 FRK 182 FRK 183 FRK 184 FRK 185 FRK 186 FRK 187 FRK 168 FRK 189

I I

DO 260 1=13,19 FRK 190 2&0 SPBCI,II=VACII FRK 191

C FRK 192 CALL OECK IS) FRK 193 I

C FRK 194 C STO~E NEW ELEMENT STIFFNESS INTO TEMPORARY STORAGE SBT AND ST FRK 195 C FRK 1'96

270 DO 280 1=1,361 FRK 197 I 280 SBTCil=SPBCil FRK 198

DO 290 1=1,400 FRK 199 290 STCil=SCIJ FRK 200

GO TO 300 FRK 201 C FRK 202

I C IF ELEMENT IS THE SAME AS PREVIOUS ELE~ENT FRK 203 C FRK 204

100 WRITE (JUM31 ST,S9T FRK 205 WRITE (JUM4l 5T FRK 206 I DO 310 !=1,12 FRK 207

110 IJATCil=\/AIII FRK 208 C FRK 209 C ADD NODAL FORCE VECTOR TO GLOBAL FORCe \/ECTOR FRK 210 I C FRK 211

IF CNEN.EQ.2.0R.NEN.EQ.51 GO TO 350 FRK 212 DO 330 I=l,NEN FRK 213 IF INEN.£1.51 GO TO 31t0 FRK 214 I K=NPTCil FRK 215 IA=S•K-3 FRK 216 IS=3•CI-1l FRK 217

C FRK 218 I C TRANSFORM CONSISTENT FORCE \/ECTOR IF NECESSARY FRK 219 G FRK 220

PHI=ROTCK,2l FRK 221 GN=COSCPHil FRK 222 IF CCN.EQ.1.1 GO TO 320 FRK 223

I SN=S!N(?HII FRK 22~ IS2=IS+2 FRK 225 IS3=ISt3 FRK 226 F1=JATCIS2l FRK 227 I F2=VATCIS31 FRK 228 VAT IIS21=Ft•CNtF2"'SN FRK 229 \/ATCIS3l=F2•CN-F1•SN FRK 230

320 C0NTINUE FRK 231 I DO 330 J=1,3 FRK 232 IA=Il\+1 FRK 233 IS=!Stl FRK 234

330 RIIAl=RCIAI+VAfCI~l FRK 235 I 340 CONTINUE FRK 236 350 CONTINUE FRK 237

RETURN FRK 238 C FRK 239 C FRK 240 I

360 FORMAT C/SX,•NODE•,gx,•X-COOR•,9X,•Y-COOR•,tl FRK 241 370 FOR~AT C5X,I~,5X,F10.5,5X,F10.5) FRK 242 380 FORMAl C/5x,•aENDING STRESS HATRIX•,/5X,3E16.5,/5X,JE16.5,15X,lE16FRK 243

1. 5, II FRK 244 3~0 FORMAT {15X,•IN-PLANE STRESS MATRIX•,ISX,oE16.5,/l FRK 2~5

I 400 FORMAT (/5X,+NOOE"',4X,+LOCAL X-GOOR•,4X,•LOCAL Y-COOR•,4X,•THIKNESFRK 246

iS • ,II FRK 247 I -80-

I I I


~10 FORMAT C5X,I5,6CF10.5,5X)) ~20 FORMAT C10E12.~) 430 FORMAT C/5X,•STIFFNESS MATRICES II IJ JI JJ•,!I

END

FRK 246 FRK 249 FRK 250 FRK 251-

SUBROUTINE SPLATE CNTRI' SPL 1 C SPL 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SPL 3 C SPL 4 C THIS SUBROUTINE ASSEMBLES THE STIFFNESS MATRIX AND CONSISTENT SPL 5 C ELE~ENT LOAD VECTOR OF EITHER A QUADRILATERAL FORMED av FOUR SPL & C LCCT-11CNT~I=41 OR A SINGLE LCCT-9 TRIANGLE(NTRI=1) SPL 7 C SPL 6 C • • • • • • + • + • • • + • • • + + + • • • • • + • • + • • • • + SPL 9 C SPL 10

COMMON /PLSTRI XAC41,YA(fti,CSC61,SPDC12,121,R1U2),ESIGC5,3) SPL 11 COMMON /PLBDG/ X C51, Y (51 ,CM CJ, 31 ,p( S I, BM C 3, 51 ,Cit CJ, 51, S( 19,191, F ( 1SPL 12

191 SPL 13 COMMON /TRIAG/ dLH,ACJI,CMTC3,:JI,THIKC31,PTC31,STl12,121,FTC121 SPL 14

C SPL 15 DIMENSION LOCC17,41, IPERt1Citl, NCC31 SPL 16

C SPL 17 LOGICAL TRIG SPL 16

C SPL 19 DATA IPERM/2,3,4,t"I,LOC/1,2,3,ft,5,6,13,14,15,17,1&,20,21,24,25,26,SPL 20

129,4,5,&,7,8,g,13,14,15,18,17,21,22,24,2&,27,29,7,6,9,10,11,12,13,SPL 21 21lt,15,19,16,22,23,24,27,28,29,10t11,12t1t2t3t13,14,15,1&,19,23,20,SPL 22 324,28,25,291 SPL 23

C SPL 24 C NBF PLATE BENDING DEGREES OF FREEDOM SPL 25 C 11 . FOR SLCCT-11 SPL 26 C 9 FOR SLCCT0'3 SPL 27 C NEF EXTERNAL DEGREES OF FREEDOM SPL 28 C 12 FOR QUADRILATERAL C3•NPI SPL zg C g FOR TRIANGLE SPL 30 C NIF INTERNAL DEGREES OF FREEDOM SPL 31 C 7 INTERNAL NODES FOR A QUADRILATERAL SPL 32 C 0 INTERNAL OOF FOR A TRI4NGLE SP~ 33 C SPL 34

TRIG=NTRI.EJ.1 SPL 35 IF CTRIGI GO TO 10 SPL 3& NBF=11 SPL 37 NEF=12 SPL 38 NIF=7 SPL 39 GO TO 20 SPL 40

10 NBF=9 SPL 41 NEF='3 SPL 42 NIF=O SPL 43

20 NDF=NBF SPL 44 NTF=NEF+NIF SPL ~5 NCC31=N3F-& SPL 46 DO 30 I=t,380 SPL 47

30 SCI,il=O. SPL 48 C SPL lt'3 C DETERMINE INTRINSIC DIMENSIONS OF ELEMENT OR SUBELEMENT SPL 50 C SP!.. 51

-81-

c

c

c

00 50 N=1,NTRI M=I~ERHINI NC 111 =N NG12l=H L=NC I 31 A 111 =X ILI-X IMI A(21=X(NI-X(Ll AI31=XCHI-XCNI 8111=Y011-YCLI BIZI=Y(U-YINI 8C3l=YCNI-YIMI DO 40 I=l,J L=NCCII THIKCII=PCLI PT CI I =8!1 l l,U DO 40 J=1,3

40 CMT<I,JI=CMII,JI

CALL SLCCT CNBFI

IF CTRIGI GO TO 60

C INSE~T CONT~I3UTION OF TRIANGULAR STIFFNESS LCCT-11 INTO C QUAuRILAT~RAL STIFFNESS c

c

FTC111=-FTC11l 00 50 I=1,NOF K=LOCII,NI F ( K I =F ( K I +FT (!I ST(I 1 111=-STCI,111 SH 11,!1 =-ST 111dl oo sa J=t.I L=LOG(J,NI C=SCK,LI•STII,Jl SIK,U=C

50 S!L,KI=C GO TO 1\0

C dfNDING STIFFNESS OF A SI~GLE TRIANGULAR F.LF.MENT LCGT-9 c

c

bO uO 70 I=1,NOF F < U =FT CI I DO 70 J=1,NDF

10 S!I,JI=ST!I,JI GO TO 100

C STATIC CONDENSATION OF 1 INTERNAL DEGREES OF FREEDOM FOR A C QUADRILATERAL ELEMENT c

dO DO go M=i,NIF L=NTF-M N=L+1 PIVOT=SIN,Nl FN=FINI FINI=FN/PIIIOT DO 90 I=1oL C=S<I,NI/PIVOT SCI,NI=C

-82-

Si"L !:J2 SPL 51 SPL Sit SPL 55 SPL 56 SPL 57 SPL 58 SPL 59 SPL 60 SPL 61 SPL 62 SPL 63 SPL 64 SPL 65 SPL 66 SPL 67 SPL. &8 SPL 69 SPL 70 SPL 71 SPL 72 SPL 73 SPL 7'+ SPL 75 SPL 7& SPL 77 SPL 76 SPL 79 SPL 80 SPL 81 SPL 82 SPL 83 SPL 84 SPL 85 SPL 86 SPL 87 SPL 68 SPL 89 SPL 90 SPL 91 SPL 92 SPL 93 SPL 9'+ SPL 95 SPL 96 SPL 97 SPL 98 SPL 99 SPL. 100 SPL 101 SPL 102 SPL 103 SPL 10ft SPL 105 SPL 106 SPL 107 SPL 108 SPL 109


I I I I I I I·

I I I I I I I I I I I I

F Ul =F (I) -C•FN DO 90 J=I,L SCI,Jl=SCI,Jl-C•SCN,Jl

90 S!J,Il=S!I,Jl 100 RETURN

ENO

SPL 110 SPL 111 SPL 112 SPL 113 SPL 114 SPL 115-

SUBROUTINE Q8011 CINTl Q80 1 c Q80 2 c • • • • • • • • • • • • • • • • • • • • • • • • 4 • • • • • • • • Q80 3 c Q80 .. C THIS SUBROUTINE COMPUTES THE STIFFNESS OF AN 8 OOF QUADRILATERAL Q80 5 C 6 FUNDAMENTAL DEGREES OF FREEDOM AND 3 INTERNAL DEGREES FOR Q8D 6 C AN INTERNAL NODE AND A CONSTANT SHEAR STRAIN VARIATION Q8D 7 C AN ANISOTROPIC MATERIAL LAW IS U~EO Q80 8 c Q8D q C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Q8D 10 C Q8D 11 G INPUT Q80 12 c Q80 13 C INT•INT GAUSSIAN INTEGRATION RULE Q80 14 C DCil CONSTIT LAW RELATING STRESS-RES TO STRAINS Q8D 15 C I=1,& COMPONENTS OF 0 (11t22,33t12t13 9 231 Q80 1& C XA .GLOBAL X-COORDINATES Q8D 17 C VA GLOBAL Y-COOROINATES Q8D 18 c Q80 19 C OUTPUT Q80 20 c Q80 21 C S!I,Jl 8•8 STIFFNESS MATRIX OF PLANE STRESS ELEMENT Q80 22 C IN GLOBAL XA-YA COORDINATES (FORMATION IN Q80 23 C LOCAL CON~ECTEO X-Y COORDINATES! Q80 2~

C I=1,8 NODAL DISPLACEMENTS CU1 1 V1,U2,V2, •• t Q80 25 C I=9,10 CONDENSATION OF CENTER NODE OOF Q80 2& C I=11 CONDENSATION OF CONSTANT SHEAR STRAIN OOF Q80 27 c Q80 28

COMMON /CROO/ JUM1,JUM2,JUH3,JUH4,IN,IO Q80 29 COMMON /PLSTRI XA!4l,YA(~l,O(o),S!12,12l,R1!12t,ST(5,3l Q80 30

C Q8D 31 DIMENSION P!5,2), OC!4,2), A!2,2l, U!St, V!5l, ETA(2), IPERMf2), XQ80 32

1K(4,4l, WGT(4,4), X(l+), 'f(lt), TEHP!8,4l Q80 33 C Q8D 34

DATA XKIO.,o.,o.,o.,-.~773502&9189&,.577350269189&,0.,0.,-.77459&6Q80 35 1&9241S,.ooooooooooooo,.7745966&92415,o.,-.e&11J&J115941,-.J39981D4Q8D 3& 235849,.3399810435349,.8&113&3115941/ Q80 37

DATA wGTiz.ooo,o.,o.,o.,1.ooouooooooooo,1.ooooooooooooo,o.,o.,.sssaeo 38 15555SSS556,.8883888888~89,.5555555SS555&,o.,.34785~8451375,.65Z145Q80 39 Z1548625,.&521451548&25,.3478548451l75/ Q80 40

DATA OC/-1.,1.,1.,-1.,-1.,-1.,1.,1.1,IPERM/2,1/ Q80 41 c Q80 42 C INITIALIZATION Q80 43 c Q80 44

DO 10 I=1,11 Q80 45 00 10 J=1,11 Q80 46

10 S!I,Jl=O.O Q80 47 NA=O Q60 48 NINT=INT Q80 49

-83-

I I

C Q.!ID 50 C TRANSFORMATION OF COORDINATES INTO LOCAL CONVECTED COORDINATES Q8D 51 c Q80 52

OX=XAI21-XA11l Q80 53 I DY=YAI2l-YAI1l Q8D 5~ AL=SORT 1 ox••z•ovu·zl aso 55 CO=DXIAL Q8D 56 SI=OY/AL Q80 57 DO 20 I=1,~ Q80 58 I XIIl=IXAIII-XAI111•CO+IYAIII-YAI11l•SI Q8D 59

20 YIII=-IXAIII-XAI111•SI+IYAIII-YAI1li•CO Q8D 60 c Q80 61 C LOOP FOR DETERMINING INTEGRAND$ AT SAMPLING POINTS OF Q8D 62 I C NUME~ICAL INTEGRATION SCHEME Q80 63 c Q80 64

JO 00 100 LX=1,NINT Q80 65 DO 100 LY=1,NINT Q80 &6 I ETAI1l=XKILX,NINTI Q80 67 ETAI2l=XKILY,NINTI Q8D 68

c Q80 69 C FORMATION OF LOCAL DERIVATIVES Q80 70 I C Q8D 71

DO 50 I=1,2 Q80 72 J=IPERMIII Q80 73 AII,1l=O.O Q80 74 AII,ZI=O.O Q80 75 I DO 40 L=1,~ Q80 16 C=0.250•DCIL,I1•(1~·o+DCIL,JI•ETAIJII Q80 77 PIL,II=C Q80 78 AII,1l=AII,11+C•XILI Q8D 79 I

~0 AII,2l=AII,2l+C•Y!Ll Q80 80 50 PIS,II=-2.Q•ETAII1•!1.0-tTAIJI••2J Q8D 81

All=Aill Q80 82 A21=AI21 Q80 83 I A12=AI31 080 84 A22=AI~I Q8D 85 OfT=A11•A22-A12•A21 Q80 66 IF IDET.U::.u.OI GO TO 160 Q80 67 I FAC=WGTILX,NINTJ•WGTILY,NINTI/OET Q80 88

c Q80 8<} C FO~MATION OF GL09AL DERIVATIVES Q60 90 c Q80 91

. 00 &0 J=1,5 Q80 92 I

UIJI=A22•P(J,1l-A12•PCJ,21 Q80 93 &0 VIJI=-A21•P!J,1l+A11•PIJ,?l Q80 94

C Q8D 95 C FORMATION OF TRIPLEPROOUCT Q8D 96 I c Q80 <}7

DO 90 I=1,5 Q8D 98 KZ=I+I Q8D 9<:J K1=K2-1 Q80 100 I IF INA.EQ.U GO TO 80 Q80 101 DO 70 J=I,S Q80 102 l2=J+J Q80 103 L1=L2-1 Q80 104 I UU=UIII•U!JI Q80 105 VV=VItl•VIJI Q8D 106 UV=UIII•V!JI Q8D 107

-84- I I I I

I I I I I I I·


c

IJU=I/Ul•U(Jl SIK1,L1l=SCK1,L1l+FAC•fDI1l•UU+OtSt•CUI/+I/Ull StK2,L2l=SIK2,L21+FAC•fOt21•VV+DI61•(UV+VUII SlK1,L2l=SCK1,L2l+FAC•IOI~I•UV+OI51•UU+OC&I•VVI IF I I. EQ.JI GO TO 70 SfK2,L1l=SIK2,L1l+FAC•tDf~l•VU+O(SI•UU+Of&l•VVl

70 CONTINUE GO TO 90

60 SIK1,11l=SCK1,111+FAC•Of31•VCII•OET SIK2,111=SIK2,111+FAC•Ot3t•U(Il•OET IF li.EQ.1l SC11,11,=S(11,111-FAC•OC3l•DET••z

90 CONTINUE 100 CONTINUE

NA=NA+1 NINT=INT-1 IF f NINT .LT .11 NI!IIT=1 IF INA.£Q.11 GO TO 30

C TRANSPOSE STIFFNESS FOR SYMMETRY c

c

DO 110 I=2,11 K=I-1 DO 110 J=1, K

110 SII,JI=SCJ,II

C STATIC CONDENSATION c

c

DO 130 M=1,3 K=11-M L=K+1 PII/OT=SIL,LI IF fPII/OT.EQ.O.Ol GO TO 130 DO 120 I=1,K C=SCI,Ll/PII/OT SU,LI=C DO 120 J=I,K SII,JI=S<I,JI-C•SCL,Jl

120 SfJ,Il=Sfi,JI 130 CONTINUE

C TRANSFO~M CONVECTED STIFFNESS INTO GLOBAL CARJESIAN c

ss=si•sr GC=CO•CO sc=sr•co DO 150 K=1,4 IQ=K+K IP=IQ-1 DO 140 J=1, B IF IJ.EQ.IPI GO TO 140 IF IJ.E1.IQI GO TO 140 TEMP(J,KI=SIJ,IPI•SI+SIJ,I~I•CO SIJ,IPI=S(J,IPI•CO-SIJ,IQI•SI SIIP,JI=SIJ,IPI SIIQ,JI=TEMP(J,Kl SIJ,IQI=TEMPIJ,KI

140 CONTINUE TEMP(IQlKI=SIIP,IPl•SS+SIIQ,IQI•CC+2.•S(IP,Ili•SC

-85-

Q80 108 Q80 1013 Q80 110 Q80 111 Q80 112 Q8D 113 QBD 114 Q80 115 Q8D 116 Q8D 117 Q80 118 Q80 119 Q80 120 Q80 121 Q80 122 Q8D 123 Q8D 124 Q8D 125 Q80 126 Q8D 127 Q80 128 Q80 129 QBD 130 Q80 131 Q8D 132 Q80 133 QBD 134 Q80 135 Q80 136 Q8[) 137 Q80 138 Q8D 139 Q8D !ItO Q80 141 Q80 142 Q8D 143 Q80 144 Q80 145 Q8D 14& Q80 147

COOROINATESQ80 146 Q80 149 Q81) 150 Q8D 151 Q80 152 QBD 153 Q8D 154 Q8D 155 Q8D 15& Q8D 157 QSO 158 Q60 159 Q80 160 '180 161 Q8D 162 Q8D 163 Q8D 164 Q80 165

I I

TEHP!IP,KI=-!S(IQ,IQI-SliP,IPII•SC+S!IP,IQt•lCC-SSI Q80 166 SliP,IPI=SliP,IPJ•CC+SliQ,IQI•SS-2.•S!IP,IQI•SC Q80 167 S!IP,IQI=TEHPliP,KI Q80 168 S!IQ,IPt=TEHPliP,Kt Q80 169 I S!IQ,IQI=TEHPliQ,Kt Q80 170

150 CONTINUE Q80 171 GO TO 170 Q8D 172

160 WRITE (!0,1801 OEf Q80 173 WRITE U0,190 I lXUI,YCit,I=1,4l Q80 17 ..

I STOP Q8D 175

170 CONTINUE Q8D 176 RETURN Q80 177

c Q80 178 I c Q80 179

180 FORMAT (//30H QETERMINANT OF JACOciiAN IS E15.J//J Q80 180 190 FOR"'AT ( 5 X, ZF 1 0 • 3 I Q80 181

END Q8D 182- I SUB~OUTINE DECK !Sl DEC 1 I

C DEC 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • DEC 3 C DEC 4 C THIS SUBROUTINE FORMS THE GLOBAl DECK ELEMENT STIFFNESS DEC 5 C ASSEMBLING THE PLATE BENDING STIFFNESS SPB !12•12) OR !9•91 DEC 6

I C COMPUTEO BY SPLATE AND THE IN PLANE STIFFNESS SPD!8•81 OR l&•&IDEC 7 C ST~ESS STIFFNESS. Q8D11 DEC 8 C DEC 9 C + • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • DEC 10 I C DEC 11

COMMON /PLSTR/ XA!4l,YA(41,CSl61,SPDU2,121,aiU2l,ESIG!5,31 DEC 12 COMMON /PLSDG/ XXl51 ,YY!51,CM(3,3l,PP!SI,8~(J,SI ,C~(3,51 ,SPtH19,190EC 13

11,VAl191 DEC 14 I C OEC 15

DIMENSION S!20,201, IUI4), IV!4l, IW!Itl DEC 16 C DEC 17

uATA IU/1,6,11,16/,IV/1,3,5,7/,IW/1,4,7,10/ DEC 18 I C DEC 19 C INITIALIZATION DEC 20 C DEC 21

00 10 I=1,400 DEC 22 10 S<II=O.O DEC 23

I C DEC 24 C ADO PLANE STRESS AND PLATE 3ENDING STIFFNESS INTO S DEC 25 C DEC 26

00 30 I=1,4 DEC 27 I IA=IU!II DEC 26 IB=I A+1 DEC 29 IC=I A+2 DEC 30 ID=IA+3 DEC 31 I IE=IAH DEC 32 Ii=IV!II DEC 33 I2=I1+1 DEC 34 I3=IWIII DE: 35 I Ilt=I3+1 DEC 36 I5=I3+2 DEC 37 DO 20 J=1,4 DEC 38

-86- I I I I

I I I I I I I· I I I I I I I I I I I I

c c c

c c c c c c c c c c

20 30

ItO

JA=IUCJI JB=JA•1 JC=JA+2 JO=JA+3 JE=JA+4 J1=IVCJI J2=J1+1 J3=IW(JI Jlt=J3+1 J5=J3+2 SCIA,JBI=S?OCI1,J21 SCIA,JAI=SPDCI1oJ11 SCIB,JBI=SPDCI2,J21 SCIC,JDI=SPBCIJ,J .. I SCIC,JEI=SPBCI3,JSI SCIO,JEI=SPBCI4,J51 SCI~,JCI=SPdCI3,J31

SCIO,JOI=SPBCIIt,J41 SCIE,JEI=SPBCI5,J51 CONTINUE CONT!N!JE

TRAN!iPOSE S FOR SYMI'1ETRY

DO 1+0 1=1,4 IA=IUCII I9=IA+1 IC=Ih2 ID=IA+J IE=IA+It DO 40 J=1,4 JA=IUCJI JB=JA+1 JC=JA+2 JO=JAt3 JE=JA+4 SCIB,JAI =SCJA.I31 SCIO,JCI =StJC, IOI SCIE,JCI=SCJC,IEI SCIE,JOI=SCJD,IEI CONfiNUE RETURN END

SUBROUTINE SLCCT <NBFI

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • THIS SUBROUTINE COMPUTES THE ELEMENT STIFFNESS MATIX FOR THE LINEAR CURVATURE COMPATIBLE TRIANGLE WITH NSF BENDING OOFCNBF= 12,11,10,91-- ORTHOTROPIC ELASTIC MATERIAL, AND LINEARLY VARYING THICKNESS

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • COMMON /TRIAG/ B(JI ,A(Jt ,Cr1T (3,31 ,Trl!K(JI ,?TC31 ,SH12,121 ,FT (121

-87-

"DEC 39 DEC ItO DEC 41 DEC 42 DEC 43 DEC 44 DEC .. 5 DEC 46 DEC 47 DEC 46 DEC .. 9 DEC so DEC 51 DEC 52 DEC 53 DEC 54 DEC 55 DEC 56 DEC 57 DEC 58 DEC 59 DEC 60 DEC 61 DEC 62 DEC 63 DEC 6 .. DEC 65 DEC o6 DEC 67 DEC 68 DEC 69 DEC 70 DEC 71 DEC 72 DEC 73 DC 74 DEC 75 DEC 76 DEC 17 DEC 78 DEC 79 DEC 80 DEC 81-

SLC 1 SLC 2 SLC 3 SLC 4 SLC 5 SLC 6 SLC 7 SLC 6 SLC 9 SLC 10 SLC 11 su: 12

I I

C SLC 13 DIMENSION Pl21t12J, HIZU, UIZU, QC3,61, HTI3J, IPER.MI31t TXIJI, SLC

1TYI31, NKNC4,31, NSNI4,31 SLC C SLC

14

I 15 16

EQUIVALENCE ICM11, CMT Ul J, CCH12 ,CHHZII, ICM13,CMH311, ICM22,CHTSLC 1(511, CCM23,CI'tH61l, ICM33,CMTC91l SLC

C SLC DATA IPERH/2,3,1/,NKN/2,5,3,6,8,2,9,3,5,8,&,91,NSN/2,3,5,6,3,1,6,4SLC

11 18

I 19 20

1,1,2,4,5/ SLC 21 C SLC C INITIALIZATION SLC C SLC

NDF=NR~ SLC

22

I 23 24 25

AREA=AI31•3121-AI2l•BC3l SLC 26 TO=ITHIKI1l+THIK121+THIKC3JI/3. SLC FAC=To••J•AREA/864. SLC 00 10 1=1,3 SLC

27 I 28 29

J=IPE~HIII SLC 30 K=IPER~IJl SLC X=AIII••z+BIIl••z SLC UIII=-IAIIl•ACJl+91II•dCJJl/X SLC

31 I 32 33

X=SQRTCXI SLC 34 HTII1=4.0•AREA/X SLC TYUI=-o.s•aUI/X SLC TXIII=O.S•ACIJ/X SLC

35

I 36 37

A1=AIII/AREA SLC 38 A2=AIJI/AREA SLC B1=BIIJ/AREA SLC 82=81JJ/AREA SLC

39

I 40 41

Q(1,IJ=at•Bi SLC lt2 QCZ,II=At•Ai SLC 43 Q(3,Il=2.•A1•B1 SLC QI1,I+ll=Z.•at•B2 SLC QCZ,I+3l=2.•A1•A2 SLC

44 I 45 46

QC3,I+31=2.•CA1•92+A2•B1J SLC 47 10 CONIINUE SLC

DO 20 1=1,3 SLC J=IPERMIII SLC

48 I 49 50

K=I~ERMIJl SLC 51 II=3•I SLC JJ=J•J SLC KK=J•K SLC

52

I 53 54

A1=AIII SLC 55 A2=AIJl SLC A3=AIKl SLC B1=31Il SLC

5&

I 57 58

82=BIJI SLC 59 83=8 IKI SLC 60 U1=U III SLC UZ=UIJl SLC U3=UIKI SLC

61 I &2 63

W1=1.-U1 SLC 64 W2=1.-U2 SLC W3=1.-U3 SLC 910=2.•81 SLC

65 I 6& &1

920=2.•32 SLC &a B3D=2.•3l st: A10=2.•A1 SLC

-88-

&9

I 70

I I I


c c c

A2D=2.•A2 A30=2.•AJ C21=81-B3•U3 C22=-810+92•W2+93•U3 C31=A1-A3•U3 C32=-A10+A2•W2+A3•U3 C51=BJ•WJ-B2 C52=92D-B3•W3-B1'"U1 Co1=A3•W3-A2 C&2=A20-AJ•~J-A1•U1 C81=83-d20-B2•U2 C82='31D-B3+B1•W1 C91=A3-A20-A2•U2 C92=A10-A3+A1•W1 U37= 1. •u3 W27=7.•W2 U34=4.•U3 W2~=4.'"W2

CONSISTENT NODAL LOADS FOR LINEARLY ~ARYING LATERAL ~RESSURE

SLC SLC SLC SLC SLC SLC SLC SL:: SLC SLC SLC SLC SLC SLC SLC su: SLC su: SLC SLC SLC

FTIII-21=1190.+U37+W271•PTIII+I3&.+U37+W2~1•PTIJI+(3o.+U34+W271•PTSLC iiKil•AREA/1080. SLC FTIII-11=11154.+W271•B2-154.+U371•B31•PTIII+IC15.+W241•B2-1~9.+U37SLC 1t•Bli•~TIJI+CC39.+W271•B2-115.+U341•B31•PTIKII•AREAI6480. SLC

FTII11=11154.+W271•A2-154.+U371•A31•PTIII+I115.+W241•A2-139.+U371•SLC 1AJt•PTIJI+I139.+W271•A2-(15·+U3~1•A3t•PT(KII•AREA/6~SO. SLC FTIK+91=(7.•1PTIII+PTIJ11+4.•PTIKli•AREA•HTIKI/&480. SLC 00 20 N=1,3 SLC L=&•II-11+N SLC Q11=QIN,II SLC Q?.2=QIN,Jl SLC Q33=QIN,KI SLC Q12=QIN,I+31 SLC Q23=QIN,J+31 SLC Q31=QIN,K+31 SLC Q2333=Q23-Q33 SL:: Q3133=Q31-Q33 SLC PIL,II-21=5.•1-Q11+W2•~33+U3•Q2333l SL:: PIL,II-11=C21•Q23+C22•Q33-BJO•Q12+82D~Q31 SLC PIL,Ili=C31•Q23+C32•Q33-A30•Q12+A20•QJ1 SLC PIL,JJ-2l=&.•ll22+WJ•Q23331 SLC PIL,JJ-11=C51•Q2333+830•Q22 SLC PIL,JJI=C&1•Q2333+A3Q•Q22 SLC PIL,KK-21=6.•11.+U2l•QJ3 SLC PIL,KK-1l=C81•Q33 SLC PIL,K~I=C91•Q33 SLC PIL,I+91=0. SLC PIL,J+91=HTIJI•Q3J SL: PIL,K+9l=HTIKI•Q2333 SLC PIL+3,II-21=&.•1Q11+U3•Q31331 SLC PIL+3,II-11=C21•Q3133-330•Q11 SLC Pll+3,IIt=C31•QJ133-A30•Q11 SLC PIL+J,JJ-21=&.•1-Q22+U1•QJ3+W3•Q3133t SLC PIL+J,JJ-11=C51•Q31+C52•Q33+B3D•Q12-B10•Q23 SLC PIL+l,JJI=C&1•QJ1+C&2•033+AJO+Q12-A1D•Q2J SLC Pll+J,KK-21=&.•!1.+W11•QJ3 SL: PIL+3,KK-11=C82•Q33 5LC

-89-

71 12 73 7ft 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 11& 117 118 119 120 121 122 123 124 125 126 127 128

I I

PCLtJ,KKJ=C92•Q33 SLC 12'1 PCL+J,I•9t=HTCti•QJl SLC 138

I P(L+3,J+9l=O. SLC 131 PCL+J,K+91=HTCKt•QJ1Jl SLC 132 PCN+18,II-21=Z.•CQ11+UJ•Q12+W2•Q31) SLC 133 PCNt18,KK-11=CCa1D-920I•Q3J+C82•QZJ•CB1•Q311/3. SLC 13ft P(N+16,KKI=CCA10-A2DJ•QJJ+C92•Q23+C91•Q311/3. SLC 135 I 20 PCN+18,K+9J=HTCKJ•Q12/3. SLC 136

c SLC 137 c STATIC CON~ENSATION OF HI OSI DE NODE SLC 138 c su: 139 I NK=12-Nc3F SLC 140

IF tNK.LE.DI GO TO 40 SLC 11+1 DO 30 N=l,NK SLC 142 K=13-N SLC 143

I DO 30 L=1,4 SLC 14 .. J=NKNCL,Nt SL:: 145 IF (L.LE.2) C=TXCK-9t SLC 146 IF CL.GT.ZJ C=TY CK-91 SLC 147

I FT(JI=FT(JitC•FTCKI SLC 146 DO 30 I=1,21 SLC 149

30 PCI,Jt=PCI,Jl+C•Pcl,Kl SLC 150 c SLC 151 c FORMATION OF MOMENT VECTOR u (21J SLC 152 I c SLC 153

40 00 80 J=1,NOF SLC 154 DO 50 L=l,J SLC 155 KK=L+18 SLC 156 I II=L-6 SLC 157 PJ=PCKK,Jl SLC 158 HCKKI=O. SLC 159 DO 50 N=1,3 SLC 160

I II=II+& SLC 161 JJ=II+J SLC 162 P1=P UI, J l SLC 163 PZ=PCJJ,Jl SLC 164

I SUM=P1+P2+P3 SLC 165 T1=SUMtP1 SLC 166 T2=SUM+P2 SLC 167 TJ=SUH+PJ SLC 166 HCIII=T1 SLC 169 I HCJJI=T2 SLC 170 HCKKl =TJHHKKI SLC 171

50 CONTINUE SLC 112 DO 60 N=1,19,3 SLC 173 I UCNI=CI111•HCNI+CI112•H(N•1l+CH13•H(N+21 SLC 174 UCN+1l=CH12•H(NI•CM22•H(N+11+CH23•HCN•21 SLC 175

60 UCN+21=CH13•H(NI+CM2J•HCN+11+CMJ3•H(N+2l SLC 176 c SLC 117

I c FORMATION OF STIFFNESS MATRIX SLC 176 c SLC 179

DO 80 I=1,J SLC 160 X=O. SLC 181

I DO 7 0 N=1, 21 SLC 182 70 X=X+U CNI•P CN, I I SLC 183

ST (I, JJ =X•FAC SLC 184 80 ST(J,II=STCI,JI SLC 185

RETURN SLC 186 I -90-

I I I

I I I I I I I·


END SLC 187-

SUBROUTINE S8EAM IS) BEA 1 C BEA 2 C • • • • • • • • • 4 4 • • • • • • • • • R • • • • • • • • • • • • BEA 3 C BEA It C GENERATION OF SEAM ELEMENT STIFFNESS MATRICES BEA 5 C BEA 6 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • BEA 1 C BEA 8

DIMENSION ESXI11, ASXIU, SSX11l, XLENGTHI11, EIX<U, GKEIXI1h BSBEA 9 1115,51, BS215,SI, BS315,51, BS415,5), Sl20,201, IPERMIZ,zt, JPERH<BEA 10 26, 2), ILAST 121 BEA 11

C BEA 12 COMMON /CBOO/ JUM1,JUM2,JUMJ,JUM4,IN,IO :lEA 13 C 0 M ·'1 0 N I P U3 D G I X X I 5 I , YY I 5 I , 0 M I 3 , 3 I , P P I 5 I , B M I 3 , 5 I , C 1/ CJ , 5 ) , S P 9 11 9 , 1 98 E A 14

11, 1/A !191 BEA 15 C BEA 1&

DATa IPERMI2t7,5,10/,JPERMI1,2,6,7,0,U,J,4,5,8,9,101,ILASTI4,61 SEA 17 C BEA 18

ECC=PPIJ) BEA 19 ESX11l=OMI1) BEA 20 AS X I 11 = P P I 4 t :IE A 21 A=XXI21-XXI1) BEA 22 B=YY12J-VY(1) BEA 23 XL2=A•AtB•~ BEA 24 XL=SQRfiXL21 BEA 25 XLENGTHI11=XL BEA 2& SSXI11=ASXI11•ECC BEA 27 EIX111=PPI1)tASX!11•ECC•FCC BEA 28 GKEIXI11=PP121 4 0HI91/0~(11 SEA 29

C BEA 30 C INITIALIZE BEAM STIFFNESS. :lEA 31 C BEA 32

00 10 I=1,20 3EA 33 DO 10 J=1,20 9EA 34

10 SII,JI=O.O BEA 35 N=1 BEA 36 MM=S 3EA 37 NN=S 9EA 38 DO 20 I=1,MM BEA 39 DO 20 J=1,NN BEA 40 BS11I,JI=O.O BEA 41 BS21I,JI=O.O SEA 42 aSJII,Jl=O.O BEA 43 BS41I,JI=O.O SEA 44

20 CONTINUE 3EA 45 BS1t1,11=ASXINI•XLENGTHIN1 4 •2 9EA 46 BS111,51=SSXINI•XLENGTH!NI 4 •2 SEA 47 BS1!3,JI=12.•EIXINI BEA 48 9S113,51=-&.•EIXINI•XLENGTH!NI 3EA 49 BS114,41=GKEIXINl•XLENGTHINI 4 •2 BEA 50 6S1!5t3l=-&.•EIX1Nl 4 XLENGTHINI BEA 51 BS115,1l=SSXINl•XLENGTHINl••z qEA 52 dS1(5,51=4.•EtXINl•XLENGTHINl••z BEA 53 dS211,1l=-ASX!N)•XLENGTH!N)••z BEA 54

-91-

I I

BS211,5l=-SSXINt•XLENGTHINt••z BEA 55 BS213,3l=-12.•EIXIN) tlEA 56

I BS2!3,5l=-6.•EIXINI•XLENGTH!NI BEA 57 BS2!4,4l=-GKEIX!Nt•XLENGTHINJ••z BEA 58 BS215,11=-SSXINJ•XLENGTHINI••2 BEA 59 aS215,31=6.•EIX!NI•XLENGTHINl SEA 60

I 3S2!5,5J=2.•EIXINt•XLENGTHINI••z BEA 61 BS~I1,11=ASX!Nl•XL£NGTHINI••z BEA &2 BS4!1,51=SSXINI•XLENGTHINI••z BEA &J BS4!3,JI=12.•EIX!NI BEA 6ft BS413,5J=6.•£IX(NJ•XLENGTHINJ BEA 65 I B3414,4J=GKEIX!~I•XLENGTHIN1••2 IJEA && BS4!5,1J=SSXINJ•XLENGTHINI••z tlEA 67 BS415,31=&.•EIX!Nt•XLENGTH!Nl 9EA 58 dS415,51=4.•EIXINI•XLENGTHINI••z BEA 69 I DO 30 I=1,HM BEA 70 DO 30 J=l,NN 9EA 71

30 BS31I,JI=aS21J,II SEA 72 ZFAC=ESX!Nl/IXLENGTH(NJ++J) 9EA 73 I DO 40 1=1,5 3£11 74 DO 40 J=1,5 SEA 75 SII,Jl=ZFAC•BS1!I,Jl SEA 76 SII,J•5l=as2!I,JJ+ZFAC SEA 71

I SII•5,Jl=ZFAC•3S3!I,JI :3EA 78 40 SII•5,J•5l=ZFAC•BS4!I,JI 3EA 79

CN=A/XL BEA 80 IF ICN.EQ.t.l GO TO 90 SEA 81

I SN=a/XL 9EA 82 c BEA 63 c IN PLANE ANO OUT OF PLANE TRANSFORMATION Pt= 1 AND 2 RESP£CTI lfEL YJ BEA 8ft c 3EA 85

DO 70 M=1,2 9EA 86 I IL=ILAST I~~ SEA 87 DO 60 JJ=1,2 BEA 88 J=Ii>ERMIJJ,HI BEA 89 DO 50 II=l,IL tlEA 90 I I=JPERMIIItMl BEA 91 S1=SII,J-ll BEA 92 S2=SU,JJ SEA 93 SII,J-1~:S1•CN-S2•S~ an 94

I 50 SII,JI=SZ•CN•S1•SN SEA 95 DO 60 II=1,Il SEA 96 I=PERMIII,l11 9EA 97 S1=S IJ-1,11 3EA 98

I S2=SIJ,II 9EA 99 SIJ-1,Il=S1•CN-S2•SN BEA 100

60 SIJ,Il=S2•CN•S1•SN BEA 101 70 CONTINUE 3EA 102

CC=CN•CN 9EA 103 I SS=SN•SN SEA 104 SC=SN•CN BEA 105

c BEA 106 c TRANSFORHATION OF DIAGONAL TERMS i3EA 107 I c BEA 108

AS=SU,5t BEA 109 Sl1,ft)=-AS•SC >3EA 110 s<t,5l=As•cc BEA 111

I 512,4)=-AS•ss 9EA 112

-92-

I I I

I I I I I I I· BG

90

I I c

c c

I c c c c c

I c c c c

I c c c c

I c c c c

I c c c c c

I c c

I c

I I I

SI2,51=AS•SC BEA 113 AS=SI1,UJ) BEA 11~ SI1,91=-As•sc SEA 115 s u, 101 =As•cc BEA 116 SI2,91=-As•ss SEA 117 SI2,10I=As•sc BEA 118 AS=SI5,&1 BEA 119 Sllt,61=-A;;i•SC BEA 120 Sllt,7l=-AS•SS SEA 121 SI5,&1=As•cc SEA 122 SI5,1)=AS•SC BEA 123 AS=S Hlti 0 I BEA 12ft Slo,91=-As•sc SEA 125 SI&.10I=As•cc BEA 126 SI7,91=-As•ss 9EA 127 s 11,101 =As•sc REA 128 00 80 J=1,10 :3EA 129 DO 30 1=1,10 SEA 130 SII,JI=SIJtll SEA 131 CONTINUE BEA 132 RETURN BEA 133 END SEA 134-

SUBiOUTINE QUSP12 .(NNI QUS 1 QUS 2

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • QUS 3 QUS It

THIS SUBROUTINE ASSEMBLES THE ~LANE STRESS STIFFNESS MATRIX QUS 5 Sl12,121 FOR A QUADRILATERAL ELEMENT WITH 12 DEGREES EMPLOYING QUS 6 CORNER ROrATIONS IOV/OXI NORMAL TO THE PLANt TO PROVIOE A COMPLETEQUS 7 U,W, OY GLOBAL DISPLACEMENTS QUS 8

QUS 9 THIS ROUTINE IS FROM REFERENCE 2 QUS 10

QUS 11 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • QUS 12

QUS 13 INPUT QUS lit

QUS 15 NN•NN GAUSSIAN INTEGRATION ~ULE QUS 16 DIII CONSTITUTIVE LA~ RELATING STRE~S-RES TO STRAINS QUS 17 1=1,6 COMPONENTS OF 0111 9 22,J3,12,13,231 QUS 16 XORDI~I LOCAL X- COORDINATES QUS 19 YORDI~I LOCAL Y-COOROINATES QUS 20 OUTPUT QUS 21

QUS 22 SII,JI PLATE STIFFNESS MATRIX QUS 23 I=1,4 U-DISPlACEMENTS QUS 24 I=5,3 V-DISPLACEMEN7S QUS 25 1=9,12 ROTATIONSIOV/DXI QUS 26 R=.TRUE. STATIC CONDENSATION Of ROTATIONS QUS 27

QUS 28 COMMON ICBOQ/ JUM1,JUM2tJUM3,JUM~tiN,IO QUS 29 COMMON IPLSTR/ XORO(Iti,YORDI41,0161,SI12,12),R1(121,STI5,.3) QUS .30

QUS 31 DIMENSION WTI3,1tl, OR!H3,41, FX4141 9 FY~I~), fXI41, FY141 QUS 32 DIMENSION F.XXI'+I, £YY(81, EKY(41, EYXI81, X!lltl, X2141, YU41, Y2(QUS 33

-93-

141, ITE<21, ITAl41, ITU41, FT1<41, FT2(41, VXC81, VYI81 QUS J .. C Q~ H

EQUIVALENCE !FX,X11, !FY,YU, IEXX,X21, IEXY,Y21 QUS 3& C QUS 37

LOGICAL ~ QUS 38 C QUS 39

DATA WTI1.000000000000000,0.555555555555556,0.3~7854845137454,1.00QUS 40 10000000000000 1 0.688888688888669,0.&521451548625\6,0.0,0.5555555555QUS 41 zs5ss&,o.&521451546&2546,o.o,o.o,o.J47854645t3745\/ aus 4Z

DATA ORD/-.577350269189626,-.774596669241483,-.661136111594053,.57QUS ~3 173502&9189&26,o.ooooooooooooooo,-.33996104358485&,o.o,.77459&&&924QUS 44 21483,.319981D4358485&,o.o,o.o,.s&113&311594053/ QUS 45

DATA FY4/-1.0,-1.0,1.0,1.0/,FX4/-1.0,1.0,1.0,-1.0/ QUS 46 DATA ITE/1 9 4/,ITAI1,2,2,1/,ITI/4,3,3,4/ QUS 47

C QUS 48 C INITIALIZATION QUS 49 C QUS 50

R=.FALSE. QUS 51 DO 10 !=1,12 QUS 52 00 10 J=1,12 QUS 53 S!I,JI=O.O QUS 54

10 S(J,II=S<I,JI QUS 55 C QUS 56 C GEOMETRICAL TRANSFORMATION OF QUADRILATERAL 90UNOA~IES QUS 57 C QUS 58

X1(11=0.5•<XOR0!21-XORD<1ll QUS 59 X1l3l=0.5•<XOR~<JI-XOR0!411 QUS 60 X1l21=X1(11 QUS 61 X1l41=X1131 QUS 62 Y1l1l=0.5•CYOROI21-YOR0(1JJ QUS 61 Y1(JI=0.5•1YOk0(31-YOROI411 QUS 64 Y1121=Y1(1J QUS 65 Y1l41=Y1l3J QUS 66 X2(1I=0.5•!X0~0(41•XOR01111 QUS 67 X212I=0.5•(XOR0(31-XORDC211 QUS 68 X2(31=X2(21 QUS 69 X2(41=X2111 QUS 70 Y211I=0.5•(YORDC41-YORD(111 QUS 71 Y2(2I=O.S•CYOROl3J-YORDl211 QUS 72 Y2(31=Y2(21 QUS 73 Y2l41=Y2(11 lUS 74 DO 20 I=1,4 QUS 75 DET=X11II•Y21II-Y1(IJ•X21II QUS 76 FCT=OETtX2lii•Yt<Il QUS 77 FT1(II=Y11I)•X1!II/2.0/FCT QUS 78

20 FT2lii=X11IJ•!1.0-Y1(IJ•X2<Il/FCTI QUS 79 C QUS 80 C LOOP FOR DETERMINING INTEGRANOS AT SAMPLING POINTS OFNUMERICAL QUS 81 C INTEGRATION SCHEME QUS 82 C QUS 83

DO 110 II=l,NN QUS 84 DO 110 JJ=1,NN QUS 85 X=ORD<NN-1,1II QUS 86 Y=OROINN-t,JJI QUS 87 XA=X•X QUS 88 XB=X•XA QUS 89

C QUS 9G C FORMATION OF LOCAL DERIVATIVES QUS 91

-94-


I I I c aus n

00 30 I=1,4 QUS 93 FXIII=0.25•FX~CII•I1.0•FY41Il•Yl QUS 94

30 FY1ll=0.25•FY~CII•C1.0•FX41IJ•Xl QUS 95 C QUS 96 C FORMATION OF JACOBIAN TRANSFORMATION MATRIX QUS 97 C QUS 98 I

X11=0.0 QUS 99 X22=0.0 QUS 100 X12=0.0 QUS 101 X21=0.0 QUS 102 I DO ~0 1=1,~ QUS 103 X11=X11+FXIII•XOROIII QUS 104 X22=X22+FYIII•YORDIII QUS 105 X12=X12+FXIII•YOROIII QUS 10&

40 X21=X21+FYIIJ•XOROCII QUS 107 I C QUS 108 C CALCULATION OF JACOBIAN DETERMINANT QUS 109 C QUS 110

OET=X11•X22-X12•X21 QUS 111 I· FAC=WTINN-1,III•WTINN-1,JJI/OET QUS 112 IF IOET.LE.O.Ol GO TO 150 QUS 113

C QUS 114 C FOR~ATION OF LOCAL OERI~ATIVES QUS 115 I C QUS 11&

00 50 !=1 9 4 QUS 117 VYIII=0.125•FY4CII•C2.0+3.0•FX41Il•X-FX41Il•XSI QUS 118 VXCil=0.375•(t.O+FY4(IJ•YI•(FX411l-FX41II•XAl QUS 119 I VYII+~I=0.125•FY41Il•I-FX4(11-XtFX41II•XAtX81 QUS 120

50 VX(!+41=0.125•11.0+FY4CIJ•Yl•l-1.0t2.0•FX41Il•X+3.0•XAI QUS 121 C QUS 122 C FORMATION OF GLOBAL DERIVATIVES QUS 123 C QUS 124

I DO oO !=1,4 QUS 125 EXXIII=X22•FXII)-X12•FYIII QUS 12&

oO EXYCil=-X21•FXIll+X11•FYIII QUS 127 DO 70 !=1 9 ~ QUS 128 I K=ITAIII QUS 129 J=ITIIIl QUS 130 AA=VXIII+FY4CII•FT11KI•VXIK+41+FY41Il•FT1(JI•VXIJ+41 QUS 131 83=VYIII•FY41Il•FT11Kl•VYIK+4l+FY41Il•FT11JI•VYIJ+41 QUS 132 I EYYII+~I=-X21•FT2CII•VXII+41+X11•FT21II•VYII+4l QUS 133 EYXII+~l=X22•FT21II•VXII+4l-X12•FT21Il•VYII+41 QUS 134 EYYIII=-X21•AA+X11•BB QUS 135

70 EYXIIl=X22•AA-X12•gg QUS 136 I C QUS 137 C FORMATION OF T~IPLE PRODUCT QUS 138 C QUS 139

DO go !=1,4 QUS 140 EA=EXXC!l QUS 141

I EB=EXYIII QUS 142 00 80 J=1,~ QUS 14l

80 SII,JI=SCI,JI+FAC•CEA•IOI1l•ExX(Jl+0(5)•EXYCJII+EB•COI31•EXYIJI+OIQUS 144 151•EXXIJIII QUS 145 I

DO 90 J=1,8 QUS 146 90 s<I,J+4t=sci,J+41+FAc•<EA•Io<4l•EYviJI+D<5l•EvxiJll+Ea•coi31•EvxiJQUS 1~1

1l+D(61•EYY<Jill QUS 148 00 100 !=1,8 QUS 149 I

-95-

I I I

c c c

c c

c c

c c c c c c c c c c c

c

EC=EYYIII QUS ED=EYXIII QUS 00 100 J=1,8 QUS

100 SII•~,J•Iti=SII•4,J•41+FAC•!EC•IOI21•EYYIJI•Dl61•EYXIJII+EO•(O(JI•EQUS 1YXIJI•Dl6J•EYY(Jitl QUS

110 CONTINUE QUS

120

130 140

150

1&0 17'0

TRANSPOSE FOR SYMMETRY

00 120 I=2,12 K=I-1 DO 120 J=1, K S!I,JI=SIJtii IF I.NOT.RI GO TO 170

STATIC CONDENSATION OF CP ROTATION

00 140 '1=1t4 K=12-1'1 L=K•1 PIV=SIL,U IF IPII/.EQ.O.OI GO TO 140 00 130 I=1,12 C=SII,LI/PI\1 SII,LI=C DO 130 J=I,K SII,JI=SII,JI-C•SCL,JI SIJ,Il=SII,JI . CONTINUE GO TO 1o0 WRITE (!0, 180 I OET WRITE II0,1g01 IXOROIII,YOROIII,I=1,41 STOP CONTINUE RETURN

180 FORMAT (/JOH DETERMINANT OF JACOBIAN IS 190 FORMAT 15X,2F10.31

E15. 3//1

QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS flUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS QUS a us QUS END

SUB~OUTINE SONEW SNW SNW

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SNW

THIS SU9ROUTINE FORMS A ONE WAY BENDING 8 X 8 STIFFNESS MATRIX loENDING IN Y-OI~ECTIONI IN FO~M OF A 12 X 12 MATRIX. INPUT AND OUTPUT SAME AS IN SPLATE.

THIS ROUTINE IS DIRECTLY FROM REFERENCE 2

SNW SNW SNW SNW SNW SNW SNW

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SNW SNW

COMMON I PLBDG/ X (51 , Y I 51 , C M ( 3, .H , P ( 5 I , 3M I 3, 5 I , C V ( 3, 5 I , S C 19,191 , F ( 1S NW 191 SNW

SNW -96-

150 151 152 153 151t 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 18ft 185 186 167 188 189-

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15



c

c c c

c

c c c

c c c

c c c c c c c c c c c

10

20

30

40

DIMENSION ITEC2,21, IPEC21, Al (2) SNW SNW

DATA ITE/1,10,4,7/,IPE/0,3/ SNW SNW

INIT IALI Z AT ION SNW SNW

DO 10 1=1,12 SNW DO 10 J:1,12 SNW SU,JI=O.D SNW ALC1l=YC41-Y(11 SNW AU21=YC31-YC21 SNW

SNW FT=CHC1,11•CXC21-XC1J+X(3J-XC411/2.0 SNH FT=FT•Pctt••3112. SNH

SNW FOR!'IATION OF STIFFNESSES OF TWO EQUIVALENT 8€ A MS IN Y DIRECTION SNW

SNW DO 30 I=1,2 SNW XL=AUU SNW SlG=-1.0 SNW DO 20 J=1,2 SNW IA=ITECJ,II SNW SIG=-SIG SNW SCI~,IAI=&.O/CXL••31•FT SNW SIIA+1,IA+11=2.D/XL•FT SNW SCIA,IA+11=3.G/CXL••2>•SIG•FT SNW IA=1+IPE C II SNW JA=tO-IftE II I SNW SCIA,JAI=-&.O/CXL••3t•FT SNW SCIA,JA+11=3.0/IXL••zi•FT SNH SCIA+t,JAI=-3.0/CXL••zi•FT SNW SCIA+1,JA+11=1.0/~L•FT SNH

SNW TRANSPOSE FOR SYMMETRY SNW

SNW DO 40 I=2,12 SNW K=I-1 SNW DO ItO J=1,K SNW SCI,Jl=SCJ,Il SNW RETURN SNW END SNW

SUBROUTINE WEB CS,SI,COI WEB WEB

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • WEB WEB

THIS SU3ROUTINE FORMS THE GLOBAL ELEMENT STIFFNESS MATRIX FROM THEWEB ~ERTICAL wEa ELEMENTS ASSEMBLING THE ONE WAY BENOING STIFFNESS WEB SPBC12X121 COMPUTED 9Y SONEW WITH THE INPLANE STIFFNESS SPDC12X121WEB COMPUTED 8Y QUSP12. WEB THIS ROUTINE IS FROM REFERENCE 2 WEB

WEB • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •wEB

WE9 COMMOi~ /PLSlRI XA 141, YAC41, CS C&l, Sftu <12,121, R1112), ESIG 15,31 WEB COMMON I PL BiJG/ X X ( 5 I , YY ( 5 I , C M I 3, 3 I , PP I 5 I , SM C 3, 51 , CV C 3, 51 , SPa ( 19, 1 9W£ B

-97-

1& 17 18 19 20 21 22 23 24 25 2& 21 28 29 30 31 32 33 34 35 36 31 36 39 40 41 42 43 44 45 4& 47 48 49 50 51 52 53 54 55 5&-

1 2 3 4 5 6 1 8 9

10 11 12 13 14

I I

U,VAU91 WEB 15 c WEB 16

I DIMENSION Sl20,201, IUI41, I W 141 WEB 17 c WEB 18

DATA IUI1,&,11t161,IW/1,4,7,10/ WEB 19 c WEB 20

I c INITIALIZATION WEB 21 c WEB 22

DO 10 I=1,400 WEB 23 10 SIIl=O.O WEB 24

c WEB 25 I c ADO PLANE STRESS AND PLATE BENDING STIFFNESS INTO S AND APPLY WEB 26 c TRANSFORMATION INTO GLOBAL COORDINATES WEB 21 c WEB 28

DO 30 I~1 ,4 WEB 29 I IA=IUI!l WEB 30 IB=IA+1 WEB 31 IC=IA+2 WEB J2 ID=I A+3 WEB 33

I IE=IA+4 WEB 34 !1=! WEB 35 !2=!+4 WEB 3& I 3=! +6 WEB 37

I I4=IW<II WEB 38 !5=!4+1 WEB 39 oo 20 J=1,4 WEB 40 JA=IUIJI WEB 41 JB=JA+1 WEB 42 I JC=JA+2 WEB 43 JO=JA+3 WEB 44 JE=Jh!t WEB 45 J1=J WEB 46 I J2=J+4 WEB 47 J3=J+6 WEB 46 Jft=IWIJI WEB 49 J5=J4H WEB 50

I SIIA,JAI=SPOII1,J11•Co••Z+SP81I!t,J4J•SI••z WEB 51 SIIB,JBI=SPDII1,Jii•SI••z+SP81I4,J41•Co••2 WEB 52 SIIC,JCl=SPOII2,J21 WEB 53 SIIO,JDI=SP31I5,J51•CO••Z+SPOII3,J31•SI••2 WEB 54

I SIIE,JEI=SPBII5,J51•SI•SI+SPOII3,J3l•Ga••z WEB 55 SIIA,JCI=SPOII1,J2l•Co WEB 56 SIIA,JOI=SPOII1,J31•Co•SI WEB 57 SIIA,JEI=-SPOII1,J31•CO•Co WEB 58 SII9,JCI=SPOII1,J2t•SI WEB 59 I SII3,JOI=SPDII1,J31•SI•SI WEB 60 SII8,JEt=-SPOII1,J3l•SI•CO WEB 61 S<IC,JOI=SPu<I2,J3t•SI WEB 62 S<IC,JEI=-SPDIIZ,JJI•Co WEB 63 I S1Id,JDI=SIIB,JDI-SPBII4,J5t•co•co WEB 64 SII3,JEI=SIIB,JEI-SPBII4,JSI•CO•SI WEB 65 SIIA,JOI=SfiA,JOI+SPB<I4,J51•SI•CO WEB 66 SIIA,JEI=SIIA,JEI+SPBII4,J5J•SI•SI WEB 67

I SIIA,JBI=ISPOII1,J11-SPBII4,J4ti•SI•CO WEB 66 SIIO,JEI=ISPBII5,J5t-SPOII3,J311•SI•CO WEB 69

zo CONTINUE WE6 70 30 CONTINUE WEB 71

I c WEB 72

-98-

I I I


c c

c

c c c c c c c

c c c c c c c c c c c c c

TRANSPOSE FOR SYMMETRY

DO 40 1=1,4 IA=IUIII IB=I A+1 IC=IA+2 ID=IA•3 IE=IA+It DO 40 J=1,4 JA=IUIJI JB=JA+1 JC=JA+2 JD=JA+3 JE=JA •It SIIC,JAI=SCJA,ICI SCIC,JBI=SCJB,ICI SCIO,JCI=SCJC,IOI SCIE,JCI=SIJC,IEI SIIO,JBI=SCJB,IOl SIIE,JBl=SCJB,tEl SCIO,JAl=StJA,tOI StiE,JAI=SIJA,IEI ~IIB,JAl=StJA,IBl

SIIE,JDI=SCJO,IEI 40 CONTINUE

RETURN END

O~ERLAY I?LATE,3,01

PROGRAM FO~TJ

• • • • • • • • • • • • • • • • ~ • • • ¥ • • • • • • • • • • • •

DETERMINE AND SET THE FIELD LENGTH FOR STIFFNESS MATRIX

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • COMMON ICBOO/ JUM1,JUM2,JUM3,JUM1t,IN,IO COMMON /C801/ NUHEL,NUMNP,NUHBC,NMAT,NLCS,NN,MM,NPSEGM COMMON /CBD2/ NUM3LK,N~LKL,IBANOW,NEQ8C COMMON /SOL~/ ~A1,LWIOTH,NFREE,NA5,LAMA,ISEGM,JUM5,JUM6,JUM?,JUM8

COMMON A ( 1l

DEFINITIONS

NBLK NO NH NZ NF KSHIFT

LA Nl4

9L DC K NUM3ER NUMBER OF EQUATIONS IN A BLOCK LAST EQUATION NUM9ER IN LOWER BLOCK LAST EQUATION NUM9ER IN UPPER BLOCK FIRST EQUATION NUMBER IN UPPER 3LOCK AMOUNT OF SHIFTING TO OCCUPY NON PDPULATEO STOlAGE S~ACES IN C ~ATRIX

GLOBAL NOOAL POINT NUMBER OF AN ELEMENT GLO~AL STIFFNESS NUHaER AS ASSE~8LED

-99-

WEB WE9 WEB WEB WEB WEB WEB WEB WEB WE9 WEB WEB WEB WEB WEB WER WEB WEB WEB WEB WEB WEB WEB WEB WEB WEB WEB

FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FTJ FTl FTJ FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3 FT3

73 74 75 76 11 78 79 80 61 82 83 8ft 85 86 87 88 89 90 91 92 93 94 95 96 97 911 99-

1 2 3 4 5 6 7 8 9

10 11 12 13 11t 15 16 17 18 19 20 21 22 23 24 25 26 27 28

I I

C IL LOCAL NODE NUMBERING FOR A CURRENT ELEMENT FT3 2~ C M THE OTHER NODE POINTS ASSOCIATED WITH THE CURRENT EL-FT3 30 C EMENT FT3 31 C J~ COUNTER AS TO WHICH NODE OF THE ELEMENT FT3 32 C NM NEW COLUMN NUMBER OF THE OTHER NODES ASSOCIATED FT3 33 C WITH THE ELEMENT FT3 3ft C MC POSITION WITHIN THE BLOCK FTJ 35 C NR NL PLUS 1,2,3,4, OR 5 FT3 36 C NC HC-1,2,3,4, OR 5 FT3 37 C IR ROW NUMBER OF LOCAL NODE POSITION FT3 36 C IC COLUMN NUMBER OF LOCAL NODE NUMBERING FT3 39 C FT3 40

L~IOTH=IBANDW FTJ 41 NFREE=S•NUMNP FT3 ft2 NUH3LK= ( NFREE+NdLKL-11/NBLt<L FTJ 43 N3LKL2=~8LKL•2 FT3 44 NEQ3C=S•NUHBC FT3 ItS JUM1=1 FTJ 46 JUH2=2 FT3 47 JUM3=3 FT3 46 JUM4=4 FT3 49 JUM5=5 FTJ 50 JUH6=o FT3 51 JUM7=7 FT3 52 JUM8=8 FT3 53

C FT3 54 Nl=l FT3 55 N2=N1+4•NUMEL FT3 56 N~=N2tN3LKL2•IBANOW FT3 57 N4=N3+NEQBC FT3 58 N5=N4+NEQBC FTJ 59 N6=N5tNU"EL FT3 60 N7=N6+NUMNP FT3 61 WRITE IIO,tOl FT3 62 N6=N7+2•NUMNP FT3 63 NLOC=LOCFIAI1tl FT3 b4 NKFL=NLOCtNS FTJ 65 NRFL=MAXOINRFL,350008l FT3 66 WRITE {10,201 NRFL,NRFL FTJ 67

C FT3 66

CALL REQMEMX INRFLI FT3 69 C FT3 70

CALL 8IGK (A(Nli,A(N21,A(N31 ,AIN41,NUMEL,NBLKL2,IBANDW,NEQdC,NUHBLFT3 71 1K,A(N51,A(N61,NUMNP,AIN71l FT3 72

C FTJ 73 C FTJ 74

10 FORMAT (15X,•FORT3•,1n FT3 75 20 FORMAT 110X,•FIELO LENGTH•,I5X,010,• IN OCTAL•,/SX,IlO,• IN DCFTJ 76

1CH1AL•,, FT3 77 END FTJ 78-


SUS~OUTINE aiGK INP,C,NE8C,ANGLE,IE,In,Id,I3CtNMBLKtXtNTAG,IP,ROTIBIG 1 G BIG 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • BIG 3 C !HG It C THIS SU3ROUTINE FORMS THE COMPLETE ST~UCTURAL STIFFNESS MATRIX IN 3IG 5

-100-

I I I I I


c c c c

c

c

c c c

c c c

c c c

aLOCKS,IHPOSES BOUNDARY CONDITIONS, AND STORES IT ON TAPE. BIG BIG

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • diG BIG

!HHENSION XIIEl, NTAGHPl, NPIIE,Ltl, CIIH.IBI, NEBCIIBCl, ANGLEUBBIG 1Cl, STQI20,20l, ROTIIP,21 BIG

COMMON COMMON COMMON COMMON

/CBO 0/ I C 80 1/ /C902/ /SOL 'II

JUM1,JUM2,JUM3,JUMLt,IN,IO NUMEL,NU~NP,NUMBC,NMAT,NLCS,NN,MM,NPSEGH

NUM8LK,N3LKL,IBANDW,NEQBC NA1 9 LWIOTH,NFREE,NA5,LAHA,ISEGM,JUM5,JUM6tJUH7,JUM8

EQUI'/ALENCE INEQ,NFREEl

INITIAL! ZATI ON

REWINO 1 REWIND 4 REWIND K

READ NODAL POI~T ARRAY

READ 111 NP,x,x,x,x,x,x,X,NTAG,NTAG,NTAG,ROT

RfAD NODE NUMOERS WITH 8.C. ANGLES

J=O DO 20 N=1 9 NUMNP L=NTAGHII IF IL.EQ. Ol GO TO 20 NS=N•S PHI=i<OT(N,11 J=J+1 K1=N5-'+ N£8C!Jl=K1 ANGLEIJI=PHI K2=N5-3 J=J+1 NEBCIJl=K2 ANGLEIJI=PHI K3=N5-2 J=J+1 NEBCIJl=K3 ANGLEIJI=O.O PHI= 1WTIN,2l J=J+1 Klt=NS-1 NE9CIJl=K4 ANGLE IJI =PHI J=J+1 K5=N5 NE9CIJl=K3 ANGLEIJJ=PHI DO 10 K=1,5 IF IMODIL,21.EQ.OI GO TO 10 M=J-S+K ANGLE IMl =2· OE+ 3

10 L=L/2 -101-

9IG BIG BIG BIG BIG BIG BIG BIG 3Iii BIG RIG BIG i3IG BIG BIG fHG BIG 9IG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG BIG diG BIG BIG BIG BIG 3IG BIG BIG diG diG BIG BIG :3IG BIG BIG BIG

6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 2.3 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 4'+ 45 46 47 48 49 so 51 52 53 34 55 56 57 58 59 60 61 62 63

G

20 CONTINUE READ IJUMU WRITE IJUMU NEaG,ANGLE IFLAG=O ND=NBLKL NN=IH•IS N BL K= 0 DO 30 N=1,NN

30 CINI=O.O

C FORMATION OF STIFFNESS MATRIX IN BLOCKS c

c

40 NdLK=NBLK+-1 NH=INBLK+U•ND NZ=~H-ND

NF=NZ-ND•1 KSHIFT=NF-1 REWIND 4

C CONTRIBUTION OF DECK ELEMENTS TO UPPER BLOCKS c

DO 120 N=1,NUMEL IF CNPIN,11.LT.OI GO TO 110 DO 50 I=1,4 LA=NPIN,II NL4=LA•5-4 IF CNZ. L T .NL41 GO TO 50 IF !NF.LE.INL4+4ll GO TO oO


60 READ 141 STQ DO 100 I=1,1t L=NPCN,I) IL=5•I-5 NL=L•S-KSHIFT-5 DO 90 J=1,1t M=NPIN,JI IF IL.GT.MI GO TO 90 JM=5•J-5 NM=M•5-KSHIFT-5 MC=NH-NL+1 DO 80 II=1,5 N~=NL+II

MC=~C-1

NC=MC IR=IL+II oo 70 JJ=1,5 NC=NC+1 IF INC.LE.OI GO TO 70 IC= JM+J J CCN~ 9 NCI=CINR,NCI+STQIIR,ICI

70 CONTINUE 80 CONTINUE 90 CONTINUE

100 CONiiNUE NPIN 7 1)=-NPIN 7 11 GO TO 120

110 READ 141 STU -102-

BIG 64 BIG 65 BIG &6 BIG 67 BIG 68 BIG 69 BIG 70 BIG 71 BIG 72 BIG 73 BIG 74 BIG 75 BIG 76 BIG 71 !JIG 76 BIG 79 BIG 60 BIG 61 13IG 62 8IG 83 BIG 84 BIG 85 BIG 86 iHG 87 BIG 88 BIG 89 BIG 90 BIG 'H BIG 92 BIG 93 BIG 94 BIG 95 BIG 96 BIG 97 BIG 98 B!(; 99 BIG 100 BIG 101 BIG 102 diG 103 BIG 104 BIG 105 BIG 106 BIG 107 BIG 11J8 BIG 109 BIG 110 BIG 111 BIG 112 BIG 113 RIG 114 BIG 115 BIG 116 BIG 117 SIG 118 ar:; 119 BIG 120 BIG 121


I I .I

I I I I I I I I I I I I I I I I

120 CONTINUE c C EFFECT OF BOUNDARY CONDITION ON BIGK c

c

DO 160 I=1,IBC IF tNEBCtii.LE.OI GO TO 180 NL=NEBC ( U NL1=NL-1 PHI=ANGLE!II IF !PHI.Ea.o.l GO TO 110 IF <PHI.GE.1.E+21 GO TO 160

C SKEWED 30UNDARY CONDITION IN UPPER BLOCK c

c

IF (NH.LT.NLI GO TO 180 IF CNF.GT.NU GO TO 180 NR=NL-KSHIFT t1 NtU=NR-1 CC=COS !PHil SS=SINCPHII IF !NZ.LT.NLU GO TO 140 C<N~1,1l=C<NR1,1l•cc•cc•z.•c<NR1,2l•ss•cc•c<NR,11•ss•ss L=NiU DO 130 J=3,IBANDW CtNR1,JI=CtNR1,JI•CC+C!NR,J-1l•SS L=L-1 IF ( l • L E. 0 I GO T 0 13 0 CCL,J-11=CCL,J-1l•CC+C(L,JI•SS

130 COtHHWE NEBCCII=-NEBCCII GO TO 130

C EFFECT OF BOUNDARY CONDITIONS IN LOWER BLOCK ONTO EQUATIONS OF C THE UP~ER BLOCK c

c

140 NK=NR-ND L=N0+1 IF <NK.GE.IaANQWI GO TO 180 IBAND=IBANDA-1 DO 150 J=NK,IBANO L=L-1 CCL,JI=GCL,Jl•CC+C(L,J+11•SS

150 CCL,J+11=CCL,J+ti•CC+CIL,JI•Ss GO TO 180

C SI~~LE 30UNuARY CONuiTIONS IN U?PER BLOCK c

c

160 IF tNH.LT.NLl GO TO 1~0

IF !NF.GT .NLI GO TO 160 NR=NL-KSHIFT IF ( N Z .L T. NL I G 0 T 0 1 8 0 C <NR, U =1.0E+30

170 NEBCCII=-NEBC<II

C EFFECT OF SIMPLE ~OUNDARY CONDITION IN LOWER BLOCK ONTO THE C EJUATIONS 3F UPPER 3LOGK c

180 CONTINUE

-103--

BIG 122 BIG 123 BIG 124 BIG 125 BIG 12& BIG 127 BIG 128 BIG 129 BIG 130 BIG 1l1 BIG 132 BIG 133 BIG 134 BIG 135 BIG 136 BIG 137 BIG 138 9IG 139 BIG 140 BIG 141 BIG 142 BIG 143 BIG 1'+4 BIG 145 BIG 11t6 BIG 147 BIG 148 3IG 149 BIG 150 BIG 151 BIG 152 BIG 153 BIG 154 BIG 155 BIG 15& BIG 157 BIG 158 BIG 159 ai:; 160 BIG 161 BIG 1&2 BIG 163 BIG 161t BIG 165 BIG 166 BIG 167 BIG 168 BIG 169 BIG 170 BIG 171 BIG 172 BIG 173 EHG Hit BIG 175 t3IG 176 BIG 177 BIG 178 BIG 179

I I

C BIG 180 C WRITE UPPER BLOCK ON TAPE AND SHIFT LOWER BLOCK UP BIG 181 C BIG 182

WRITE (8) ((CU,JI,J=1,I8t,I=1,NDI BIG 163 I WRITE CI0,231ll NBLK,ND,IB 3IG 16ft DO 190 N=1,ND BIG 185 K=N+ND BIG 16& DO 191l 11=1,IBANDW BIG 187 C(N,Mt=C(K,MI BIG 166 I

190 G!K,Mt=O.O BIG 169 C BIG 190 C CHECK FO R THE LAST BLOCK BIG 191 C BIG 192 I

IF ( NZ.L T .NEQI GO TO 40 BIG 193 C BIG 19ft C CHECK FOR COMPLETENESS OF STIFFNESS INPUT ON TAPE BIG 195 C BIG 196 I

DO 200 N=1,NUMEL BIG 197 IF (NPCN,U.LT.OI GO TO 200 BIG 196 W~ITE II0,2~01 N BIG 199 IFLAG=1 BIG 200 I

200 NPCN,11=-NPIN,11 BIG 201 DO 210 N=!,IBC BIG 202 IF INEBCOH.LE.OI GO TO 210 BIG ZOJ WRITE U0,250J N BIG 204 IFLAG=1 BIG 205

I 210 NEBCCNt=-NE3CINI BIG 20&

IF INM6LK.EQ.NBLKI GO TO 220 BIG 207 WRITE CI0,260t NMBLK,N9LK 9IG 206 !FLAG=! BIG 209 I

220 IF <IFLAG.NE.Ot STOP 3I~ 210 WRITE (!0,2701 BIG 211 RETURN BIG 212

C BIG 213 I C BIG 211+

230 FORMAT ISX,•BLOCK NO.=•,IS,/SX,•No. OF EJS/BLOCK=•,I10,/5X,•BANOWIBIG 215 !DTH=•,It0,//1 BIG 21&

240 FORMAT ISX,•ELEMENT MISSING•,sx,•ELEHENT•,ISI BIG 217 I 270 FOR~AT <SX,•BOUNOARY CONDITION MISSING NODE NUMBER•,ISI BIG 216 260 FORMAT (/t•NUM3ER OF BLOCKS DIFFER•,I5,10X,I51 BIG 219 270 FORMAT I//5X,•LINK NO. 2 COMPLETED•,ttl BIG 220

END BIG 221- I Cn/ER.LA '( !PLATE ,4,0 I FTit 1

c FTit 2 I

PROGRAM FORT4 FH 3 c FT4 It c • . .. • • .. .. • "' . .. • • • • • . .. . • • • . ..... • • • "' . • • •FT4 5 c FT4 6 I c THIS PROGRAM COMPUTES AND RESETS THE FIELD LENGTH FT4 7 c Flit 6 c • • • • • • • • . .. . • • • • • • • . . . .. ... . .. . .. • • • • • • FTI+ 9 c Fflt 10 I c QUANTifiES ON TAPES FT4 11 c FT4 12 c TAPE RECORD CONTENTS FT4 13

-104- I I I I

I I

C JUMS 1 All FT~ 14 C JUMo 1 LILA FT~ 15 C JUM& 2 FORCE FT~ 16 I C JUMo 3 DIS!J FH 17 C JUM7 1 SCRATCH TAPE FT~ 18 C FTit 19 C DEFINITIONS FT4 20 C Flit 21

I C LHIDTH HALF BANO WIDTH FT4 22 C ti!AS COLUMN DIMENSION OF 0111< FTit 23 C OIIK <S•NA51 TEMPORARY STO~AGE OF STIFFNESS FT4 24 C ~IETE L~IOTH-t ••• COLUN DIMENSION OF AL FT~ 25 I C AL TEMPORARY MATRIX VECTOR IN CHOLESKI DECOMPOSITION FT4 2& C NFREEt TOTAL NUM3ER OF DEGREES OF FREEOOM •• S•NUHNP FT~ 27 C NOF,NA1 FT4 28 G LILA FJRGE DISPLACEMENT CODE IIEGTOR FT4 29 I C FTit 30

COMMON Al11 FT~ 31 COMMON /C300/ JUM1,JUH2,JUH3,JUM4oiN,IO FT~ 32 COMMON /C801/ NUMEL,NUMNP,NUMBC,NMAT,NLCS,NN,HM,N!JSEGM FT~ 33 1-COMMON tCB02/ NUH3LK,NBLKL,IaANOH,NEQ8C FT4 34 COMMON ISOL\1/ NA1,LWIOTH,NFREE,NA5,LAMA,ISEGM,JUH5,JUM&,JUM7,JUM6 FT~ 35 COM~ON /PLTS/ NTOTP,N9P,NGPH FT4 36 COMMON /NTRUN/ NRUN FT4 37 I COMMON /CB03/ MINFL FT~ 36

C FT4 39 NA1=NFREE FT4 40 MINFL=350008 FT4 41 LAMA=NBLKL FT~ ~2

I NA5=NA1+LWIDTH-1 FT4 43 NIETE=LWIOTH-1 FT4 44 N1=1 FT4 45 N2=N1+NFREE FT~ ~6 I N3=N2+NFREE FT4 47 N~=N3+NFREE FT4 48 N5=N4+NFREE FT4 49 N6=N5+NA5 FT~ 50 I N7=N6+LHIDTH•LAMA FT4 51 N8=N7+LWIOTH•(LWIOTH-11 FT~ 52 N9=NB+LHIDTH FT4 53 N10=N9+LWIOTH FT4 54 I N11=N10+NA5+1 FT4 55 NLOC=LOCFIAIN1ll FT4 56 NRFL=NLOC+N11 FT4 57 NRFL=MAXO(NRFL,HINFLI FT4 58 WRITE <I0,101 NRFL,NRFL FT~ 59 I

C FT4 60 CALL REQMEM (NRFLI FT4 61

C FT4 62 CALL SFRT (A(N1l,A(N2),A(N3J,A(N4),A(N51,AIN6l,A(N7t,A(N81,A(N9t,AFT4 63 I

11N10l,NFREE,NA5,LWIOTH,LAHA,NIETEI FT4 64 C FT4 o5 C FT4 56

10 FORMAT 15X,•FIELO L€NGTH•,t5X,010,• IN OCTAL•,;sx.ItO,• IN DECFT4 67 I 1IMAL•tll FT4 68

I END FT4 69-

I -105-

I I

I I

SUBROUTINE SFRT fLILA,FORCE,C,QISP,X,ALLtALtH,V,Y,NOF,NNA5,NLHOTH,F4R 1NLAMA,NIETEI FltR.

C F4R

1

I 2 3

C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • F4R .. C F4R C THIS SU~ROUTINE SOLJES THE BASIC EQUATIONS AND PRINTS THE GLOBAL F4R C OISPLACEME~T VECTOR F4R

5

I 6 7

C F4R 8 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • F4R 9 C F4R

DIMENSION LILAINDFI, FORCEINOFI, CINDFI, OISPfNDFI, XINNA51, AUNLFitR. 1WOTH,NIETEI, HINLWDTHt, JINLHOTHl, YINNA5l, ALLCNLWOTH,NLAHA) F4R

10 I 11 12

C F4R 13 COMMON /CBOO/ JUM1,JUM2,JUM3,JUM4,IN,IO F4R COMMON /Cd01/ NUHEL,NUMNP,NUMBC,NHAT,NLCS,NN,MH,NPSEGM F4R COMMON /C302/ NUMBLK,N3LKL,IBANOW,NEQ8C F4R

14 I 15 16

COMMON /SOLJ/ NA1,LWIDTH,NFRE£,NA5,LAMA,ISEGM,JUM5,JUM6,JUM7,JUM8 F4R COMMON /PLTS/ NTOTP,N8P,NGPH F4R COMMON /NTRUN/ ~RUN F4R COMMON /TITLE/ TITELUOI FltR

17 18 !

19 I 20 C F4R 21 C READ IN DISPLACEMENT COO£ VECTOR FROM TAPE F4R C FltR

REWIND JUH7 FltR

22

I 23 24

READ IJUM7l FORCE F4R 25 00 10 I=1,NA1 F4R CIII=FORCEIII F4R

10 CONTINUE F4R NIETE=LWIOTH-1 F4R

26 27 I 28 29

ISEGM=NUMNP/N?SEGM F4R 30 C FltR C SOLUTION QF THE SIMULTA~EOUS EQUATIONS F4R C FltR

31 I 32 33

CALL SOLV1 IC,X,LAMA,NIETE,ISEGM,ALL,AL,H,V,Y,NLWOTH,NDF,NAS) F4R 34 C F4R

DO 20 I=1,NA1 FltR DISPIIl=XCII F4R

35

I 36 37

20 CONiiNUE F4R 38 WRITE II0,30l TITEL F4R W~ITE 1!0,701 NRUN F4R WRITE IIO,oO) FltR

39

I 40 41

WRITE (10 9 501 F4R 42 WUTE UO ,ItO I 01,0ISP (5•M-ftl, DISP <5•M-31, OISP <5•M-2 I ,OISP I 5•M-11 ,OF4R

11SP!S•Hl ,M=1,NUMNPI FltR REWIND JUM7 F4R WRITE IJUM71 OISP F4R

43 44 I 45 46

RETURN F4R 47 C F4~ C FltR

30 FORMAT 11rl1,/110X,10AR//) F4R

48 I lt9 50

40 FORMAT I&X,I5,2X,5F20.61 FltR 51 50 FORMAT I&X,11HNOOAL POINT,9X,6HOISPXX,14X,6HO!SPYY,15X,5HOISPZ,15XF4R

1,5HOISPX,15X,5HDISPY//t F4~ &0 FORMAT (1HO,I/10X,31H~ECTOR OF UNKNOWN DISPLACEMENTS,I/1 F4R

52

I 53 54

70 FORMAT 15X,.-LOAO CASE = •,ISI FltR 55 END F4~

-106-

56-

I.

I I I

I I I SUaROUTINE SOLV1 !C,X,NLAHA,NIETE,ISEGM,ALL,AL,H,V,V,NLWDTH,NOF,NNSLV 1

1A5) SLV 2 C SLII 3 c • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ••sLv 4 C SLV 5 I C SOLUTION OF BANDED SIMULTANEOUS EQUATIONS BY CHOLESKY SCHEME SLV 6 C SLII 1 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • SLV 8 C SLV q

DIMENSION ALL! NLWOTH, NLAHA), C !NOF), X !NNAS), AUNLWDTH, NIEJE), H !SLV 10 I

1NLWOTH), V!NLWOTH), Y !NNAS) SLV 11 C SL V 12

COMMON /CdOO/ JUM1,JUM2,JUH3,JUM4,IN,IO SLII 13 COMMON /C901/ NUHEL,NUMNP,NUHBC,NMAT,NLCS,NN,MM,NPSEGM SLV 14 I COMMON /SOLI// NA1,LWIOTH,NFREE,NA5,LAMA,ISEG,JUM5,JUM&,JUM7,JUH8 SLV 15

C SLI/ 16 EQUIVALENCE II9ANOW,LWIOTH) SLII 17

C SLV 18 I· C DECOMPOSITION INTO LOWER AND UPPER TRIANG.MATRIX SLV 19 C AND GENERATION OF AUXILIARY VECTOR Y SLV 20 C SLV 21

l=LWIOTH SLV 22 I N=LAMA SL V 23 REWIND JUM7 SLV 24 REWIND JUMd SLII 25 00 10 K=1,NIETE SLV 26 I

10 Y!KI=O. SLV 27 DO 20 J=1,NIETE Slll 28 DO 20 I=t ,L SLV 29 ALII,Jt=O. SLV JO

20 CONTINUE SLV 31 I KOUNT=O SLV 32 GO TO 40 SLV 33

30 IF !KZ2.EQ.~A11 GO TO 160 SLV 34 KZ1=1+KOUNT•N SLV 35 I KZ2=NA1 SLV 36 GO TO 50 SLV 37

40 IF IKOUNT.GE.I'5EGMI GO TO 3J SLII 38 KZ1=1+~0UNT•N SLII 39 I KZ2=KZ1+N-1 SLV 40

50 READ IJUH8) ALL SLV 41 ~ZJ=O SLV 42 DO 150 KZ=KZ1,KZ2 SLII 43 I KZ3=KZ3+1 SLV 44 DO 6 0 I= 1, L Sl\1 45

60 V!li=ALL!I,KZ31 SLV 46 SUM=O. SLV 47 DO 70 K=2,L SLV 48 I SUM=SUM+AL!K,L-K+11••z SLI/ 4q

70 CONTINUE SLV 50 11!1)=1.0/SQRT!I/(1)-SUMI SLV 51 NN=L-1 Slll 52 I DO 90 M=2,NN SLI/ 53 U1=:-1-1 Sll/ 54 MH=L-11 SLII 55 SUM=O. SLII 56 I

-107-

I I I

c

DO 80 K=1,MM SUH=SUM+AL(lM+(+1,l-Kt•ALCK+1 9 L-Kl

60 CONTINUE V!Hl=!VCMI-SUHI•VC1)

90 CONTINUE vcu=vcu•vcu DO 100 I=1,L

100 ALLCI,KZ31=VCII DO 110 I=1,~IETE K=L-I+1

110 HIII=AL<K,Il SUM=O. 00 120 J=1,NIETE

120 SUM=SUM+HCJI•YCJ+KZ-11 YCNIETE+KZI=CCCKZI-SU"I•VC11 NIETA=NIETE-1 00 130 J=t,NIETA uO 130 I=1,L ALCI,JI=ALII,J+11

130 CONTINUE DO 140 I=1,L ALCI,NIETEI =VIII

litO CONTINUE 150 CONTINUE

W~ITE (JUM71 ALL t<OUNT=KOUNT+ 1 GO TO ItO

150 DO 170 K=1,NA1 170 YCKI=YC(+L-11

C GENERATION OF UNKNOWN VECTOR X. G

NA=NA1+1 Na=L +NA 1-1 DO 180 K=NA,NB

180 XIKl=O. BACKSPACE JUM7 KOUNT=O KZ2=0 KWP=NA1 IQUANT=ISEGM•N~SEGM-NU~NP

IF I I QUANTI 190,200,200 190 ISEGM=ISEGM+1

IQUANT=ISEGM•NPSEGM-NUMNP KZ1=1 +S•I QUANT KZ2=N KZ3=5•IQUANT KWP=S•ISEGM•NPSEGM GO TO 210

200 IF C KZ2. GE. NAil GO TO 250 KZ1=1+KOUNP·N KZ2=KZ1+N-1 KZ3=0

210 REAu (JUI't71 ALL DO 2'+0 KZ=KZ1,KZ2 DO 220 I=1,l

220 HIII=ALLCI,N-KZ31 5UM=O.

-108-

SLV 57 SLV 58 SLV 59 SLV 60 SlV 61 SLV 62 Slll 63 SLV 64 SLV 65 SLV &6 SLV &7 SLV 68 SLV &9 SLV 70 SLV 71 SLit 72 SLV 73 SLit 74 SLV 75 SLV 76 SLV 77 SLII 78 SLII 79 SLV 80 SLit 81 SLII 82 SL'J 133 SLV 84 SLII 85 SL II 11 Ei SLII 87 SLit 88 SLV 89 SLV 90 SL II 91 SLV 92 SLII 93 SLII 94 SLV 95 SLV 96 SLV 97 SLV 98 SL V '39 SLII 100 SLV 101 SL II 102 SLV 103 SLV 104 SLV 105 SLII 106 Sl II 107 SLV 108 SLV 109 SLII 110 SLV 111 SLV 112 SLV 113 SLV 114



c

c c c c c c c c

c

c

c c c c c c c c c c c c c c c

230

240

250

DO 230 J=2,L SUM=SUMtHIJI 4 XIKWPtJ-KZI X!KWP-KZt11=1YIKHP-KZt11-SUM1 4 H111 KZl=KZ3t1 CONTINUE BACKSPACE JUH7 BACKSPACE JUM7 KOUNT=KOUNTt1 GO TO 200 RETURN END

OVERLAY I~LATE,5,01

PROGRAM FORTS

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ThiS PROGRAM READS IN INFO~MATIONS FOR OUTPUT OPTIONS AND RESETS THE FIELD LENGTH

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • COMMON /C300/ JUM1,JUM2,JUM3,JUM4,IN,IO COMMON /CB01/ ~UMEL,NUMNP,NUHSC,NMAT,NLCS,NN,MH,NPSEGH COMMON /Ca02/ NUMBLK,NBLKL,IBANOW,NEQAC COMMON /SOLJ/ NA1tLWIDTH,NF~EE,NA5,LAMA,ISEGM,JUH5,JUM6,JUH7,JUM8 COMMON /PLTS/ NTOTP,NBP,NGPH COMMON /NT~UN/ ~RUN COMMON A (1)

EQUIVALENCE INEQ,NFREEI

INTEGER T1,T2

CONT~OL INFORMATION OF OUTPUT OPTIONS T1.EQ.1 P~INT FORCES AT ALL NODAL POINTS T2.EQ.1 PRINT STRESS RESULTANTS AT CENTER OF ELEMENT

DEFINITIONS NSTOR ALF

NPO NEO SCT SNP NWT

NUMBER OF NODES WHERE STRESS RESULTANTS ARE PRINTED A~GLE FROM THE X-AXIS WHERE THE STRESS RESULTANT FORCES ARE DESIRED NUMBER OF DESIREn NODAL POINTS NU~BER OF DESIRED ELEMENTS TO BE CONSIDERED INTERNAL FORCE VECTOR AT CENTER OF AN ELEMENT INTERNAL NODAL FORCES AT THE NODES OF THE ELEMENT JECTOR OF NODES WHERE STRESS RESULTANT IS DESIRED

REAO IINt1DI T1,T2,NSTOR,ALF,NBP,NGPH WRITE (!0,20) T1,T2,NSTOR,ALF NEO=O NPO=O IF !T1. EQ.1 l "'PO=NEQ IF !T2.EQ.11 NEO=NUMEL N1=1

-109-

SLit SLV SLV SLV SLit SLV SL II SLit SLV SLV SLit

FT5 FTS FTS FT5 FTS FTS FT5 FT5 FTS FTS FT5 FT5 FT5 FT5 FTS FT5 FT5 FT5 FT5 FT5 FTS FT5 FT5 FT5 FT5 FT5 FTS FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FTS FT5 FT5 FT5 FTS FT5 FTS FTS FTS

115 116 117 118 119 120 121 122 123 124 125-

1 2 3 4 5 6 7 8 9

10 11 12 13 1ft 15 16 17 18 19 20 21 22 23 21t 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 lt2 1+3 44

c

c

c

G c

c c c

N2=N1+4•NUMEL N.3=N2+NUHEL N4=N3+NUH£L•4 N5=N4+NUHEL N6=NS+NUitEL N7=N6 .. NUMNP Nd=N7+NUHNP N9=N8+NUMNP N1 O=N<HNU11NP"'2 N11=N10•NUHNP N12=N11+NUMNP N13=N12+4•NUMEL N14=N13+NSTOR"'12 N15=N14+NSTOR"12 N1 &= N15 +NST OR"12 N17=N1&+NSTOR•tz N18=N17 +NSTOR"12 N19=N18+NSTOR•12 N20=N19+NSTOR"2 N21=N20+NSTOR N22=N21+NE0"12 N2J=N22+NSTOR•tz N24=N23+NEQ N25=N24+NEQ N2o=N25+NEQBC N27=N2&+NEQBC NLOC=LOCFIAI111 NRFL=NLOC+N27 NRFL=MAXOCNRFL,3500DBI

CALL REQHEM INRFLI

WRITE (!0,301 NRFL,NRFL

FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FT5 FTS FTS FT5 FT5 FT5 FT5 FT5 FT5 FT5 FTS FT5 FT5 FT5 FT5 FT5 FTS

CALL OTPr (A(N11,A(N21,AIN3l,A(N4l,A(N51,A(Nol,A(N7l,ACN8l,A(N91,AFT5 1 CN1 0 t, A ( N 11 I , A I N121 , A ( N131 , A ( N 14 I , A ( N15 I , A IN 161 , A ( N171 , A I N18) , A IN 1FT5 291,A IN2Dt 9 AIN211 ,ACN221 ,A(N231 ,A CN241 ,!IIUMEL,!IIUHNP,NHAT ,NEO,NUH8C,TFT5 31,T2,ALF,NSTOR,NPO,NEO,AIN251,ACN2oi,NEQBCI FTS

FT5 FT5

10 FORMAT 13I4,F8.0,2I41 FTS 20 FORMAT C1H1,/SX,•CONTROL PARAMETERS FOR OUTPUT•,!ti,SX,•GLOBAL NOOFT5

1Al FOR~ES CALCULATED AND PRINTED •,I4/,SX,•STRESS RESUFTS 2LTANT AT CENETER OF PLATE ELEMENT ~~INTED •,I4/,5X,•NO. OF NOOESFT5 3 WHERE STRESS RES A~ER AND PRINiEO •,I41,5X,•ANGLE FROM X-FT5 4AXIS TO DIRE OF STRESS RESULTANT•,Ft7.51 FT5

30 FORMAT 15X,•FIELD LENGTH•,!5X,010,• IN OCTAL•,!SX,IlO,• IN OECFTS 11~AL•,tl FT5

END FTS

SU9~0UTINE OTPT INP ,MAT, THI K,£AGLC:. NEP, XORO, YORO ,NT AG,ROT ,SOlS, COUOTP 1NT,OF,XXNS,YYNS,XYNS,XXMO,YYMO,XYMO,NWT,NPS,SCT,SNP,O,P,IE,IP,IM,IOTP 2Q,N~3G,T1,T2,ALF,NSTOR,NPO,NEO,NE3C,ANGLE,NQ1C) OTP

OTP • + • • • • • • • • • • + • + • • " • • • • • • • • + • • • • • + OTP

OTP -110-

45 . 46

47 48 49 50 51 52 53 54 55 5& 57 58 59 60 61 62 63 64 &5 6& 67 68 69 70 71 72 73 74 75 76 77 78 79 80 ll1 82 83 84 85 86 87 88 89 90 91 92 93-

1 2 3 4 5 6



I

C THIS SU9ROUTINE CALCULATES AND PRINTS THE GLOBAL DISPLACEMENTS OTP 7 C AND FO~GES AND DETERMINES THE CENTER ANO NODAL STRESS RESULTANTS OTP 8 C TOGETHER WITH THEIR AVERAGES AND PRINCIPAL VALUES OF THE OTP 9 C PLATE ELEMENTS OTP 10 C OTP 11 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • OTP 12 C OTP 13

COMMON /CBOO/ JUM1,JUH2,JUM3,JUM4,IN,IO OTP 14 COMMON /C301/ NUMEL,NUMNP,NUMBC,NHAT,NLCS,NN,MM,NPSEG~ OTP 15 COMMON /CBD2/ NUMBLK,NBLKL,IBANOW,NEQBC OTP 16 COMMON /SOL'/ NA1,LWIOTH,NFREE,NA5,LAMA,ISEGM,JUH5,JUM6,JUH7,JUM8 OTP 17 COMMON /PLTS/ NTOTP,NBP,NGPH OTP 18 COMMON /NTRUN/ NRUN . OTP 19 COMMON /PLBOG/ XXI5t,YYI51,CM!3,Jl,PP!51,BH!3,51,CVI3t51,SPBC19,190TP 20

1l,RAI19l OTP 21 COMMON /PLSTR/ XAI41,YAC4l,CS!6l,SPD!12,12l ,R1!12t,ST!5,31 OTP 22 COMMON /BNOOE/ NI,NK OTP 23 COMMON /WEB/ NWEB,NTP,NTB OTP 2~ COMMON /LOGIC/ OLOAO,GLOAO OTP 25

C OTP 26 DIMENSION NP!IE,Itl, HAT!IEl, THIKUE,41, EAGLEUEI, NEPIIflt XORO!OTP 27

1IPl, YORO!IPl, NTAGUPI, ROTCIP,2l, SDIS!IPlt COUNTUPI, OFCIE,Iti,OTP 28 2 XXNS!NSTO~t12l, YYNSINSTOR,12l, XYNSINSTOR,121, XXMOINSTORt12l,'YOTP 29 3YMO!NSTOR,121, XYMO!NSTOR,121, SNPCNSTOR,121, NEBCINQBCI, ANGLECNQOTP 30 4BCI, SKI20,20l, ITEI2l, ILEI2lt RBI201, RQU21, OUQI, PINPOI, NPSOTP 31 51NSTORI, SCTINE0,121, NWTINSTOR,2l, PRIN171 OTP 32

C . OTP 33 COMMON /BFOR/ FXXC21,FYYI21,FZC21,FX121,FY!21 OTP 34 COMMON /BPROP/ 01,D2,Dl,D4 OTP 35 COMMON /HEAD/ HEA01C13t,HEA021131,QEQ OTP 36 COMMON /TITLE/ TITELC101 OTP 37 COMMON /CARDS/ OATA,OATA1,DATA2 OTP 38 COMMON /NFB/ NB,NNO,NSN OT~ 39

C OTP 40 INTEGE( OATA,OATAt,nATA2 OTP 41 INTEGER T1,T2 OTP ~2

C OTP 43 LOGICAL OLOAO,GLOAO OTP 44

C OTP 45 DATA ITE/1 0 4/,ILE/9,4/ OTP 46

C OTP 47 C INITIALIZATION OTP 48 C OTP 49

NUHJC=NMaC OT 0 50 REWIND 1 OTP 51 READ (1) NP,MAT,THI~tEAGLE,NEP,XORQ,YORO,NTAG,ROT,SOIS,COUNT,OF OTP 52 REWIND JUH7 OTP 53 REAO IJUM71 0 OTP 54 IF (NRUN.LE.11 REWIND DATA OTP 55 NMAT=IN OTP 56 WRITE (DATA,8301 TITEL OTP 57 WRITE I DATA, 840 l HEA01 OTP 58 WRITE IDATA,8401 HEA02 OTP 59 WRITE (QATA,850l OTP 60 00 10 N=1,IQ OTP 61 OO=DINI OTP 62 IF IABSIDDI.LE.1.E-10l DINI=O.O OTP 63

10 CONTINUE OTP 64 -111-

I I

c OTf) 65 C OUTPUT OF NODAL POINT DISPLACEMENTS OTP 66 c ~p g

REWIND JUM7 OTP 68 I

READ IJUMU OTP 69 READ IJUMU NE9C,ANGLE OTP 70 READ (JUI1U NEBC, ANGLE OT~ 71 00 20 I=1,NEQBC OTP 72 I PHI=ANGLEIII OTP 73 NR=NEBGlii OTP 74 IF CPHI.EQ.O.I GO TO 20 OTP 75 IF IPHI.GE.1.5E•31 GO TO 20 OTP 76 I

C OTP 77 C T~ANSFORM SKEW DISPLACEMENTS INTO GL03AL COO~DINATE DISPLACEMENTS OTP 76 C OTP 79

NR1=NR+1 OTP 80 I ONR=DCN~I OTP 81 O!NRI=DNR•COSIPHII OTP B2 O!NR11=DN~•SINIPHII OTP 83

20 CONTINUE OTP 8ft WRITE CIO,S501 OTP 85

I DO 3u I=t,NUMNP Off) 86 K2=I•5 Off) 87 K3=K2-1 OTP 88 Kft=K2-2 OTP 89 I K5=1(2-3 OTP 90 K6=K2-4 OTP 91 WRITE U0,8701 I,O!K6J,Q(KSI,O<K4t,JIK31,0(K21 OTP 92

C OTP 93 I C TEMPORARY STORAGE OF NODAL DISPLACEMENTS IN SNP OTP 9ft C OTP 95

N=I OTP 96 $NP<N,71=01K61 Off) 97 I SNP(N,8l=OlK51 OTP 98 SNP!N,9t=DIK41 OTP 99 SNP(N,101=DIK~I OTP 100 SNP!N,11t=D<K21 OTP 101 I

JO CONTINU~ OTP 102 C OTP 103 C TEMPORARY STORAGE OF CENTER DISPLACEMeNTS IN SCT OTP 104 C OTP 105

IF (NGPH.EQ.OI GO TO 90 OTP 106 I DO 50 N=1,NUMEL OTP 107 IF INP(~ 9 2l.EQ.NP!N,31t GO TO 50 OTP 108 SUM1=0. OTP 109 SUM2=0. OTP 110 I SUH3=0. OTP 111 SUM4=0. OTP 112 SUM5=0. OTP 113 Do 40 I=1,4 or~ 114 I L=NP(N,II OTP 115 SUH1=SUH1+SNP!L,71 OTP 116 SUM2=SUM2+SNP!L,81 OTP 117 SU113=SU~3•SNP<L,91 OTP 118 I SUM4=SUM4+SNP<L,10t OTP 119

40 SUM5=SUM5+SNP(L,111 OTP 120 SCTIN,71=0.25•SUM1 OTP 121 SCT<N,81=0.2S•SUM2 OTP 122 I

-112-

I I I


c

SCT!N,91=0.ZS•SUH3 SCT!N,10t=0.2S•SUM~ SCT!N,111=0.25•SUM5

SO CONTINUE DO 50 I.:7,11

GO WRITE (7) CSNP(N,II ,N=l,NUMNPI ,(SCT!N,II ,N=t,NUMELI WRITE U0,1090l DO 70 N=l,NUMNP

70 W~ITE U0,11601 ISNP(N,IJ,I=7,111 WRITE U0,11001 DO 80 N=l,NUMEL IF CNPP~ 9 21.EQ.NP!N,311 GO TO 80 WRITE U0,11EIOI CSCT(N,IJ,I=7,111

80 CONTINUE

C DETERMI~ATION OF GENERALIZED FO~CES A~O REACTIONS c

c

90 IF !T1.NE.11 GO TO 200 DO 100 I=1,IQ

100 P!Il=O.O REWINO JUr13 DO 150 N=1 9 NUMEL READ !31 SK,SP'3 DO 140 L=1t 4 LA=NP!N,U•S-S DO UO K=1,5 IA=!L-11•5+K SUM=O.O DO 120 I=1,4 KA=NP!N,II•5-5 DO 110 J=1 9 5 JA=!I-11•S+J

110 SUM=SUM+SK!IA,JAI.O!J+K~I 120 CONTINUE

P!K+LAI=P!K+LAl+SUM 130 CONTINUE 140 CuNTINUE 150 CONTINUE

C PRINT OF REACTIONS IN JIRECIIu~ OF ROfATEu AXIS c

DO 160 I=1 7 IQ OO:P(!) IF !A8S!OJt.LE.1.E-10l P!II=O.

160 CONTINUE WK.ITE !!0,880) DO 170 N=1, NUI-'NP L=NTAG!NI IF !L.E'}.OI GO TO 170 PHI1=ROT!N,11 PHI2=ROT(N,21 KA=N•S KA1=KA-~ KA2=KA-3 KAl=KA-2 KAit=KA-1 KAS=KA CN=CO:i!PHI11

-113-

OTP 123 OTP 124 OTP 125 on 126 OTP 127 OTP 128 OTP 129 OTP 130 OTP 131 OP 132 OTP ill OTP 134 OTP 135 OTP 136 OTP 137 OTP 138 OTP 1 H OTP 140 OTP 141 OTP 142 OTP 143 OTP 11+~ OTP 145 OTII H6 OTP 147 OTP 11t8 OTP 149 OTP 150 OTP 151 OTP 152 OTP 153 OTP 15ft OTP 155 OTP 15& OTP 157 OTP 158 OTP 159 OTP 160 OTP 161 OTP 162 OTP 163 OTP 1o4 OTP 165 OTP 166 OTP 167 or~ 168 OTP 159 OTP 170 \HP 171 OTP 172 OTP 173 OTP 174 OTP 175 OTP 17& OTP 177 OTP 178 OTP 179 OTP 180

SN=SI!'H PHIU F1=P(KA1J•CN+P(KA2J•SN F2=P<KA2J•CN-P(KA1J•SN FJ:P(KA31 CN=COS(PHI21 SN=SIN<PHI21 F4=P(KA4t•CN+PlKA5l•SN F5=P<KA5t•CN-PlKA4J•SN W~ITE U0,870l N,F1,F2,F3,F4,F5 WRITE IDATA,8901 N,F1,F2,F3,F4,F5

170 CONTINUE c C PRINT JF GENERALIZED FORCES c

DO 180 N=1,IQ DD=P!Nt IF (AdS(OuJ.L£.1.£-10) P<NJ=O.O

180 CONTINUE WRITE !IO,'lOOI DO 190 J=1,NUMNP KA=J•S

190 WRITE <!0,8701 J,P<KA-'+1 ,P(KA-31 ,P<KA-21 ,P(KA-11 ,PIKA I c C DETERMINATION OF INTERNAL FORCES AT THE CENT~R. AND NODES OF C EACH ELEMENT c

G

200 IF INSTOR.Lt::.G.AND .. T2.NE.U GO TO 820 REWIND 1 READ (11 NP,MAT,THIK,EAGLE,NEP,XORQ,YORO,NTAG,ROT,SOIS,COUNT,OF IF INSTOR.LE.OI GO TO 260 IF INSTOR.NE.NUMNPI GO TO 220 DO 210 I=1,NUMNP

210 NPSIII=I GO TO 230

220 READ !IN,910l (NPS(U ,I=1,NSTOIU

C INITIALIZATION OF ARRAYS FOR NODAl POINT STRESSES c

c

230 DO 250 J=1,NSTOR DO 240 L=1,12 XXNS (J,Ll=O.O YYNSIJ,LI=O.O XYNS!J,Ll=O.O XXMO!J,Ll=O.O YYMO(J,Ll=O.O

240 XYMO<J,LI=O.O NWT(J,11=0

250 NWT(J,21=0 WRITE (I0,9201 WRITE (I0,9301 (NPSlil,I=1,NSTORl

C DETERMINATION OF STRESS RESULTANTS AND MOMENTS FOR DECK ElEMENTS c

260 CONTINl.IE NTP=1 IF lNTP. GE.1l WRITE (!0, 940 I REWIND JUI12 REWIND JUM3

-114-

OTJI 181 OTP 182 OTP 183 OTP 184 OTP 185 OTP 186 OTP 187 OTJI 188 OTP 189 OTP 190 OTP 191 OTP 192 OTP 193 OTP 194 OTP 195 OTP 196 OTP 197 OTP 198 OTP 199 OP 200 OTP 201 OTP 202 OTP 203 OTP 204 OTP 205 OTP 20& OTP 207 OTP 206 OTP 209 OTP 210 OTP 211 OTP 212 OTP 213 OTP 214 OTFl 215 OTP 216 OTP 217 OTP 218 OTP 219 OTP 220 OTP 221 OTP 222 OTP 223 OJ!» 224 OTP 225 OTP 22& OTP 227 OTP 228 OTP 229 OTP 23D OTP 231 OTP 232 OTP 233 OTP 234 OTP 235 OTP 236 OTP 237 OTP 238



c

REWIND JU~It NWEB=O DO 540 N=1,NUMEL DO 270 I=1,3 DO 270 J=1,5

270 BMII,Jt=O.O READ IJUM2t XX,YY,CM,01,02,U3,0'+,PP NEN=NEPINJ IF I NEN. EQ. 5 I ~WEB=NWE9•1 NKA=4 NKB=.l NTRI=It IF INPCN,1J.EQ.NPIN,4ll NTRI=3 IF INP!N,2l.EQ.NPIN,31l NTRI=2 IF INEN.EQ.SJ PPI5l=PP11J KKK= 0 00 290 I=1,4 JA=NP(N,Il XAUJ =XOROIJAI YAIII=YORDIJAI XXIII=XORDIJAI YY!Il=YORDIJAI KA=JA•5-NKA K3=KA+1 I1=2•I-1 I2=2•I IB!=S•ti-11+1 !82=!31+1 R11I1l=DIKAI R11I2l=::J(K81 RBUBH =D IKAI Raii62l=DIKBl KC=JA•5-N K8 IB3=IB1t1 KC2=KCH KC3=KC2+2 RQ(ll=DIKAI RQII+Itl =0 IKC2l RQ II +liJ =D IKCJI DO 280 JL=1,3 KKK=KKK+1 Id3=I33t1 KC=KC+1 R31I83l=DIKCI

280 RAIKKKl=OIKCl 290 CONTINUE

C OEFIN~ IN PLANE ELEMENT MATERIAL PROPERTIES G

CSUI=CMU,H CSI21=CMC2,21 CSI31=CMI3,3l CSI1ti=CMI1,2l CSI51=CMI1,3l CS (I) I =CM C 2, 31 DO JOO I=1,6

300 CSIII=PPCSI•CSIII READ 131 3K,SPB

-115-

OTP 239 OTP 240 OTP 2lt1 OTP 242 OTP 243 OTP 24ft OTP 2lt5 OTP 2ft& OTP 21t7 OTP 246 OTP 21t9 OTP 250 OTfl 251 OTP 252 OTP 253 OTP 254 on 255 OTP 256 OTP 257 OTP 258 OTJJ 259 OTP 260 OTP 261 OTP 262 OTP 263 OTP 2oft OTP 2&5 OTP 266 OTP 267 OTP 268 OTP 269 OTP 270 OTP 271 OTP 272 OTP 273 OTP 214 OTfl 275 OTP 276 OTP 277 OTP 278 OTP 279 OTP 260 OTP 281 OTP 282 OTP 283 OTP 264 OTP 285 OTP 286 OTP 267 OTP 288 OTP 289 OTP 290 OTP 291 OTP 292 OTP 293 OTP 294 OTP 295 OTP 296

c

c

c

G

c

c

DO 310 J=13,19 310 RAUI=O.O

IF (QLOAD.OR.GLOAOJ GO TO 320 GO TO 3'+0

320 CONTINUE DO 330 J=1J,19

330 RA(JI=SPB(J,JI 3'+0 CONTINUE

IF <NDI.EQ.5l GO TO 380 IF tNTRI.EQ.21 GO TO 360 IF (HEA01t11.EQ.5HOEBUGI WRITE <I0,970l <R1(II,I=1,6l

CALL PSD11 lNTRII

GALL FPLATE lNTRil

IF IHEAD1 Ul .NE.5HOE3UGJ GO TO 450 WRITE (10,9501 N,NEN,NEPINI 00 350 I= 1,4 NO=NPIN,Il

350 WRITE li0 9 1000l ND,ISHI,Jl,J=t,JJ,(6M(J,Il,J=1,JI GO TO '+50

3t:i0 NI=NPIN,1) Nt<=NPIN,2l WRITE ( 10,9601 N

CALL 3EAMF <RBI

DO 370 1=1,10 370 SCT<N,Il=FXX!Il

GO TO '+90 380 CONTINUE

OX=XXI21-XX(1l DY=YY<21-YYIU XL2=DX•OX+OY•OY XL =SQRT ( XL2 l SI=DV/XL CO=DX/XL .XAUI=XA(4l =0.0 YAI11=YAl2l=O.O DO 390 1=1, 2 K=I+1 J=I+2 XAIKI=XL VA(Jl=PP(2l PPUt=PPUI

390 PP(JI =PPCU 00 '+10 1=1,4 IF 1At3510Xl.GT.1.0E-51 GO TO 400 NEN=6 NEPINI=o

400 CONTINUE XX(Il=XA(Il

410 YYlil=YAlil DO 420 1=1,12

'+20 RUil=R1Ul

C TRANSFORMATION FOR WEB DISPLACEMENTS NOT AT X-AXIS

-116-

OTP 297 OTfl 296 OTP 299 OTP 300 OTP 301 OTP 302 OTP 303 OTP 304 OTP 305 OTP 306 OTP 307 OTP 306 OTP 309 OTP 310 OTP 311 OTP 312 OTP 313 OTP 314 OTP 315 OTP 31& OTP 317 OTP 316 OTP 319 OTP 320 OTP 321 OTP 322 OTP 323 OTP 324 OTP 325 OTP 326 OTP 327 OTP 326 OTP 329 on~ 330 OTP 331 OTP 332 OTP 333 OTP 33ft OTP 335 OTP 336 OTP 337 OTP 336 OTP 3 39· OTP 340 OTP 341 OTP 342 OTP 31t3 OTP 344 OTP 345 OTP 346 OP 347 OTP 346 OTP 349 OTP 350 OTP 351 OTP 352 OTP 353 OTP 354



c

c

c

c

c

DO lt30 I=1,4 NA=NPIN,II I1=NA"'5-lt 12=!1+-3 IA=3•I-2 RAIIAI=D(Ili•SI-OII1+11•Co RAIIAt11=DII21•CO-DII2t11"'SI RAIIAt-21=0. R11II=OII11"'COt-OII1t-11•SI R11It-SI=DII2l"'SI-DII2t-11•Co

!t30 CONTI~UE IF I Ht:AD1111.NE.5HDEOUGJ GO TO ltltO WRITE II0,970l IIHIIl ,!=1,121, IRQ III ,I=1,121 WRITE (!0,9801 IRAIII,I=1,121

ltltO CCNTI"'UE

CALL PLSP12

CliLL FONEW

450 CONTINUE

C OUTPUT OF INTE~NAL FORCES AT C~NTER OF EACH ELEMENT c

c

IF IT2.NE.11 GO TO 500 DO 460 J=1,3 I=J SC T IN, I I= ST I 5, J I

460 SGTIN,It-3l=3MIJ,51 IF INEN.EQ.5l GO TO 490 IF I NEtl. NE. 61 GO TO 480 WRITE II0,990l N !JO lt70 I=1,Lt ND=NPIN,Il WRITE II0,100LJI Nfl, IST(I,JI .J=1,JI, 18'11J,II ,J=1,3l

470 CONTINUE !t80 CONTINUE

SC TIN, Lt l = dr-1 I 1, 5 l 490 CONTI:-IUE 500 IF INSTOR.L!::.Ol GO TO 540

G AvERAGE I~TERNIIL FORCES OF ADJACENT ELEMENTS AT EACH NODE c

IF INE:N.EQ.Eil GO TO 51t0 00 530 '<=1,4 IF IK.EQ.4.ANO.NTRI.EQ.3l Gll TO 530 IF I:HRI. EQ. 2 I GO TO 5.50 N2=NPIN,Kl DO 510 J=l,NSTOR IF IN2.EQ.NPSIJII GO TQ 520


520 CONTINUE NJ=1 IF INEN.EQ.Sl NJ=2 NiH I J, N J I =N l<IT I J, N J l t1 L=NWTIJ,ll

-117-

OTP 355 OTP 356 OTP 357 OTP 358 OTP 359 OTP 360 OTP 361 OTP 362 OTP 363 OTP 361t OTP 365 Ofil' 366 OTP 3&7 OTP 368 OTP 3&9 OTP 370 OTP 371 OTP 372 OTP 373 OTP 37ft OTP 3 75 OTP 376 OTP 377 OTP 378 OTP 379 OTP .580 OTP 381 OT? 382 OTP 383 OTP Jolt OTP 385 OTP 386 OTP 387 OTP 388 OTP 389 OTP 390 OTP 391 OTP 392 OTP 393 OTP 39ft OTP 395 OTP 396 OTP 397 OTP 398 OTP 399 Off' LtUO OTP 401 OTP 402 OTP 40l OTP 401t OTP Ltil5 OTP 406 OTP 407 OTP 408 OTP 409 OTP 410 OTP lt11 OTP 412

c

L1=NWT(J,21 IF INEN.EQ.5t L=L1+6 XXNS(J,LJ:STIK,1t YYNSIJ,Lt=ST!K,21 XYNSIJ,L)=STIK 9 3t XXMOIJ,LI=8M(1,K) YYMOIJ,L)=9H(2,Kt XYHOIJ,LJ=BM(3,Kt

530 CONTINUE 540 CONiiNUE

IF H2.EQ.U WRITE (!0,10201 DO 550 N=1,NUMEl WRITE <10,1010) N,!SCHN,U ,!=1,61

550 CONTINUE

C OUTPUT OF INTERNAL FORCES AT CENTER OF WEB ELEMENTS c

c

c

c

c

c c

WRITE I I 0 , 1 0 3 0 I N WE 8 IF INWE3.U:":.OI GO TO 570 WRITE U0,1040t DO 560 N=1 9 NUMEL NEN=NEPINI IF INEN. NE. 5 ~ GO TO 560 WRITE (!0,10101 N,(SCT(N,Jt .J=1,6J


WRITE U0,1110 l DO 600 N=1,NUMEl IF INP(N,2t.EQ.NPlN,31) GO TO 600 NEN=NEPIN) DO 560 !=1,3

530 PRINIIJ=SCTtN,IJ

CALL POIR IPRIN(11,PRIN(4) 9 THETAI

SCTIN 9 71=PRINI4) SCT!N,8t=PRINI5J SCT!N,CJJ=0 RINI6t DO 590 1=1,3

590 PRIN!II=SCT!N,I+31

CALL PDIR IPRIN(1t,PRINf4J,GAMMAI

SCTIN 1 101=PRINI4l SCTIN,111=PRIN15l SCT<N,12t=PRINI6t IF INEN. EQ. 5) GO TO 600 WRITE U0,1010t NdSCT(N,Jt ,J=7t12t WRITE (!0,10501 THETA,GAMMA

cOO CONTINUE

C OUTPUT OF PRINCIPAL STRESSES AT GENTER OF WE9 ELEMENTS c

IF (NW!:B.LE. 0) GO TO 630 WRITE (!0,10601 DO 620 N=i,NUMEL NEN=NEPINl

-118-

OTP 41J OTP ft1ft OTP 415 OTP 416 OTP 417 OTP 418 OTP 419 OTP 420 OTP 421 OTP lt22 OTP 423 OTP 424 OTP 425 OTP 426 OTP 427 OTP 428 OTP 429 OTP 430 OTP 431 OTP 432 OTP 433 OTP 43ft OTP 435 OTP 436 OTII 437 OTP 438 OTP 439 OTP 440 OTfl 441 OTP 41t-2 OTP 443 OTP 444 OTP 445 OTP 446 OTP 447 OTP 446 OTfl 449 OTP lt50 OTP 451 OTP 452 OTfl 453 OTP 454 OTP 455 OTP 456 OTI' lt57 OTP 458 OTP 45CJ OTP 460 OTII 4&1 OTP 462 OTP 463 OTP lt64 OTI' 465 OTP lt66 OTP 467 OTP 466 OTI' 469 OTP 470

I I I I I I I I I I .I I I I I I I I I

I I I

IF CN£N.NE.51 GO TO 620 OTP 471 THETA=360. OTP 472 OB=0.5•1SCTIN,11-SCTCN,211 OTP 473 IF 189.EQ.O.I GO TO 610 OH ft71t

I THErA=57.29578•ATAN2CSCTIN,JI ,631/2.0 OTP ft7.S

o10 CONTINUE OTP 476 WRITE (!0,10101 N, I SCT IN. Jl ,J=7, 121 OTP lt77 WRITE 1!0,10501 THETA OTP 478

620 CONTINUE OTP ft79

I S30 CONTINUE OJII 480 c OTP ft81 c OUTPUT OF A~ERAGE INTERNAL FORCES AT THE NODES OTP 482 c OTP 483

I IF INSTOR.LE.OI GO TO 820 OTP It Sit ALF=ALF/57.29578 OTfl 485 £3SI=SINIALFI OTP 466 !3CO=C05 I ALF I OTP 487

I WRITE (!0,11801 OTP 488 NTt1=0 OTP 489

:,4o CONTINUE OTP 490 IF CNTM.LE.Ol GO TO 650 OP 491

I WRITE II0,10701 OTP lt92

650 CONTI:~UE OTP 1+93 QO 760 I=1,NSTOR OTP 49ft IF INTM. GE.1l GO TO 660 OTP 495 WRifE II0,11701 NPS I I I OTP lt96

I K=NPSIIl OTP 49"7 LL=O OTP 496 NN=NWT II, 11 OTP 499 IF INN.LE.OI GO TO 760 OTP 500

I NKA=1 OTP 501 NK9=N:-.l OTP 502 IF INTM.LE.OI GO TO 670 OTP 503

660 CONTINUE OTP 504

I LL=6 OTfl 505 NI~=NWT (I, 21 OTP 506 IF CNN.LE.OI GO TO 760 OTP 507 WRITE CI0,11701 NPSCII OTP 508

I NKA=7 OTP 509 NKB=NN+LL OTP 510

570 SNXX=O.O OTP 511 SNYV=O. 0 OTP 512 SNXY=O.O OTP 513

I SMXX=O.O OTP 514 SM'I'Y =0. 0 OTP 515 SMXY=O.(] OTP 516 DO b80 L=NKA,NK8 OTP 517

I WRITE ({0,11601 XXNS I I ,U, YYNS II ,u, XYNS (! ,LI, XXMO U ,L I, YYMO U ,L I ,OTP 518 1XYMOCI,U OTP 519

SNXX=SNXX+XXNSCI,LI OTP 520 SNYY=SNYY+YYNSCI,LI OTP 521

I SNXY=~NXY+XYNSCI,LI OTP 522 SMXX=SMXX+XXMOII,LI OTP 523 SMYY=SMYY+YYMOII,LI OTP 524 S~XY=SMXY+XYMOII,Ll OTP 525

I 580 CONTINUE OTP 526

SNPCI,LL+11=SNXX/NN OTP 527 SNPCI,LL+2l=SNYY/NN OTP 528

-119-

I I I

c

SN~CI,LL+31=SNXY/NN SN~CI,ll+~t=SMXX/NN SNPCI,LL+51=SHYY/NN SNPII,LL+&t=SMXY/NN WRITE CI0,1140t ISNPCI,LL+Jl ,J=1,61

C DETERMINATION OF PRINCIPAL VALUES OF INTERNAL FORCES c

IF CBSI.NE.O.OI GO TO 730 AB=O.S•CSHXX+SHYYl/NN BA=O.S•ISHXX-SHYY)/NN AA=O.S•ISNXX+SNYYt/NN 89=0.5•1SNXX-SNYYI/NN TAV=SQRTI3A••2+CSHXY/NNt••2J TAU=SQRTIBB••2+1SNXY/NNt••zt SHHAX=AB+TAV SHHIN=AB-TAV SNHAX=AA+TAU SNHIN=AA-TAU IF CNTM.GE.11 GO TO 690 SNP(I,71=SNI1AX SNP II,81 =SNMIN SNPII,91=TAU SNP CI, 1111 =S~MA X SNPC 1,111 =SMHIN SNPII,12j =TAV

&90 CONTINUE IF IBA.EQ.O.O.ANO.SMXY.EQ.O.OI GO TO 700 8AG=57.29578•ATAN21CSHXY/NNl,BAl/2.0 GO TO 710

700 !3AG=3&Q. 710 IF CBB.EQ.O.O.ANO.SNXY.EQ.O.Ol GO TO 720

BANG=S7.29578•ATAN21CSNXY/NNl ,1381/2.0 Go ro 750

720 8ANG=360. GO TO 750

730 SS=BSI•BSI SC=BSI•l3CO CC=BCIJ•SCO SNMAX=CSNXX•CC+SNYY•SS+2.0•SNXY•SCI/NN SMHAX=ISNXX•CC+SMYY•SS+2.0•SMXY•SCI/NN SNHIN=IISNYY-SNXXJ•SC+SNXY•CCC-SSil/NN SMMIN=CISMYY-SMXXl•SC+SHXY•CCC-SSil/NN TAU=O.S•CSNMAX+SNMINl TAV=O.S•ISMMAX+SMMINl BANG=BSI BAG=BCO lL=o IF lNTH.G£.11 GO TO 740 SN?ll,LL+1l=SNMAX SNPII,LL+2l=SNHIN SNP(I,LL+3J=TAU SN?II,LL+lti=SHMAX SNPli,LL+Sl=SMMIN SNPCI,LL+6l=TAV

740 CONTINUE 750 WRITE (!0,1150) SNMAX,SNMIN,TAU,SHMAX,SMMIN,TAV

WRITE (10,1080) BANG,fiAG -120-

OTP 529 OTP SJO OTP 531 OTP 532 OTP 533 OrP 534 OTP 535 OrP 536 OrP 537 OTP 538 or~ 539 OTP 5 .. 0 OTP 541 OT~ 542 OrP 543 OTP 51tlt orP 545 OP 546 OTP 5lt7 orP 548 or~ 549 orP 550 OTP 551 OTP' 552 orP 553 OT~ 554 OTP 555 OTfl 55& OTP 557 OTP 558 or~ 559 OTP 5b0 OTP 561 OTP 5&2 OrP 563 OTP' 56ft OTP 565 OTP 566 OTP 567 on 5&8 OTP 569 OTP 570 OTP 571 OTP 572 OTP 573 OTfl 574 orP 575 OTP' 576 OTP 577 OTP 578 OTP 579 on 580 or~ 581 orP 582 OP 583 OTP 584 OTP 585 OTP 566


I I I I I I 1-


760 CONTINUE OTP 587 C OTP 588 C OUTPUT OF INTERNAL FORCES AT NODES OF WEB ELEMENTS INCLUDING OTP 58q C AVERAGED AND PRINCIPAL VALUES AT THE NODES OT~ 590 C OTP 591

NTH=NTM+1 OTP 592 IF (NT 11. LE.U GO TO oltll OTP 5q3

C OTP 5q4 C PREPARE INPUT FOR LATERAL LOAD DISTRIBUTION COMPUTATION OT~ 595 C OTP 596

REWIND ~ OTP 597 WRITE (~I SCT OTP 598 IF (~GPH.EQ.OI GO TO ~00 OTP 59q DO 770 I=1,12 OTP 600

770 WRITE (71 ISNPIN,II ,N=1,NUMNPI, (SCT<N,It ,N=l,NUHEU OTP 601 WRITE (I0,11201 OTP 602 DO 780 N=1,NUMNP OTP 603 WRITE (I0,11601 (SN!JIN,II,I=1,61 OTP 604

780 WRiiE (!0,11601 (SNPIN.IJ,I=7,121 OTP 605 WRITE (I0,11301 OTP 606 DO 790 N=t,NUMEL OTP 607 IF INPCN,21.EQ.NP(N,311 GO TO 790 OTP 608 WRifE (!0,11601 <SCT<N,II,I=1,61 OTP &oq WRITE (!0,11601 ISCT(N,II,I=7,121 OTP 610

790 CONTINUE OTP 611 REWIND JUM7 OTP 612

800 WRHE (!0,11901 OTP 613 IF (NWE~.GE.t.ANO.HEA02(11.EQ.6HTRUCK I GO TO 810 OT~ 614 IF INWE:3.GE.1.AND.HEAD2UI.EQ.6HDISTRIJ GO TO 810 OTP 615 GO TO 820 OTf» 616

C OTP 617 810 CALL LT~DBX ISNP,NUMNP,NBI OTP 618

C OTP 619 820 RETURN OTP 620

C OTP 621 C OTP 622

d30 FORMAT 11H0,10A81 OTP 6?3 840 FORMAT !1H0.13A6l OTP 624 'i:.O FORMAT 15X,"REACTIOIIIS.. ONC: CARD PER NODE"l OTP 625 860 FORMAT 11H1,1/10X,•DISPLACEMENT VECTOR",////,10X,10H NODAL PT.,7X,OTP 626

17H U-DIS.,~X,7H V-DIS.,9X,7H W-DIS.,8X,8H X-ROTAT,8X,8H Y-RJTAT,//OTP 627 21 OTP 628

870 FORMAT !10X,I5,~X,1P5E15.51 OTP 629 880 FOR~AT 11H1,1/10X,•REACTIONS IN THE DIRECTION OF ROTATED AXIS•,!t,OTP 630

110X,10H NODAL PT.,6X,8H U-FORCE,dX,10H V-FORCE ,8X,6H W-FO~CE,7X,OTP 631 2~H X-MO~ENT,7x,9H Y-HOMENT,I/1 OTP 632

690 FOR~~T (15,5E12.5l OTP 633 900 FORMAT !1H1,//10X,•GENERALIZEO FORCE VECTO~•,!t// 1 10X,10H NODAL PTOTP 634

1.,6X,8H U-FORCE,SX,8H V-FORCE,6X,8H W-FORCE,7X,9H X-MOMENT,7X,qH YOTP 635 2-~0~ENT,////1 OTf» 636

'HO FORMAT 12!1HI OTP 637 920 FORMAT I//55H NOD~S WHERE INTERNAL FORCES COMPUTED,AVERAGEO AND OTP 638

1 OUTPUT 11/1 OTP 639 330 FOR~AT 120I41 OTP 640 940 FORMAT 1/SX,•ST~ESSES 4T NODES OF DIAPHRAGM ELEMENTS•,I/5X,•NOOE •OTP 641

1,15X,12H NXX ,5X,12H NYY ,SX,12H NXY ,5X,12H OTP 642 2 MXX ,5X,12H MYY ,5X,12H MXY ,//t OTP 643

950 FORMAT 15X,•TOP 0~ BOTTOM ELEMENT•,I5,"NEN=•,rs,•NEPINI=•,I5t OTP 64~

-121-

9&0 FORMAT l12H ELEMENT ,I5,5X,•tBEAM ELEMENTJ•t OTP &~5 970 FORMAT (/5X,•ELEHENT NODAL DISPLACEMENT U1234,V12J4,012J4•,15X,~tEOTP 646

112.5,5XI,/5X,~tE12.5,5XI,/5X,~(E12.5,5XII OTP 647 980 FORMAT 1/SX,•NOOE I,J,K,L '"'OX,OYI OISPLACEMENTS•,I5X,3lE12.4,3XIOTP 648

1,/5X,J(E12.~t3Xt,/5X,JtE12.4,JXJ,/5X,JlE12o4t3XI,//t OT~ 5~9 990 FORMAT (/5X,•OIAPHRAGH ELEMENT•,ISI OTP 650

1000 FORMAT t13X,I5,&E17.5l OTP 651 1010 FORMAT t12H ELEMENT ,I5,&E17.51 OTP &52 1020 FORMAT t5DH1 INTERNAL FORCES AT CENTER OF DECK ELEMENTS ,/2X,OT~ 653

t•ANO INTERNAL FORCES AT NODES OF BEAM ELEMENTS•,I/25X,12H NXX OTP 654 2 ,5X,12H NYY ,5X,12H NXY ,6X,12H MXX ,5X,120TP &55 JH MYY ,SX,12H MXY ,I&X,12H ,5X,12H OR FOTP 656 4XX ,5X,12H OR FYY ,23X,12H OR FZ ,5X,12H OR H-Y ,SXOT~ &57 5,12H OR M-Y ,11 OTP 658

1030 FORMAT (/5X,•NHE3=•,I5,/l OTP 659 1040 FOR~AT (/1X,•INTERNAL FORCES AT CENTER OF WEB ELEMENTS•,I/25X,12H OT~ 660

1 NXX ,SX,12H NYY ,5X,12H NXY ,12H HXX ,OTP 6&1 25X,12H MYY ,5X,12H MXY ,//) OTP 662

1050 FORMAT 117H ,34X,E17o5tl4X,E17.51 OTP 663 1060 FORMAT 1/SX,•PRINCIPAL VALUES AND ANGLE FOR HEa ELEMENTS•,t/J OT~ 664 1070 FORMAT ti1X,•INTERNAL FORCES AT NODES OF WEB fLEHENTS•,tll OTP 665 1080 FORMAT t2X 1 17H ANGLE W/X-AXIS,JSX,E17.5,34X,E17.5,/I OTP 666 1090 FORMAT <15X,•NOOAL DISPLACEMENTS TO BE PLOTTED•,ttl OTP 667 1100 FORMAT t15X,•CENTER DISPLACEMENTS TO BE PLOTTED•,/11 OTP 668 1110 FORMAT tSX,•PRINCIPAL iALUES AND ANGLES•,II25X,12H N1 ,sx,OTP 669

112H N2 ,5X,12H N12/THETA ,&X,12H Hi ,SX,12H MOTP 670 22 ,5Xt12H M12/GAHMA ,lit OT~ 671

1120 FORMAT (/SX,•NODAL VAlUES TO B€ PLOTTE0•,/11 OTP 672 1130 FORMAT 1/SX,•CENTROIO VALUES TO BE PLOTTEO•,t/1 OTP 673 11~0 FORMAT (/5X,12HNPo AVERAGE ,3X,&E17.51 OTP &74 1150 FORMAT 12X,16H PRIN NP QUANT,2X,&E17.51 OT~ 675 1160 FORMAT (20X,&E17.5t OTP 676 1170 FORMAT 112H NODAL .POINT,ISI OTP 677

c c c c c c c c c

c

1180 FORMAT (48H1 INTERNAL FORCES AT NODES OF DECK PLATES //25X,10TP 678 12H NXX ,SX,12H NYY ,5X,12H NXY ,&X,10H MXX OT~ 679 2 ,7X,10H MYY ,7X,10H MXY Ill OTP 680

1190 FORMAT (//23H LINK NO 5 COMPLETED //l OTP 681 END OTP 682-

SU3~0UTIN£ LTRD3X ISNP,NN,NdOXI LT~ 1 LTB 2

• • • • • •• • • • • • • • • • • • • ~ • • • • • • •• • • • • • • LTB 3 LTB ~

THIS SUBROUTINE COMPUTES THE MOMENTS OF THE 30X8EAHS AT THE LTB 5 SPECIFIED SECTIONS FROM THE INPLANE AND OUT OF PLANE STRESS LTB 6 RESULTANTS LTB 7

LTB 8 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LT~ 9

LTB 10 DIMENSION SNP(NN,12t, PCTt10l, NTPt10,&J, NTBt10,31, NTWl10,\l, XMLTB 11

1Bl10t, FTPt61, FTBIJI, FTWI~l, XTPI61, XTB<31, WTPl10,6J, WTBI10,&LTB 12 21, ~TWl10,2l LTB 13

LTB 14 COMMON ICBOO/ JUM1,JUM2,JUM3,JUM4,IN,IO LTB 15

c COMMON /STE~E/ NWAX,XLBR LTB 16

LTB 17

-122-



C REAO IN NOOES ANO EFFECTIVE HIOTHS OF TOP FLANGE BOTTOH FLA~GE, C AND WEB ELEMENTS OF EACH BOX c

c

DO 10 N=1,NBOX READ <IN,110l CNTPCN,II,I=1,&1 READ CIN,120) IHTPCN,Il,I=1,&1 Rf.AO IIN,110l CNT9CN,Il,I=1,3l READ UN,120l OH3CN,Il,I=1 9 31 REAu CIN,110l CNPI(N,Il ,I=1,ttl PEAD CIN,120l CWTWCN,Il,I=1,21

10 CONTINUE DO 80 N=l,NBOX WRITE UO,l301 N WRITE CI 0, 1 '+ 0 I

G COMPUTE IN PlANE ~ORCES AT TOP FLANGE c

c

wRITE CI0,1501 FT1=0. XT1=0. i.JO 20 1=1,6 J=NTPCN,Il IF CJ.U.Ol GD TO 30 E=WTPIN,Il EW=WTW 01,11 FTPIII=SNPIJ,!I•E. XTPIII=SNPlJ,!ti•E FT1=FT1 tFTP II I XT1=XT1tXTPIJ) FEW=FTPIIl•EW WRITE CIO,l&Ol J,E,FTP<Il,EW,FEW,XTPIII


C IN PLANE FORGES AND MOMENT AT NODES OF BOTTOM FLANGE G

c

WRITE CI0,1701 XNUL=O. FTZ=O. XTZ=O. DO ItO !=1,3 J=NTBIN,Il IF C J.EQ. 01 GO TO 50 E=WT30l,II XTBIII=SNP(J,!ti•E FTBCII=SNPCJ,!l•E FTZ=FT2+FTaCII XT2=XT2tXT81Il WRITE liO,lbOI J,E,FTBCil,XNUL,XNUL,XTBCII

ItO CONTINUE 50 CONTINUE

C COMPUTE IN PLAi~ FO~CE5 AND MOEMNTS IN WEA ~LEMENTS

c WRITE li0,130l XT3=0. NW:Z N3=NTWIN,31

-123-

LTB 18 LTB 19 LTB 20 LTB 21 LTB 22 LTB 23 LTB Zit LTB 25 LTFI 26 LTB 27 LTB 28 LTB 29 LTB 30 LTB 31 LTB 32 LTB 33 LTB 34 L TB 35 LTB 3& LTB 37 LTB 3A L TB 39 L B ItO LTB '+1 LTB 42 LTB lt3 LTB 44 LTB 45 L TB '+6 LTB ItT LTB 48 LTB 49 L TB 50 LTB 51 LT5 52 LTB 53 LTB 54 LTa 55 LTB 56 LTB 57 LTB SA LTB 59 LTB 60 LTB 61 LTI3 62 LTa 63 LTB 64 LTB 65 LTB o6 LH 67 LTB 66 LTB 69 L TB 70 LTB 71 LTB 72 LTB 73 LTB 74 LT8 75

I I

IF !NJ.EQ.Ol NW=1 LTB 76 DO 10 I=1 9 NW LTB 77 EW=WTWCN,Il LTB 76 K1=2•!I-11 LTB 79 I K11=K1+1 LTB 60 K12=K1+2 LTB 61 J1=NTWCN,K111 LTB 62 J2=NTW(N,K121 LTB 63 I F1=SNPIJ1,71 LTB 8~ F2=SNPCJ2,71 LTB 85 Xl=EW•~1/!F1-F2l LTB 86 X1=A3SCX11 LTB 87 I X2=EW-X1 LTB 86 01=X2+2.•X1/3. LTB 89 D2=X2/3. LTB 90 IF (A3S!FU.LT.A8S(F1-F2tt GO TO 60 LTB 91 Xl=EW LT3 92

I X2=EW LTB 93 D1=0.75•EW LTB 9~ D2=0.25•Ew LTB 95

60 CONTINUE LT9 96 I FTWIK111=.5•Ft•X1 LTB 97 FTWIK121=.5•F2•X2 LTB 96 FEW1=FTWCK111•D1 LTB 99 FEW2=FTWCK121•02 LTB 100 I WRITE II0,160t J1,X1,FTWCK111,D1,FEW1,XNUL LTB 101 WRITE {I0,1601 J2,X2,FTW!K121,02,FEW2,XNUL LTB 102 XT3=XT3+FEW1+FEW2 LTB 103

70 CONTINUE LTB 10~ I C LTB 105 C ADD UP THE MOMENT~ LTB 106 C LTB 107

FT1W=FT1•EW LTB 108 XM9CNI=FT11thXT1+XT2+XT3 LTB 10CJ

I WRITE 1!0 9 1901 N,XMB!NI LTB 1Hl

80 CONTINJE LTB 111 C LTB 112 C COM~UTE ANO PRINT OUT MOMENT PE~CENTAGE LTB 113 I C LTB 11~

SUM=O.O LTB 115 DO 90 N=1,N30X LT3 116 SUM=SUH+XHBINI LTB 117 I

90 CONTINUE LTB 116 WRITE !!0,2001 SUM LTB 119 WRITE 110,2101 LTB 120 WRITE (17,2101 LTB 121 I DO 100 N=1,NBOX LTB 122 PCTCNI=XMBCNI/SUM LTB 123 WRITE <!0,2201 N,XMtHNl,PCTINl LTB 124 WRITE (17,220) N,XMBCNI,PCT!Nl LTB 125

100 CONTINUE LTB 126 I

C LTB 127 C LTB 126

110 FORMAT 1&!41 L TB 129 120 FOR~AT <6F6.01 LTB 130 I 130 FORMAT CSX,•BOX 9EAM NO.•,ISI LTB 131 140 FORMAT (6X,•NOOE•,qx,•EFF. WIDTH•,3X,•IN PLANE FORCES!FXXI•,7x,•HOLTB 132

1MENT ARMCOI•,ax,• FOO X D •,SX,•PLATE MOMENTS•,I/l LTB 133 I -124-

I I I

I I I 150 FORMAT 1/SOX,•TOP FLANGE•,/) LTB 134

160 FOR~AT 15X,I5,5F20.1tl LTB 135 170 FORMAT (/50X,•BOT FLANGE•,II LTB 1J6 180 FORMAT I/50X,•WE8 ELEHENTS•,tl LTB 137

I 190 FORMAT (//5X,•SECTION HOHENT BOX BEAM NO.•,I5,5X,F20.~,//) LTB 138 200 FOR~AT ISX,•TOTAL MOMENT AT SECTION•,sX,F?.O.~I LTB 139 210 FORMAT 1/SX,•MOMENT PERCENTAGE•,t5X,•NOOE•,12X,•MO~ENT•,9X,•PERCENLTB 140

1T/100•,5X,•DF•,Il LTB 141 220 FORMAT 15X,I4,8X,E12.6,8X,E12.61 LTB 142

END l TB 11t3-I I SUBROUTINE PSD11 INTRII PSO 1

C PSO 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • PSO 3 C PSO It C THIS SUBROUTINE COMPUTES THE STRESS RESULTANTS FOR THE PLANE PSO 5 C STRESS ELEMENTS Q8D11 AT THE NODES AND AT THE CENTER PSO 6 C PSD 7 I C • • + • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • •PSD 8 C PSIJ 9 C INPUT PSO 10 C PSD 11 I C DIII CONSTITUTI~E LAW RELATING STRESS-RES TO STRAINS PSD 12 C T=1,6 ELEM~NTS 11,22,33,12,13,23 PSD 13 C XAI41 GLOBAL X-COORDINATES OF NODES PSD !It C YAI41 GLOBAL Y-COOROINATES OF NODES PSD 15 I C R1CII GLOVAL U-~ DISPLACEMENTS AT THE NODES PSO 16 C PSO 17 C OUTi'UT PSD 18 C PSD 19 I C STCI,JJ INT£~NAL STRESS RESULTANTS AT THE CENTER AND AT PSD 20 G THE CORNER NODES PSO 21 G !=1,4 CO~NER NODES PSD 22 C I=5 CENTER NODE PSO 23 C J=1,2,3 NXX,NYY,NXY STRESS RESULTANTS PSO 24 I C PSO 25

COMiON /C300/ JUM1,JUM2,JUM3,JUM4,IN,IO PSD 26 CO~HON /PLSTR/ XAI41,YA(Itl,u(61,SI12,121,R11121,STI5,31 PSO 27

C PSD 28 I DIMENSION Pt~,21, 0C(It,21, At2,2l, ETAI21, IPERMC2J, ITI5), AXC51,PSD 29

1 AYI5J, X14l, YC41, 0!5181, Ul4l, Vl41 PSO 30 C PSO 31

EQUI~ALENCE IA11,AI111, U21,Al21), tA12,AtJII, IA22,At41J PSO 32 I C PSO 33

DATA OGI-1.,1.,1.,-1.,-1.,-1.,1.,1./ PSD 34 8ATA AX/0.,-1.,1.,1.,-1./ PSO 35 DATA AY/0.,-1.,-1.,1.,1.1 PSO 36 I DATA IT/5 1 1 1 2,3,4/,IPERM/2,1/ PSO 37

c ~so 38

I C INITIALIZATION PSO 39 C P$0 40

0010 J=1,3 PSO 41 DO 10 I=1,5 ~S~ 42

10 ST(I,JI=O.O PSO 43 EXY=O. PSO 44

C PSD ItS I -125-

I I I

C TRANSFORMATION INTO LOCAL CONVECTED COORDINATES c

c

DX=XA 121-XA I U DY=YAC21-YACU AL=SQRTCDX••2+0Y••21 CO=OXIAL SI=OY/AL DO 20 I=1,1t XIII=IXACII-XAC1)1•CO+CYAIII-YAI111•SI

20 YCII=-CXACII-XAUII•SI+CYAUI-YA<lii•CO cc=Co•co SS=SI•SI SC=5P·CO DO JO I=l,lt I2=Itl 11=!2-1 DISII11=R11I11•CO+R1CI21•SI

30 DISCI21=-R1CI11"'SI+R1CI21•CO

C COMPUTE STRESS RESULTA~T AT SAMPLING POINTS c

c

DO 100 II=1,5 JJ=ITIIII IF III.GT.1.ANO.NTRI.EQ.31 GO TO 110 ETA lti=AX (Il) E1AI21=AYIIII

C FO~MATION OF lOCAL DERIVATIVES c

00 50 I=1 '2 J=IPERM <I I AII,ti=O. A<I,21=u. DO ItO L=1,1t C=0.250•occL,II•C1.0+0C<L,JI•ETAIJII PIL.II=C AII,11=AII,11+C•Xtll

40 AII,21=ACI,21+C"'YILI 50 CONTINUE

OET=A1t•A22-A12•A21 IF IDET.GT.O.OI GO TO 50 WRITE (I0,11t01 OET,ETAUI,EiAI21 WRITE II0,1501 WRITE 110,1601 lXlii ,Y(JI .I=1,1tl

c C FORMATION OF GLJSAL DERIVATIVES c

c

60 DO 70 J=1,4 UIJl=A22"'PIJ,11-A12•P(J 9 21

70 VIJI=-A21"'P(J,11+A11"'PIJ,21

C DETERMINATION OF STRESS RESULTANTS AT NODES AND CENTER c

XX=O.O YY=O.O ZZ=O.O DO CIO I=1,1t K=I+I

-126-

PSD lt6 PSD lt7 PSD lt8 PSD lt9 PSO 50 PSO 51 PSD 52 PSD 53 PSD 54 PSD 55 PSD 56 PSD 57 PSO 58 PSD 59 PSD 60 PSD &1 PSD 62 PSD 63 PSD 64 PSD b5 PSD 66 PSD 67 PSQ 68 PSD 69 PSD 70 PSD 71 PSO 72 PSD 73 PSO 74 PSD 75 PSO 76 PSD 77 PSD 78 PSD 7CI PSD 80 PSO 81 PSD 82 PSD 83 PSO 81t PSD 85 fJSD 86 PSO 87 PSO 88 PSD 89 PSD 90 PSO 91 PSO 92 PSD 93 PSD ·94 PSD 95 PSD 96 PSD 97 PSD 98 PSD 9q PSD 100 PSD 101 fJSD 102 PSD 103


I I I I I I I·


c c c

c c c

c c

c c c c c c c

c

c

c

c

c c c c c

J=K-1 IF III.NE.11 GO TO 80 EX~=EX~+IVIIJ•OISIJI+UIIJ•OISIKII/OET

80 XX=XX+DI1J•U!IJ•OISIJJ+OI4J•VCIJ•OIS!KI YY=YY+D14t•UCIJ•OISIJI+DI2J•~IIJ•DISCKI ZZ=ZZ+OI51•UIIJ•DISIJI+OI61•VCIJ•OIS!Kl

PSD PSD PSO PSD PSO PSO PSD PSO PSD PSO PSO PSD PSD PSD PSD PSO ?SO PSO

90 CONTINUE SXX=XX!OET+OC51•EXY SYY=YY/DET+Dioi•EXY SXY=ZZ/DET+DI31•EXY

100

110

120 130

TRANSFORM STRESS RESULTANTS INTO GLOBAL COORDINATES

srcJJ,11=sxx•cc•svv•ss-2.o•sxv•sc STIJJ,21=SXX•SS+SYY•CC+2.0•SxY•sc STCJJ,31=1SXX-SYYJ•SC+SXY•CCC-SSI CONTINUE IF INTRI.NE.Jl GO TO 130

DETERMINATION OF NODAL STRESSES FOR CONSTANT STRAIN TR~ANGLE

DO 120 I=1,4 DO 120 J=1, 3 ST!I,Jl=STI5,JI RETURN

PSD PSO ?SO ?SO PSD PSD PSO PSO PSIJ

1~0 FORMAT 1//JOH DETERMINANT OF JACOBIAN tE15.51,30H AT LOCATION Y

,II

SAMPLING ATPSD 1 LOCATION X ,E15.51,30H SAMPLING

150 FORMAT I//30H ELEMENT COORDINATES 1&0 FORMAT 110X,2E15.51

END

,E1S.51PSD PSO PSD PSO

SUB~OUTINE FPLATE INTRII FPL FPL

• • • • + • • • • • • • • • + + • • • • • • + • • • • • • • • • • FPL FPL

INTER~AL STRESS SU5ROUTINE FOR PLATE 3ENDING ELEMENT FPL FPL

• • • • • • • • • • • • • • • • • • • • • • • • • • + • • • • • + FPL FPL

COMM0:-.1 /T~IAG/ 3131 ,AIJI ,CMTC3,Jl ,TH131 ,CVTn,JJ,STU2,12J,RU21 FPL FPL

COMI'lON /PLBOG/ 1191

X ( 5 l , Y I 51 , C M I 3, 3 l , PI 5 l , tlM I 3, 51 , C VI 3, 51 , S I 19,19 J , fU IF PL

DIMENSION IPERM141, NC(JJ, FACI3l

LOGIC!lL TRIG

DATA IPERM/2,3,4,1/,FAC/.5,.5,.25/

DEFINITIONS CMI3,31 Xl41 y 141

CONSTITUTIVE LAW RELATING MOMENTS TO CURVATURE GLOBAL X-COORDINATES OF ~ODES GLOBAL Y-COOROINATES OF NODES

-127-

FPL FPL F?L FPL FPL FPL FPL FPL FPL FPL FPL FPL

101t 105 10& 107 108 109 110 111 112 113 11ft 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 13,. 135-

1 2 J 4 5 & 7 8 9

10 11 12 13 14 15 16 17 18 1CJ 20 21 22 23

c c c c c c

c c c

c c c

c c c

Plltl BN (I ,J) I=1,3 J=1,4 J=5

NODAL LOAD INTENSITIES OF DISTRIBUTED LOADS INTERNAL MOHENTS AT CORNER ANO AT CENTER NODES MXX,MYY,MXY MOMENT COHPONENETS

DO 10 I=1,3 DO 10 J=1,5

CORNER NODES CENTER NODE

10 cvn,JI=o.o TRIG=NTRI.EQ.t IF <TRIG) GO TO 20 NBF=11 L1=13 L2=19 GO TO 3U

20 NBF=9 L1=10 L2=15

RECOVER OIS?LACEMENTS FOR OOF ELIMINATED BY STATIC CONDEN5ATION

3G 00 40 L=Lt,L2 M=L-1 00 40 K=1,M

40 R1CLI=R1CLI-S!K,LI•Rt!KI

PREPARE INPUT FOR MOMENT CALCULATION OF EACH LCCT TRIANGLE

NC !31 =N3F-6 00 50 I=1,3

50 BIH=O. DO 100 N=1,NTRI M=IPERMINI NCI11=N NCI21=M L=NC<31 AI11=X!LI-XIHI Al2l=XI~l-XIU Al3l :X(:-11-X IN) Blti=YIMI-Yill 8<21 =YIU-Y INI BI31=YINI-YIMI IF I TRIG I GO TO 70 DO &0 K=1 ,3 KI=3•!N-11+K KJ=J•tM-1,.K RIKI=RtiKII RIK+3l=R1CKJI

bO RIK+ol=R1CK+121 R I 1 Dl =~ 1 (11+151 RI111=-R11N+151 GO T 0 9 0

70 DO tlO I=1,9 80 RIIl=R11II 90 CALL FLGCT INBFI

ACCUMULATE AND AVERAGE CURVATU~E AT THE NODES

-128-

FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL FPL

Zit 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Jq 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6& 67 b8 69 70 71 72 73 74 75 76 77 78 79 80 81



c

00 100 J=1.3 L=NCIJI C=FACIJI IF I T RI G I G = 1 • DO 100 I= 1, 3

100 CIIII,U=CIJU,Ll +C•CIJT II,JI

C DETERMINE INTERNAL MOMENTS AT NODES AND CENTER OF ELEMENT

FPL 82 FPL 83 FPL 84 FPL 85 FPL 86 FPL 87 FPL 88 FPL 89 FPL 90 FPL 'H FPL 92 FPL 93 FPL 94 FPL 95 FPL 96-

c

c c c c c c c c c

c

G c c

c c c c c

DO 110 K=1,5 C=PIKIH3/12. DO 110 1=1, 3

110 BMII,KI=C•ICMII,1l•CIJI1,KI+CMCI,ZI•CIII2,Kl+CMII,31•CIJI3,Kll RETURN END

SUB~OUTIN€ REA~F IOISPI dEA 1 BEA 2

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • BEA 3 an 1t

THIS SUBROUTINE COMPUTES THE BEAM NODAL FORCES GillEN THE GLOGAL SEA 5 NODAL DISPLACEMENTS. THE d~AM STIFFNESS MATRIX IS STORED BEA 6 IN ~S1 TO dSit AS 4-5X5 SUBMATRICES. SEA 7

BEA 8 • • • • • • • • • • • 4 • • • • • • • • • • • • • • • • • • • • • 3EA q

BEA 10 COMMON /CdOO/ JUM1,JU~2,JUM3,JUMit,IN,IO BEA 11 COMMON /CB01/ NUHEL,NUMNP,NUMBC,NMAT,NLCS,NN,MM,NPSEGM BEA 12 COMMON /PLBDGI XI51,YI51,DMI3,31,PPI5l,BMI3,5l,CVI3,51,SPBU9,191,!3EA 13

1VAt191 BEA 14 COMMON /ONODE/ NI~NK BEA 15 COMMON /BFOR/ F"XX(21 ,F'f'YI21 ,FZI21 ,F.<I21 ,FYI21 BEA 16 COMMON /BPROPI 31,82,~3,8~ oEA 17

SEA 16 0I11ENSIOill ESXI1), ASXIU, SSX11l, XLENGTHI11, EIXI!), GKEIX111, OIBEA 19

1SP1201, 93115,51, B$215,51, BS315,51, BSitl5,51 '3EA 20 BEA 21

DEFINE )EAM PROPERTIES SEA 22 BEA 23

E~XI11=DM111 BEA 24 ASXI1l=PPtltl BEA 25 ECC=PP(31 SEA 26 SSXI11=ASXI11•ECC BEA 27 EIXI11=PPI11+ASXI11•ECC•ECC BEA 28 GK£IXI1l=PPI21•0MI91/0M(11 3EA 29

BEA 30 TRANSFORM GLOBAL DISPLACEMENTS TO LOCAL COORDINATES BEA 31

BEA J2 IN PLANE TRANSFORMATION 6EA 33

BEA 34 A=XC21-JC(1l BEA 35 B=YI21-'((1) SEA 36 XL2=A•A+a•a XL=SQRTCXL2l XLENGTH11l=XL CN=I\/XL

-129-

dEA 37 BEA 38 3£A 39 BEA 40

c c c

c c c

c c c

SN=8/XL IF CCN.EQ.1.l GO TO 30 00 10 J=2,7,5 D1=DISP <J-11 02=DISP(Jl DISPCJ-1J=D1•C~+D2•SN

10 OIS~(JJ=02•CN-D1•SN

BENDING ANO TO~SION TRANSFORMATION

DO 20 J=5,10,5 01=0ISP <J-U 02=DISPCJl DISP(J-1J=01•CN+D2•SN

20 OIS~IJl=02•CN-01•SN 30 CONTINUE

INITIALIZE 8S1 TO BS4.

DO It 0 I= 1, 5 00 itO J=1,5 BS1CI.Jl=O.O BS2CI,JJ=O.O BSJ<I,Jl=O.O 8Sit II,Jl =!I. 0

ItO CONTINUE

COMPUTE THE NON-ZERO ELEMENTS OF THE BEAM ELEMENT STI~FNESS

N=1 8~111t1l=ASXCNI•XLENGTHINI••z BS1C1,5l=S5X(Nl•XLENGTH1Nl••2 SS113,3l=12.•EIXCNJ BS113,5l=-&.•EIXCNI•XL£NGTHCNl BS1Cit,ltl=GKEIXINl•XLENGTHINI••2 85115,1l=SSXCNt•XLENGTHCNl••2 8S115,3l=-&.•F.IXCNl•XLENGTHINI 8~1(5,5J=4.•EIXINt•XLENGTHINl••z BS211,1l=-ASXINl•XLENGTHCNl••z 85211,51=-5SXINI•XLENGTHCNI••z BS213,3l=-12.•EIXINJ 8~2(3 1 5l=-6.•EIXCNJ•XLENGTHINl 8521ft,ltl=-GKEIXINI•XLENGTHINJ••2 852(5,11=-SSXINJ•XLENGTHtNJ••z 952Cj,Jl=6.•EIXCNI•XLENGTHINl B5215,51=2.•EIXINJ•XLENGTHINl••z BS1tl1,1l=ASXINI•XLENGTH(NJ••2 B5411,51=S5XINI•XLENGTHINl••2 8Sitl3,3l=12.•EIXCNl BSitC3,51=6.•EIXCNl•XLENGTHCNl BS414,1tl=GKEIXCNI•XLENGTHCNI••? BS415,11=SSXINI•XLENGTHCNt••2 BS415,3l=S.•EIXINI•XLENGTHINI dS4(5,51=4.•EIXINI•XLENGTHCNt••z DO :>il !=1,5 DO 50 J=1,5

50 BS31I,Jl=B52CJ,Il ZFAC=ESXINl/IXLENGTH(Nl••3l

-130-

SEA SEA BEA 3EA SEA SEA IJEA SEA BEA BEA SEA SEA SEA BEA BEA i3EA SEA BEA !JEA SEA BEA 3EA SEA 3EA SEA SEA SEA

HATRI X3EA SEA BEA BEA 3EA BEA BEA BEA 9EA BEA BEA BEA BEA ilEA BEA 9EA BEA 8EA 9EA 3EA SEA IJEA BEA BEA SEA BEA 3EA SEA !3EA BEA BEA

41 42 ftJ 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 &5 66 &1 58 69 70 71 72 73 74 75 16 77 78 79 80 81 82 83 84 85 86 87 d8 1i9 90 91 92 93 94 95 96 97 98



c

DO & 0 I =1, 5 oo &0 J=1,5 dS11I,JI=ZFAC•3S11I,JI BS21I,JI=ZFAC•BS2(I,JI BS31I,JI=ZFAC•BS31I,JI BS~II,JI=ZFAC•BS41I,Jl

60 CONTINUE 11=0 K1=5

C COMPUTE FORCES AT NODE I !LEFT ENOl. UNITS ARE KIPS AND KIP-IN.

BEA 99 BEA 100 6EA 101 BEA 102 BEA 101 ilEA 104 BEA 105 BEA 106 BEA 107 BEA 108 BEA 109 BEA 110 SEA 111 BEA 112 BEA 113 BEll 11 .. BEA 115 dEA 11& BEA 117 BEA 118 BEA 119 dEA 120 BEA 121 BEA 122 BEA 123 BEA 124 BEA 125 BEA 126 aEA 127 BEA 128 9EA 129 BEA 130 tJEA 131 BEA 132 BEA 133 SEA 13ft BEA 135 BEA 136 BEA 137 BEA 138 BEA 139 SEA 140 BEA 141 dEA 142 BEA 143 BEA 144 BEA 145 BEA 14&-

c I=1 FXXIIJ=O. FYYIII=O. FZIII=O.O FXIII=O.O FYIII=O.O 00 70 II=1,5 FXXIII=FXXIII+BS111,III•DISPII1+III+BS2!1,III•OISPIK1+III FYYIII=FYYIII+B$1(2,III•OI~P(I1+lll+BS212,III•DISPCK1+Ill

FZIII=FZIII+BS1!3,IIl•JISPI11+III+BS213,Ill•OISPCK1+III FXIII=FXCII+9S114,1II•DISPCl1+1Il+BS2!4,IIl•DISPCK1+1II FYIIl=FYIII+OS115,IIl•DISPII1+IIl+SS2!5,III•OISPIK1+IIJ

70 CONTINUE c C COMPUTE FORGES AT NODE K !RIGHT ENOl. UNITS ARE KIPS AND KIP-IN. C

C c

c C c c c C

K=2 FXXIKI=O. FYY(KI=O. FZIKl=O.O FXIKI=O.O FYIKI=O.O DO 80 II=1,5 FXXIKI=FXX1Kl+BS311,III•OISPCI1+II1+8S~C1,III•OISPCK1+1II

FYYIKI=FYYIKI+aS3!2,IIl•OISPII1+IIl+BS412,III•OISPIK1+III FZIKl=FZtKI+dS313,III•OISPII1+III+3S413,III•DISPIK1+1II FXIKl=FXIKI+8S314,III•OISPII1+III+BS41~,III•DISPCK1+III

FYIKI=FY(KI+BS315,Ill•DISPII1+II1+8S415,III•DISPCK1+III 60 CONTINUE

WRITE CI0,90l NI,FXXC1l,FY'f(11,FZI11,FXtli,FYI1l WRITE 1!0,901 NK,FXXI21,FYYI21,FZ12l,FXC21,FYI21 RETURN

90 FORMAT 11H0,24X,•NOOE•,I5,511PE17.511 END

SUBROUTINE ?LSP12 PLS PL:i

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •PLS PLS

THIS SUBROUTINE DETERMINES THE STRESS RESULTANTS AT THE NODES ANO PLS AT THE GENTtR OF THE PLANE STRESS ELEMENT QUSP12 PLS

PLS -131-

1 2 3 4 5 6 7

c c c c c c c c c c c c r. c c c c c c G c c c c

c

c

c

c

c

THIS R~UTINE FROM REFERENCE 2 PLS PLS PLS

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •PLS

INPUT

10 U I I=1,6 XORD IU YORDIII VI II 1=1,4 1=5,8 I='l,12 R=.TRUE.

OUTPUT

CONSTITUTIVE LAW RELATING STRESS TO STRAINS ELEMENTS 11t22,J3,12,10,23 OF DIIJ LOCAL X COORDINATES OF NODES LOCAL Y-COOROINATES OF NODES DISPLACEMENT VECTOK U OISPILS,RS,RT,LTI V OISPL(ld,RB,RT,LTl 0 ROTATIONS OV/OXILd,~d,RT,LTI ROTATIONS HAVE BEEN ELIMINATED 8Y STAT CONO.

fiLS PLS PLS PLS fiLS PLS PLS PLS fiLS PLS PLS PLS IlLS PLS PLS

ST(!,JI I=1,4 I=5

INTERNAL STRESS RESULTANTS AT CORNER NODES

CORNERS AND CENTER NOOEPLS

CENTER NOOE NXX,NYY,NXY STRESS ~ESULTANTS

COMMON /C~O~/ JUM1,JUM2,JUMJ,JUM4,IN,IO COMMON /PLSTR/ XORD1fti,YORDI41,0(61,SI12,121,VU2l,STIS,31

PLS PL5 PLS PLS PLS PLS PLS

DIMENSION EXX(ftt, EYY(81, EXYPtl, EYXI81, I/XI8J, 1/V'CtU, XU!tl, X21PLS 141, YU!tl, Y2141, FT114t, FT214t, FX411tl, FY4(41, FXCitl, FYI41, AXPLS 2 I 51 , A Y I 51, IT E ( 21 , IT A I 41 , IT I I It l PL S

EQUIVALENCE IFX,XU, IFY,YU, IEXX,X21, IEXY,Y21

LOGICAL R

DATA AXI-1.0,1.0,1.0,-1.0,0.0/ DATA AYI-t.il,-1.0,1.0,1.0,0.0/ DATA FY'+I-1.,-1.0,1.0,1.01,FX41-1.0,1.0,1.0,-1.0/ DATA ITE/1,~/,ITA/1,2,2,1/,ITI/~,3,3,4/

C INITIALIZATION

PLS J>LS PLS PLS PLS IlLS I'LS PLS PLS fiLS PLS PLS PLS PLS PLS PLS PLS PLS fiLS PLS PLS PU PLS PLS PLS PLS PLS PLS

c

c

R=.FALSE. DO 10 J=1,3 00 10 I=1,5

10 STII,Jl=O.O

C GEOMETRICAL TRANSFORMATION OG QUADRILATERAL qQUNDARIES c

IF <.NOT.Rl GO TO 30 c C RECOVER ROTATIONS AT CP c

00 20 L='l,12 M=L-1 DO 20 K=1,M

20 VILI=V(Ll-SIK,Ll•VIKJ 30 X1111::0.5•1xuROI2l-XORDI1)1

-132-

I I

8 q I 10

11 12 13 I 14 15 16 17

I 18 1'l 20 21

I 22 23 2ft 25 26 I 27 28 2'l 30 I 31 32 JJ 3Lt

I 35 36 37 38

I JCj 40 ft1 42 43 I 4ft '+5 46 47 I 48 49 50 51

I 52 53 54 55

I 56 57 58 59

I 60 61 62 63 64 I 65

I I I


G

X1(3t=O.S•<XORD<3t-XOR0<4tt X1121=X1(11 X1 (It) =X1 ( 31 Y1(1l=O.S•tYOR0(21-YOR0<111 Y1(3I=O.S•(YORO(JI-YORDf411 Y1C21=Y1CU Y1Citi=Y1C31 X2f1t=O.S•(XOR0f41-XOR0(111 X2(2l=0.5•(XQRO(JI-XORD(211 X2C31=X2121 X2 (4) =X2 HI Y2(1l=O.S•(YOR0(4t-YOR0(111 Y2(2l=0.5•1YOROI31-YOR0(211 Y21JI=Y2t21 Y2(1ti=Y2(11 DO ItO 1=1 ,It OET=X1fit•Y21II-Y1fii•X2fii FCT=OET+X2(II•Yt(II FT1<II=Y1(II•X1(It/2.0/FCT

ItO FT21II=X11I1•(1.0-Y1(II•XZIIJ/FCTI DO 130 II=1,5 X=AXIIIl Y=AY (I! I XA=x•x X3=XA•X

C FORMATION OF LOCAL OERI~ATI~ES

c

c

DO 50 !=1,4 FX(II=0.25•FXItiii•I1.0+FY41IJ•YI

50 FY(IJ=0.25•FY41II•(1.0+FX4(IJ•XI

G FORMATION OF JACOBIAN TRANSFORMATION MATRIX G

c

X11=0. X22=0. X12=0. X21=0• 00 o!l I=l,lt X11=X11+FXIII•XOROIII X22=X22+FYIII•YOROIII X12=X12+FXIII•YORDIII

60 X21=X21+FYCII•XOR~III

C CALCULATION OF JACOaiAN DETE~MINANT c

c

OET=(X11•X22-X12•X211 IF WET.GT.O.OI GO TO 70 WRITE 1!0,1401 OEr,X,Y WRITE ( IO ,150 I WRITE (10,1601 (XOROtiJ,YORO(It,I=t,ltl GO TO 130

C FORMATION OF LOCAL DERIVATI~ES

c 70 DO 80 1=1,4

VYCII=0.125•FY41I1•!2.0+J.O•FXItiii•X-FX41II•XBI VX(II=O.J75•(1.0+FY4Cll•YI•(FX4(II-FX4(li•XAI

-133-

PLS 6& PLS 67 PLS 68 PLS 69 PLS 70 PLS 71 PlS 72 PLS 73 PLS 7ft PLS 75 PLS 76 PLS 77 PLS 78 PLS 79 PLS 60 PLS 81 PLS 82 PLS 83. PLS 84 PLS 65 PLS 86 PLS 87 PLS 88 PLS 89 PLS 90 PLS 91 PLS 92 PLS 93 PLS 91t PLS 95 PLS 96 PLS 97 PLS 98 PLS 99 PL S 10 0 PLS 101 PLS 102 PLS 101 PLS 104 PLS 105 PLS 106 PLS 107 PLS 108 PLS 109 PLS 110 PLS 111 PLS 112 PLS 113 PLS 114 PLS 115 PLS 116 PLS 117 PLS 118 PLS 119 PLS 120 PLS 121 PLS 122 PLS 123

vYII+~I=0.125•FY4CII•!-FX41II-X+FX4(II•XA+X81 PLS 124 SO ~X(I+41=0.125•!1.0+FY41II•YI•C-1.0+2.0•FX4CII•X+3.0•XAI ~LS 125

C PLS 12& C FORMATION OF OERI~ATI~ES IN GLOBAL COORDINATES PLS 127 C PLS 128

DO 90 I=1,4 ~LS 129 EXXIII=X22•FX!Il-X12•FY!Il PLS 130

90 EXYIII=-X21•FXIIJ+X11•FVCII PLS 131 DO 100 1=1,4 PLS 132 K=IlAIII PLS 133 J =IT I I I I PL S 13ft AA=~XIII+FV41II•FT11KI•VXIK+41+FY41II•~T11JI•VXIJ+41 PLS 135 dB=~Yili+FV41IJ•FT1CKI•~YIK+4l+FY4(II•FT11Jt•~Y(J+41 PLS 13& E~YII+41=-X21•FT21Il•~X(I+41+X11•FT21II•VYII+41 ~LS 137 EYXII+41=X22•FT21II•VXII+41-X12•FT21Il•VY(I+41 PLS 138 EYYIII=-X21•AA+X11•~B PLS 139

100 EYXIII=X22•AA-X12•BR ?LS 140 C PLS 141 C COHPUfATION OF NODAL POINT STRESSES PLS 142 C PLS 143

XX=O.O PLS 144 n = o. a ~L s 145 ZZ=O.O PLS 14& 00 110 I=1,4 PLS 147 XX=XX+OI11•EXXIII•VIli+OISI•EXYIII•~(Il PLS 148 YY=YYt0141•EXXIII•~III+OI6l•EXYIII•VIll PLS 149

110 ZZ=ZZ+~ISI•EXXIII•V.III+OIJI•EXYIII•V!II PLS 150 DO 120 I=1,8 PLS 151 XX=XX+Ol41•EYYIII•~II+41+DC51•EYXIII•VII+41 ~LS 152 YY=YY+DI2l•EYYIII•~II+41+D(61•EYXIIJ•VII+4l PLS 153

12C Zl=ZZ+OI&l•EYYIII•V!I+4I+DI31•£YXIII•VCI+~l PLS 15~ STIII,11=XX/DET PLS 155 STIII,21=YY/OET PLS 156 STCII,31=ZZIDET PLS 157

130 CONTINUE PLS 158 RETURN PLS 159

C PLS 160 C PL S 161

c c c G c c c c c

140 FORMAT 11/JOH DETERMINANT OF JACOBIAN E15.5/30H OUTPUT AT LOCPLS 162 tATION X E15.S/30H OUTPUT AT LOCATION Y £15.51/1 PLS 163

150 FORMAT (/130H ELEMENTS COORDINATES II PLS 164 100 FORNAT <10X,2E15.5l PLS 105

£NO PLS toG-

SU3~0UTINE FO~E~ FNW FNW

.. + ..... ... .. . ...... • • + 4 ~ • • • + + 4 + • + • • • • • • •FNW FN~

THIS SUBROUTINE COMPUTES THE MY-MO~ENTS WAY BENDING IN THE Y- DIRECTION. INPUT THIS ROUTINE IS FROM REFEqENCf 2

AT EACH NODE ASSUMING ONE FNW AND OUTPUT SAME A FPLATE. FNW

FNW FNW

• • + • • + + + • • + • • + • • • + + • • • 4 • • • + • • • • • •FNW FNW

COMMON I PL :30 G/ X (51 , Y I 51 , C M I 3 ,31 , PI 5 l , 3M ( 3 • '5 l , C ~ ( 3, 51 , S ( 1 g, 1 g I , P ( 1F NW 1 g I F NW

-134-

1 2 3 It 5 6 7 8 q

10 11 12

I I I I I I I I I I I I I I I

I I I

I

I I I I I I I I I I I I I I

c

c

c c c

c c c

c c c c c c c c

c

c

c

DIMENSION FA(!t,21, ITE!!tt, ILE<Itl, IP£(21, FBlltl, FC!'tt

DATA FA/-J.0,-4.0,J.0,-2.0,3.0,2.0,-J.0,4.0/ DATA ITE/1,2,10,11/,IlE/4,5,7,8/,IPE/1,4/

INITIALIZATION

DO 10 I =1, 3 DO 10 J =1, 5

1 0 aM (I , J I = 0 • 0 FCT=C:-1!1,1tl2.0 FCT=FCT•P!11••3t12. XL= I Y ( 4 I - Y { 111 /2. 0 XR=tY(31-Y!211/2.0 FAC=0.25•(X!21-X(11+X(31-X(411

DETERMINE HY MOMENTS AT NODES ASSUMING q£AH BEHAVIOR

DO 50 I=1,2 DO 20 J=1,3,2 F3!JI=FA!J,II/Xl/XL

20 FC(Jl=FA(J,II/XR/XR DO 30 J=2,4,2 FB(JI=FA<J,II/XL

30 FC!JI=FA(J,II/XR IA=IPE!Il I6=I+1 SUM=O.O SUN=O.O DO 40 J=1,4 JA=ITEIJI JB=ILE!JI SUM=SUH+FB!JI•~(JAt

40 SUN=SUN+FC!JI•~<JSt

aMI2,IAI=FCT•SuM•FAC B~<Z,ISI=FCT•SuN•FAC

50 CONTINUE RETURN END

SUBROUTINE FLCCT <Nqfl

•••••••••••••••••••••••••••••••••• THIS SU3ROUTINE COMPUTES CURVATURES FOR A LCCT TRIANGLE WITH NaF SENDING DEGREES OF FREEDOM <NBF=9,10,11,121

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • COMMO~ /TRIAG/ BIJI,A!JI,CMTIJ,JI,TH<JI,CVT<J,Jl,ST(12t121,R<121

DIMENSION U!211, Q(3,61, HT<JI, TX(JI, TY(J), IPERMI31, NKNI2,31

DATA I~ERM/2,3,1/,NKN/2,5,S,2,5,8/

-135-

FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNH FNW FNW FN_. FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW FNW

FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC FLC

13 11t 15 16 11 18 19 20 21 22 23 2 .. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52-

1 2 3 4 5 6 7 8 g

10 11 12 13 14 15

C INITIALIZATION c

c

AREA=A!3t•B!21-A(21•8!3t DO 10 1=1,3 J=IPERH !II X=A!II••z•BIII••z UIII=-IAIII•AIJl•S!It•B!J)I/X X=SQRT!Xl T X U I= 0. 5• A (I I I X TY!II=-0.5•B!II/X HT!II=~·O•AREA/X A1=A!II/AREA Bt=B CU /AREA A2=A I Jl /AREA 92=8!Jl/AREA Q!1tii=at•at QI2,II=A1•At Q13.I1=2.•AP·81 oct,I•31=2.•s1•az Q!2,I•3l=2.•At•A2 Qt3,I•31=2.•!A1•sz•A2•31l

10 CONTINUE

C RECO~ER DISPLACEMENTS FOR OOF ELIMINATED SV KINEMATIC CONDITION c

c

M=12-NBF IF I H. L E. 0 l GO T 0 3 0 DO 20 N=1,M K=13-N l1=NKN!t,NI L2=N'<N!2,NI

20 RIKI=IRIL11•RIL211•TX!K-91•1R!l1+11•R!L2HII•TY!K-91

C DETERMINE CURVATURES AT THE NODES c

30 DO LtO I=1 ,3 J=IPER.M <I I K=IPERMIJI II=3•I JJ=3•J KK=3•K A2=A I Jl A.J=A!KI B2=8!Jl 83=8110 U2=U (Jl U3=U!KI W2=1.-U2 W3=1.-U3 C21=-12.+W21•B2-!2.+U31•B3 C22=!32"W2-93"UJ C31=-!2.•W2l•A2-(2.+U31•A3 C32=A2•W2-A3•U3 C51=4.•a3-92•BJ•W3 C52=B2-B3•W3 C61=4.•A3-A2•A3•W~ C&2;:A2-A3•W3 CB1=B3-~.·sz-az•uz

-136-

I I

FLC 16

I FLC 17 FLC 16 FLC 19 FLC 20 FLC 21 I FLC 22 FLC 23 FLC 24 FLC 25

I FLC 26 FLC 21 FLC 28 FLC 29


I FLC 34 FLC 35 FLC 36 FLC 37 FLC 38 I FLC 39 FLC 40 FLC 41 FLC 42

I FLC 43 FLC ft4 FLC '+5 FLC 46

I FLC 47 FLC 48 FLC 49 FLC so

I FLC 51 FLC 52 FLC 53 FLC 54 FLC 55 I FLC 56 FLC 57 FLC 58 FLC 59 I FLC 60 FLC 61 FlC 62 FLC &3


I FLC 68 FLC 69 FLC 70 FLC 71 FLC 72 I FLC 73

I I I


C82=32•U2-a3 FLC 74 C91=A3-4.•A2-A2•U2 FLC 75 C92=A2•U2-A3 FLC 76 DO 40 N=1,3 FLC 77 Q11=QIN,II FLC 78 Q22=QIN,JI FL~ 79 Q33=QIN,KI FLC 80 Q12=Q<N,I+31 FLC 81 023=QIN,J+31 FLC 82 Q31=~<N,K+31 FLC 83 Q1=Q22-Q33 FLC 84 Q2=Q22-l23 FLC 85 Q3=133-J23 FLC 86 Q~=Q23+Q1 FLC A7 Q5=Q23-Q1 FLC 88 CVTIN,II=I-o.•Q11+3.•1(U3-W21•Q1+1U3+W2l•Q23li•R<II-21+!6.•Q22+3.•FLC 89 1w3•Q41•~(JJ-21+16.•Q33+J.•uz•051•R<KK-21+((C21•Q1+C22•Q23+4.•CB2•QFLC 90 231-33•Q1211•~1II-11+1C31•Q1+C32•Q21+4.•<A2•QJ1-A3•Q12li•R<III+IC51FLC 91 3•Q22+C52•Q31•R!JJ-11+1G&1•Q22+C62•Q31•R!JJI+(C81•Q33+C82•Q21•RIKK-FLC 92 41l+IC91•Q3l+C92•Qzi•R<KKI+HTIKI•Q4•RIK+9l+HTIJI•Q5•R!J+911/2. FLC 93

40 CONTINUE FLC 94 RETURN FLC 95 END FLC 96-

SUB'{OUTIN£ POIR CX,XP,All POI 1 C POI 2 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • POI 3 G POI 4 C THIS SU3ROUTINE GOHPUTES P~INCI~AL VALUES AND DIRECTIONS POI 5 C OF A TWO-DIMENSIONAL TENSOR POI 6 C POI 7 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • POI 8 C IJOI 9

DIMENSION Xl31, XPIJI POI 10 C POI 11

DIF=0.5•1XI11-XI?ll POI 12 XY=X 131 IJOI 13 IF IXYI 10,20,10 POI 11t

10 A1=28.&~78897•ATAN21XY,OIFI POI 15 R=SQ~TIDIF••Z+XY••21 POI 16 GO TO Jil POI 17

20 A1=0. POI 18 IF IDIF.LT.ll.l A1=90. POI 19 R=AuSCDIFI POI 20

Jll C=0.5•(X(11+XI2ll POI 21 XPI11=C+R POI 22 XP121=G-~ POI 23 XP131=~ IJOI 24 ROURN POI 25 END POI 26-

OVE~LAY IPLATE,6,01 FTR 1 C FTB 2

PROGRAH FORT6 FT8 3 -137-

C FTB It C • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • •FTB 5 C •FTB 6 C THIS PROGRAM COMPUTES AND RESETS THE FIELD LENGTH FOR PLOTTING •FTB 7 C OR LATE~AL LOAD OISTRiaUTION COMPUTATIO~ IF nESIREO •FTB 8 C •FTB 9 C • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •FTB 10 C FTB 11

COMMON /CBOO/ JUH1,JUH2,JUH3,JUH4,IN,IO FTB 12 COMMON /CB01/ NUHEL,NUMNP 1 NUHBC,NMAT,NLCS 1 NN,MM,NPSEGH FTB 13 COMMON /SOL~/ NA1,LWIDTH,NFREE,NA5,LAMA,ISEGM,JUH5,JUM&,JUM7,JUM8 FTB 14 COMMON /HEAD/ HEAD1f13t,HEAD2113t,QEQ FTB 15 COMMON /TITLE/ TITELC10t FTB 16 COMMON /NFB/ NUMB,NNO,NSN FTB 17 COMMON /PLTS/ NTOTP,NBP,NGPH FTS 18 COMMON AUt FTB 19

C FTB 20 NSP=O FTB 21 NGPH=O FTB 22

10 CONTINUE FTB 23 NTOTP=NU~NP+NUMEL FTB 24 N1=1 FTB 25 N2=N1+~•NUMEL FTB 26 N3=N2+NUMEL FTB 27 N~=N3+NUMNP FT6 28 N5=N4+NUMNP FTB 29 N6=N5+NTOTP FTB 30 N6=N5+NTOTP FTB 31 N7=N6+NBP FTB 32 N8=N7+NGPH FTB 33 N9=N8+NUMEL•12 FTB 34 N10=N9+NUMNP•o FTB 35 N11=N10+NUMNP FTB 36 N12=N11+NUMB•2 FTB 37 N13=N12+NUM8•4 FTB 38 NRFL=LOCFIA11lt+N1l FTB 39 NRFL=MAXOCNRFL,350006l FTB 40

C FTB 41 CALL REQMEM INRFLI FTB 42

C FTB 43

c c c c c c c c c c

IF (NUI19.GE.U CALL LTROTN IAIN11,AIN8l,AIN91,AIN10l,AIN111 9 AIN121FTB 44 1,NUMEL,NUMNP,NUM6t FTB 45

END FTB 46-

SUB~OUTINE LTROTN (NP,SCT,LINK,NSPN,I9EAM,BMAX,IE,IP,IBt LTR LH

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ••LTR

THIS SU3ROUTINE COMPUTES THE CO~PDSITE SEA~ MOMENTS AND DETERMINES THE MOMENT PERCENTAG~S AT iHE MAXIMUM BEAM MOMENT SECTION

LTR LTR LTR LU LTR

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • LTR LU LTR

DIMENSION NPtiE,4l, SCTIIE,12), LINKtiP,&J, IuEAMII3,2), 8MAX!IB,4LTR -138-

1 2 3 4 5 & 7 8 q

10 11 12



c

c

c

c

1), NBPN<IPit NBNI501, 3N6NI50I, PNBNI50it EIH50)

COMMON /C300/ JUH1,JUM2,JUM3,JUM4,tN,IO COH~ON /NFB/ NUMB,NNO,NSN

COMMON /CA~OS/ OATA,OATA1,DATA2 INTEGER DATA,DATA1,0ATA2

REWIND 1 REWIND 4 READ 111 NP READ 141 SCT READ nN,21tOI IIBEAl1tN,11,N=1,IBI REA~ IIN,250l (8HAX!N,11,N=1 9 IRI

C DETERMINE aEAM LINKAGE TO A NODE c

c

DO 10 J=1,IP N3PNIJI=G DO 10 K=1,6

10 LINKIJ,Kl=O DO 20 I=1,IE J1=NP(l,1l J2=NPU,2l J3=NP<I,31 IF IJ2.~E.J31 GO TO 20 NBPNIJ1l=NdPNIJ11•i L1=Ni3PN<J11 LINKIJ1,L11 =I NBPN<J21=NePN<J2l•1 L2 =N BPN ( J21 LINKIJ2,L21=I

20 CONTINUE

C LIST SEAM MOMlNTS AND AVERAGE ~OMMENT AT COMMON NODES c

00 !; 0 N = 1 , I B WRHE II0,3101 N WRITE II0,3201 BIG=O.D TEMP=O.O L=I3EAM!N,11

30 Jl=NP (L, 11 J2=NP(L,21 AVG=ITEMP•SCTIL,91112.0 WRIT£ liO,l301 L,J1,SCTIL,9l,Jl,AVG IF !ABSIAVGI.LT.ABS!B!Gll GO TO 40 IBEAMIN,2l=J1 BIG=AliG

40 TEMP=SCT(L,10l WRITE (10,3401 J2,TEMP TEMP=- TEMP L=LINKIJZ,21 IF IL.EQ. Ol GO TO 50 GO TO 30

50 WRITE 110 9 370) 8IG,IBEAM!N,21 BMAXHl,2l =BIG

60 CONTINUE -139-

LTR 13 LTR 14 LT~ 15 LTR 16 L TR 17 LTR 16 LTR 19 LTR 20 LTR 21 L TR 22 LTR 23 LTR 24 LTR 25 LTR 26 LTR 27 LTR 28 LTR 29 L TR 30 LTR 31 LTR 32 LTR 33 L TR 34 LTR 35 LH 36 LTR 37 LTR 36 LTR 39 LH 40 LTR lt1 LTR 42 LTR 43 LH lt4 LTR 45 LTR 46 LH 47 LTR 48 LTR 49 LH 50 LTR 51 LH 52 L TR 53 LTR 54 LTR 55 LTR 56 LU 57 LTR 58 L TR. 59 LTR 60 L TR 61 lTR 62 LTR 63 LTR &4 LTR 65 LTR 66 LTR 67 LTR 68 LTR 69 LTR 70

I I

IF <NNO.LE.OI GO TO 110 LTR 71 c LTR 72 I c READ IN NOOES WHERE BEAM AND PLATE MOMENTS ARE TO dE PRINT ED LTR 73 c LTR 74

READ UN,2601 lNBtHNI ,N:1,NNDt LTR 75 WRITE (10,2701 CNBN (N l ,N=1 ,NNDl LTR 76 I WRITE U 0,280 l LTR 77 DO 100 N=1,NNO LTR 78 NO=NBNHU LTR 79 Il=LINKlNQ,11 LTR 80

I IR=LINKIN0,2l LTR 81 BML=O.O LTR 82 BMR=O.O LTR 83 IF IIL.EQ.OI GO TO 80 L TR 84 J1=NPCIL,U LTR 85 1-IF (J1.EQ.NI GO TO 70 LTR 86 BML= SCT II L, 10 I LTR 87 GO TO 80 L TR 88

70 BML=SCTIIL,91 L T~ 69 I 80 IF IIR.EQ.O I GO TO 90 LTR 90 B~R=SCT (IR, 91 LTR 91

'30 CONTINUE LU '32 BNBNCNI=O.S•IBMR-~MLI LTR '33

I WRITE (!0,2'301 N,NBNCNl ,t3N3NlNl LH. '34 100 CONTINUE LTR 95 110 CONTINUE LH 96

c LTR 97

I c COMPUTE PLATE. MOMENTS AT NODES OF MAX BEAM MOMENT LTR 98 c LTR 99

DO 120 J=1, IP LTR 100 NI3PNIJI=O LTR 101 DO 120 K=1,6 LTR 102 I 120 llt~K(J,Kt =0 LTR 103 DO 130 I=1,IE LTR 104 J1=NP <I, 11 LTR 105 J2=NPti,21 LTR 106 I J3=NPII,31 LTR 107 J4=NPCI,Itl LTR 108 IF (J2.EQ.J31 GO TO 130 LTR 10'3 N3PN!J1l=N3PNIJ1l+1 LTR 110 I N8PNIJ2l=N8PNIJ2)+1 LB 111 N8PN(J31=NB~NIJ31t1 LTR 112 NBPNCJ~)=NBPNIJ4lt1 LTR 113 L1=N3PN ( J11 LTR 114

I L2=Ni3PNIJ21 LTR 115 U=NBPN I J31 L TR 116 llt=NBPN <J41 Ln 117 LINKCJ1,L1l=I LTR 118

I LINI(!J2,L21=I LH 119 LINK(JJ, L3t =I LTR 120 LINKlJit,L4)=1 LTR 121

130 CONTINUE LTR 122 c LTR 123 I c AIIERAGE PLATE MOMENT~ ~~ MOuES LTR 124 c LTR 125

TMNT=O.O LTR 126 DO 160 N=1tiB LTR 127 I J=IBEAI1(N,21 LH. 128

-140-

I I I

I I I

WRITE 110,3501 J LTR 129 SUM=O.O LH 130 00 140 I=1' 4 LTR 131 L=LINKIJ,II LTR 132

I IF IL .Ell. 01 GO TO 150 LTR 133 WRITE (!0,3601 L,SCT(L,41 LTR 134 FAC=FLOAT U I LH 135 SUM=SUH+SCTIL,41 LTR 1J&

!ItO CONTINUE LT~ 137

I 150 PLMT=3UM/FAC LTR 138 8MAXIN,3l=PLMT LH 139

c LH 140 c MULTIPLY BY EFFECTIVE WIDTH AND AUO TO BEAM MOMENT LTR 11t1

I c LTR 142 8M=BMAXIN,2l LH 143 S=BMAX IN, U L TR 144 BC=BM+PL MT''S LTR 145

I BMAXIN,Itl=i3C LTR 146 TMNT=TI1NT +BC LH 147

160 CONTINUE LTR 148 WRITE 1!0,300) LTR 149

I WRITE 1!0,3801 LTR 150 DO 170 fii:1,IB LTR 151

170 WRITE 1!0,3901 N,BHAXIN,1l,UMAXIN,JI,B11AXIN,21,BMAXIN,41 L TR 152 c LTR 153 c PRINT OF MOMENT PERCENTAGES LTR 154

I c LH 155 WRITE (!0,410) L TR 156 DO 180 N=1,IB LTR 157 dC=3MAXIN,41 LTR 158

I PCT=SC/TMNT•100. LTR 159 WRITE I IO ,400 l N,8C,PCT L TR 160

180 CONTINUE LTR 161 IF INND.LE.OI GO TO 230 LTR 162

I c LTR 163 c COMPUTE PLATE MOMENTS AT SELECTED SECTION LTR 164 c LTR 165

WRITE I I0,420 I LTR 166

I 00 210 ;~=1, NNU LTR 167 ND=NBNINI L TR 168 SUM=O. LTR 169 00 190 I=1,4 LTR 110

I L=LINKINO,Il LTR 171 IF IL.EQ.ill GO TO 200 LH 172 FAC=FLOATIII LTR 173 SUM=SUH+SCTIL,4l LTR 174

190 CONTINUE LTR 175

I 200 PNBNINl=SUM/FAG LTR 176 WRITE II0,2901 N,NBNINI,PNGNINI LH 177

210 CONTINUE LTR 178 c LTR 179

I c READ IN EFFECTIVE WIDTH FOR EACH NODE LU 180 c L TR 181

READ IIN,4JOI (fWINl ,N=1 9 NNOI LTR 182 WRITE II0,440l IEW(Nl ,N=1 9 NNDl LTR 183

I WRITE IIO 9 450 I LH 184 WRITE 110,4601 LTR 185 DO 220 N= 1, NND LH 186

-141-

I ' I I

I I

PNBN(Nt=~~BNINl•EWINJ LTR 187 TMT=BNBN(NI•PNBN(NI LTR WRITE 1!0,3901 N8N(NI ,aNBNINI,PN8N(NI,EWOU,TMT LTR BNBNINt=TMT LTR

188 I 189 190

220 CONTINUE LTR 191 230 CONTINUE LT~

C LTR C ECHO PRINT OF THE VALUES WRITTEN ON FILE DATA LTR

192

I 193 194

C LTR 195 WRITE <I0,4701 LT~ WRITE (10,4901 LTR WRITE <I0,4801 LTR WRITE 110,5201 lN3N(NI,N=1,NNDI LTR

196

I 197 198 199

WRITE (!0,500) (t3NBNCNt,N=1,NNOI LTR 200 WRITE (!0,5101 LTR WRITE <I0,520t <I3EAH(N,2t,N=1,IBl LTR WRITE U0,5001 IBMAX(N,4J,N=1,IBI LTR

201 I 202 203

C LTR 204 C PUNCH OUT MOMENTS AT SELECTED SECTION LTR C LTR

WRITt <OATA 9 480l LTR

205 I 206 207

WRITE IDATA,5201 (N3NINI,N=l,NN0) LTR 208 WRITE IOATA,501)l IBNBNIN) ,N=1,NNDl LTR

C LTR C PUNCH OUT MOMENT AND PER~ENTAGE AT MAX. MOMtNT SECTION LT~

209

I 210 211

C LTR 212 WRITE IDATA,5201 <I·BEAf11N,21 ,N=lt!Eil LTR WRITE IDATA,500l <BHAXIN,41,N=1,I81 LTR RETURN L H.

C LTR

213

I 214 215 216

C LTR 240 FORMAT (20!41 LT~ 250 FORMAT 110F8.0l LU 260 FORMAT (20I41 LT~

217 218 I 219 220

270 FORMAT 15Xt10I5l LTR 221 280 FORMAT (/5X,•BEAH MOMENTS AT SELECTED NaDES•,t5X,• N •,!OX,•~ODELTR

t•,sx,•AVG.MOMENT•,;) LTR 290 FOR!'1AT 15X,I5,10X,I5,4X,E1o.5l LTR

222 I 223 224

300 FORMAT (//5X,•MOHENT AT SECTION OF MAXIMUM MOMENT ~ESPONSE•,/tJ LTR 225 310 FORMAT 11HO,II5X, 4 FULL SPAN q£AM•,I5l LT~ 120 FORMAT 15X,•ELEMENT•,ax,•NODES•,tOX,•MOMENT•,10X,•NOOE•,ox,•AVG. BLTR

1EA!'1 ~OMENT•,/J LTR

226

I 227 228

330 FORMAT 15X,I5,10X,I5,4X,E1&.5,5X,I5,4X,E16.5l LT~ 229 340 FORMAT 120X,I5,4X,E16.5l LTR 350 FORMAT 1/SX,•PLATE MOMENTS CONNECTED TO NOOE•,rs,/5X,•ELEMENT•,10XLTR

!,•MOMENT AT CENTER•,n LT~

230

I 231 232

360 FORMAT 15X,I5,20X,E16.51 LT~ 233 370 FORMAT 1/SX,•MAXIMUM MOMENT•,Et6.5,5X,•AT NOOf•,ISI LTR 380 FORM~T I/5X,•aEAM•,7X,•EFF. WIDTH•,7x,•PLATE-MX•,gx,•3EAM-MY•,9X,•LTR

1COM~OSITE HOMENT•,ttl LTR 390 FORMAT 15X,I5,1X,E16.5,1X,E16.5,1X,El6.5,1X,E16.51 LTR

234

I 235 236 237

~00 FORMAT (/SX,I5,5X,E16.S,5X,F10.4l LTR 238 410 FORMAT (/15X,•MOMENT PERCENTAGES•,/SX,•BEA~•,10X,•MOMENT•,10X,•PERLTR

1CENT •,/l LTR 420 FORMAT 1/SX,•~LATE HOMENT~ AT SELECTED SECTION•,ISX,• N •,SX,•NOLTR

239 I 240 241

1DE•,•AVG. MOMENT•,;) LTR 242 4JO FORMAT 110F8.01 LTR 440 FORMAT 15X,10F10.5l LTR

-142-

243

I 244

I I I


•so FORMAT 1//SX,•COMPOSITE MOMENT AT SELECTED NOOES•,ttt 460 FORMAT 1/SX,•NODE•,gx,•BEAH M-Y•,7X,•PLATE M-X•,7X,•EFF.

!,•COMPOSITE MOMENT•,!> 470 FORMAT !1H1,/5X, 4 ECHO PRINT OF VALUES ~UNCHEO OUT•,ttt ~60 FORMAT <5X,•MOMENTS AT SELECTED NODES•> 490 FORMAT (5X,•REACTIONS •••• I ONE CARD PER NODE•) 500 FORMAT 15£12.51 510 FORMAT !5X,•BEAM ~OHENTS AT MAXIMUM MOMENT SECTION•) 520 FORMAT 116I5J

END

-143-

LTR 245 WIOTH•,7XLTR 246

LTR 247 LU 248 LU 249 LTR 250 LTR 251 LTR 252 L TR 253 LTR 254-

user's manual for program skbrd - lehigh …digital.lib.lehigh.edu/fritz/pdf/400_15.pdf · i i...

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