2006 asce/sei structures congress st. louis, mo may 18-20 1 manual and inelastic-analysis based...

2006 ASCE/SEI Structures CongressSt. Louis, MO

May 18-20 1

Manual and Inelastic-Analysis Based

Design of Partially-Restrained Frames

Using the 2005 AISC Specifications

By

Christopher M. Foley, PhD, PE John Schaad, MS, EIT Marquette University Jezerinac, Geers, & Associates Milwaukee, WI Dublin, OH

2006 ASCE-SEI Structures CongressSt. Louis, MO

May 18-20


May 18-20 2

AISC Specifications are becoming more liberalized in the designer's favor and are beginning to allow software capabilities to be exploited.

There are new demands on the structural engineer to understand phenomena that software is now able to consider.

How do we teach these concepts and specification developments to students?

MOTIVATION FOR PRESENTATION

Focus can now be on SYSTEM BEHAVIOR rather than members or components and designing for target behavior is possible.

Address Wooten's Third Law of Steel Column Design - Corollary Number 2:

"The computer renders obsolete the necessity of rationalizingand simplifying problems - or even of understanding them" (Wooten 1971)

It would be very beneficial to have a manual methodology to get starting sizesfor inelastic analysis-based design.


May 18-20 3

N

TYPICAL FRAMING PLAN

PR Connections Flexible (pin) Connections

A B C D E30 ft.3@10 ft.

1

2

3

4

30 f

t.

X-Braced Bay

Superimposed DL: 63 psf• Comp. Slab: 46 psf• Ceiling: 2 psf• Fireproofing: 3 psf• MEP systems: 12 psf

Superimposed LL: 30 psf

Steel Framing: 5 psf

30 ft. 30 ft.

30 f

t.30

ft.

Wind, WL: 20 psf

Steel Material: A992

Superimposed DL: 83 psf• Comp. Slab: 46 psf• Ceiling: 2 psf• Fireproofing: 3 psf• MEP systems: 12 psf• Partitions: 20 psf

Superimposed LL: 50 psf

Roof Level:

Floor Level:

Cladding: 25 psf (wall area)


May 18-20 4

RIP R

LP

FW

15

15RW

RkR

FkR

bpkR

30

A B C D E

30 3030

FLP

REP

BASE ANALYTICAL MODEL

FIP F

EP


May 18-20 5

10 zEI

L

M

0.50 FpbM

10 zEI

L

M

0.50 RpbM

10 zEI

L

M

0.75 pcM

BILINEAR CONNECTION MODELS

FLOOR BEAM ROOF BEAM

BASE PLATE

0.50 FpbM 0.50 R

pbM

0.75 pcM


May 18-20 6

AISC APPENDIX 7 - Preliminary Design

Member design can be greatly streamlined if the following constraints on member selection are included.

• Choose a target interstory drift to meet target 2nd order sway amplification:

2, ,

11.15 0.153

10.85

Hu nt H u nt

HLB

P P

HL

• Choose member sizes to avoid stiffness reduction;

*0.50 1.00ub

y

PEI EI

P

• Choose member sizes to avoid effect;P

10.15 1.00u

eL

PB

P

Implies that behavior is "nearly" linear up to first hinge formation.


May 18-20 7


Local Buckling:

276.02 0.328 u

w y

Ph

t P

29.94 2.10 35.88u

w y

Ph

t P

• Flanges;

0.113u

y

P

P

0.113u

y

P

P

• Webs in Combined flexure and axial compression;

9.152

f

f

b

t

Stability and Nonlinear Geometric Effects

0.675u

y

P

P

Lateral-Torsional Buckling

min 113.43

by

Lr

(column members) (beam members)

min1

2

0.12 0.076 580

by

Lr

M

M


May 18-20 8

0.9cap

n

M

M

0.9u

ny

P

P

Moment capacity in presence of axial loading

0.9u

ny

P

P

0.9u

n

M

M

91 1

8 0.9 0.9u u

cap pc pcny ny

P PM M M

P P

min

15 121.96

0.12 0.076 0.5 580yr

Assume column bent in reverse curvature and theinflection point is at 2/3 column height:

Therefore, if miny yr r then;


0.20

11 0.90 0.452

u ucap pc pc

ny ny

P PM M M

P P


May 18-20 9

LOADING COMBINATIONS

ASCE 7 - 02 Strength Limit State (with corrections):

1.4 DL

1.2 1.6 0.5 rDL LL LL

1.2 0.5 1.6 rDL LL LL

1.2 0.5 0.5 1.6rDL LL LL WL

ASCE 7 - 02 Serviceability Limit State

DL LL

0.5 0.7DL L W

0.2% notional loads

0.2% notional loads

0.2% notional loads


May 18-20 10

DESIGN ASSUMPTIONS

The following assumptions are made in the design:

• Unbraced lengths for columns were taken as the story height.

• The compression flange for beams in positive flexure is fully braced.

• The compression flange for girders subjected to negative flexure is braced at column lines and at beam lines.

• Compression forces in beams is negligible.

• Columns are pin-pin for minor axis bending.

• Beams are non-composite with floor system.


May 18-20 11

Plastic Hinges:

MECHANISM 1 - BEAM STRENGTH

uPuP

- beam hinge

- connection hinge

ssu b n

pb M pb

M M

M M

M

M pbM

pbM

ssuM

1

ssu

b nM

MM

1.4 DL1.2 1.6DL LL

Plastic hinges form in beamsindicating SCWB behavior.

FuIP

RuIP R

uIP

FuIP

Loading Combinations:

Simplified GravityLoad Analysis:


May 18-20 12

PP

M 3

2

8e

PaM

L

BEAM SERVICEABILITY

Moment Diagram - Kotylar (1996)

2

2

81m

aM Pa

L

12

1mb

EI

k L

Moment-Area Principle Yields

2 2 23 4 2424CL

PaL a a

EI

L

aa

mbkmbk


May 18-20 13

BEAM DESIGN

10bL

Assume connection strength at 50% of the plastic moment capacity: 0.50M

Assume that the beams are bent in reverse curvature:

Serviceability:

Compute the ultimate simply-supported beam moment.

Compute the required strength of the PR beam.

1 2 0.50M M

Using the unbraced length establish: minyr

10 Assume that beam connection stiffness results in PR behavior:

Check total, DL and LL deflections at mid-span.

Strength:

Select a beam for strength considerations.

Check that connections do not exceed yield moment at service level loads.

Adjust beam size as required.

Beams Selected: W16x40 (roof) W21x55 (floor)


May 18-20 14

MECHANISM 2 - Gravity and Notional Loading

Plastic Hinges:

- beam hinge

- connection hinge

30

15

10 20

15

15

FuIP

RuIPR

uN

FuN

Plastic hinges formin beams indicating

SCWB behavior.

FuEP

RuEP

Loading combinations applied in a non-proportional manner (e.g. gravity load first and then lateral load to failure) will likely result in a sway mechanism forming.

Gravity and notional loading are assumed to be applied in a proportional manner - therefore, a combined mechanism is targeted.

FuIP

RuIP

FuLP

RuLP


May 18-20 15

MECHANISM 3 - Gravity and Lateral Loading

Lateral and gravity loading combinations are applied in a proportional manner - therefore, a combined mechanism is targeted.

RuH

FuH

Previous beam design indicates that plastic hinges will NOT form when gravityloading at the following magnitude is applied:

1.2 0.5 rDL LL LL

Plastic Hinges:

- beam hinge

- connection hinge

30

15

10 20

15

15

FuIP

RuIP

Plastic hinges formin beams indicating

SCWB behavior.

FuEP

RuEP

FuIP

RuIP

FuLP

RuLP


May 18-20 16

16 40W

,2cap M pcol bm

M M

SIZING FOR TARGET MECHANISMS

SCWB criteria can be used to help ensure assumed targeted mechanisms form.

16 40W 16 40W

21 55W

16 40W

,22cap M pcol bm

M M

,1 ,2

2cap cap M pcol col bmM M M

,1 ,2cap cap M pcol col bmM M M

21 55W 21 55W 21 55W


May 18-20 17

16 40W 16 40W 16 40W 16 40W

12 58W

12 58W

12 58W

12 58W

FRAME FOR FURTHER EVALUATION

The framework shown below is the system that will be used for displacement evaluation.

We will now check the columns and/or beams to ensure second-order effectsare "small" and the frame is serviceable with respect to interstory drift.

12 58W

12 58W 21 55W 21 55W 21 55W 21 55W

12 58W

12 58W

12 58W

12 58W


May 18-20 18

2

1 2 1 2 6

12i

ib c k

V h h L h h E

E I I R

Exterior Sub-Assembly

Interior Sub-Assembly

2

1 2 1 2 6

6 2e

eb c k

V h h L h h E

E I I R

SUB-ASSEMBLAGE DISPLACEMENTS

Using modifications to the work of Englekirk (1994), displacement expressionsfor interior, exterior and column base segments can be generated.

Partially Restrained Column Bases

31

1

31

3c

cbc kb

EIVh

EI R h

For simplicity, we will assume inflection points at 1/2 first story height and mid-height of the second story columns.

2L 2L

kR

kR

iV

iV1 2

i

h hR V

L

RcI

cI

bI bI1h

2h

kRcI

eV

eV

bI

1 2i

h hR V

L

2L

cI 1h

2h


May 18-20 19

Exterior and Interior Columns:

2nd Floor Beam: 21 55W

12 58W

Assume inflection points at mid-heights: 1 2 7.5 90h h

, 10 765,278Ik bp

EIR k in rad

L

, 10 918,333k beam

EIR k in rad

L

Connection and base plate stiffness:

"SMALL" 2nd ORDER EFFECTS AND SERVICEABILITY


May 18-20 20

1.2 1.6 0.5 rDL LL LL with notional loading

21.118 180 360 180 6(29,000) 1

0.04612(29,000) (1,140) (475) (918,333) 2i

2(0.559) 180 360 180 6(29,000) 1

0.046(29,000) (1,140) 2(475) (918,333) 2e

3(0.559)(90) 3(29,000)(475)1 0.02

3(29000)(475) (765,278)(90)ecb

0.06Etot OK

3(1.118)(90) 3(29,000)(475)1 0.02

3(29000)(475) (765,278)(90)icb

0.07Itot OK

"SMALL" 2nd ORDER EFFECTS - STRENGTH L.S.

4.47H k, 1,666u ntP k

180L

max

0.074H at 1st story

4.470.559

8e

kV k

1.118iV k


May 18-20 21

1.2 0.5 1.6rDL LL LL W without notional loading

28.10 180 360 180 6(29,000) 1

0.3312(29,000) (1,140) (475) (918,333) 2i

2(4.05) 180 360 180 6(29,000) 1

0.266(29,000) (1,140) 2(475) (918,333) 2e

3(4.05)(90) 3(29,000)(475)1 0.11

3(29000)(475) (765,278)(90)ecb

0.37Etot OK

3(8.10)(90) 3(29,000)(475)1 0.23

3(29000)(475) (765,278)(90)icb

0.56Itot OK

"SMALL" 2nd ORDER EFFECTS - STRENGTH L.S.

32.4H k, 1,368u ntP k

180L

max

0.65H at 1st story

32.44.05

8e

kV k

8.10iV k


May 18-20 22

0.5 0.7rDL LL LL W

23.55 180 360 180 6(29,000) 1

0.1412(29,000) (1,140) (475) (918,333) 2i

2(1.78) 180 360 180 6(29,000) 1

0.116(29,000) (1,140) 2(475) (918,333) 2e

3(1.78)(90) 3(29,000)(475)1 0.05

3(29000)(475) (765,278)(90)ecb

0.16Etot OK

3(3.55)(90) 3(29,000)(475)1 0.10

3(29000)(475) (765,278)(90)icb

0.28Itot OK

SERVICEABILITY LIMIT STATE

without notional loading

400 0.45L

14.18H k, 1,176u ntP k

180L

max

0.33H at 1st story

14.21.78

8e

kV k

3.55iV k


May 18-20 23

16 40W 16 40W 16 40W 16 40W

12 58W

12 58W

12 58W

12 58W 12 58W

The framework shown below is the system that resulted from the serviceability and 2nd order effects evaluation.

We will now simply ensure that the member sizes chosen will result in thetargeted mechanisms forming at levels higher than the strength limit statecombinations.

12 58W

12 58W

12 58W

12 58W 21 55W

FRAME FOR MECHANISM ANALYSIS

12 58W

21 55W 21 55W 21 55W


May 18-20 24

30

15

10 20

15

15

FuIP

RuIP

RR uP N F

F uP N

FuIP

RuIP

MECHANISM 2 - Combined Mechanism

1.2 1.6 0.5 rDL LL LL

1.2 0.5 1.6 rDL LL LL

1.2 0.5 1.6rDL LL LL WL RR uP H F

F uP H

RP

FP

RR uP N F

F uP N

p pbM M

, , ,min 0.75 ,p col p col cap colM M M

, 0.5p con pbM M

y nyP P

y g yP A F

y g yP A F


May 18-20 25

EVALUATION OF DESIGN USING INELASTIC ANALYSIS

The frame designed preliminarily using the preceding procedure was checkedusing MASTAN2 (Ziemian and McGuire).

The following loading combinations were evaluated:

0.5 0.7rDL LL LL W

1.2 1.6 0.5 rDL LL LL

1.2 0.5 1.6 rDL LL LL

DL LL

1.2 0.5 1.6rDL LL LL W

The yield surface of MASTAN2 was manipulated as follows:

ny

P

P

, ,p base p col

M Mor

M M 1.0

1.0

Default MASTAN2 yield surfaceconnects end points.

,ny y col gP F A

, , ,min ,x y col p base p colZ F M M


May 18-20 26


1.2 1.6 0.5 2.11r ultDL LL LL

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

2.0

2.5

Displacement (in.)

Node 15 - Horiztonal

Node 15

Elem. 35

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.000

0.025

0.050

0.075

0.100

P/P

y

M/Mp

Element 35 - Right


May 18-20 27


1.2 0.5 1.6 2.08r ultDL LL LL

Node 15

0.00 0.25 0.50 0.75 1.000.0

0.5

1.0

1.5

2.0

2.5

Displacement (in.)


Elem. 39

Elem. 35

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.00

0.01

0.02

0.03

0.04

0.05

Element 35 - Right Element 39 - Right

P/P

y

M/Mp


May 18-20 28


1.2 0.5 1.6 2.04r ultDL LL LL W

Node 15

0 2 4 6 8 100.0

0.5

1.0

1.5

2.0

2.5

Displacement (in.)


Elem. 39 Elem. 35

Elem. 100

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.0

0.1

0.2

0.3

0.4

0.5

Element 35 - Right Element 39 - Right Element 100 - Bottom

P/P

y

M/Mp

ALR = 1.0


May 18-20 29

SERVICEABILITY EVALUATION OF DESIGN

0.5 0.7rDL LL LL W

DL LL

0.0 0.1 0.2 0.3 0.40.0

0.2

0.4

0.6

0.8

1.0

1.2

App

lied

Load

Rat

io

Displacement (in.)

1st InterStory Drift 2nd InterStory Drift Roof Level Drift

No connections hit yieldmoment at service levels.

Typical limit on interstory drift is:

1800.45

400is

1 0.28is

No connections hit the yield moment

Vertical beam deflections were well below acceptable thresholds


May 18-20 30

CONCLUDING REMARKS

An approximate methodology for sizing members within the context of AISCAppendices 1 and 7 has been outlined.

The method has been shown to be relatively accurate given its overall simplicity.

The advantage of the approach is that it focuses on "system" behavior whilemaintaining flexibility to consider beam-columns, beams, and connections.

The formulas for displacement have been show to be accurate for preliminarydesign purposes and they provide the engineer with significant problem feel.

Small multiple-story multiple-bay frames can be sized using the procedure tocontrol second-order effects and the resulting designs have significant reservestrength.

The best use of the methodology would be to demonstrate the importantprovisions in the new AISC (2005) specifications in a simplified manner so thatalgorithms for computer implementation can be developed.


May 18-20 31

REFERENCES

Englekirk, R. (1994) Steel Structures - Controlling Behavior ThroughDesign, John Wiley & Sons, Inc., New York, NY.

Foley, C.M. and Schinler, D. (2003) "Automated Design of Steel Frames Using Advanced Analysis and Object-Oriented Evolutionary Computation", Journal of Structural Engineering, 129 (5), pp. 648-660.

Kotylar, N. (1996) "Formulas for Beams with Semi-Rigid Connections"Engineering Journal, AISC, Fourth Quarter, pp. 142-146.

Wooten, J. (1971) "Wooten's Third Law and Steel Column Design",Engineering Journal, 2nd Quarter, pp. 1-3.


May 18-20 32

Extra slides showing detailed computationsto follow this slide.


May 18-20 33

,

3050 5 3,750

2F

E LLP psf lbs

SERVICE LOADING

Gravity Loading

Roof Floor

,

3088 5 25 15

2

25 15 5 14,100

FE DLP psf psf

psf lbs

,

15 3068 5 25

2 2

1525 5 8,850

2

RE DLP psf psf

psf lbs

,

3088 10

2

25 15 10 16,950

FI DLP psf

psf lbs

,

3030 5 2,250

2R

E LLP psf lbs

,

3050 10 7,500

2F

I LLP psf lbs

,

3068 10

2

1525 10 12,075

2

RI DLP psf

psf lbs

,

3030 10 4,500

2R

I LLP psf lbs


May 18-20 34

SERVICE LOADING (continued)

15 9020

2 2

6,750

RW psf

lbs

Wind Loading

9020 152

13,500

FW psf

lbs

Leaning Columns

Roof Floor

, 88 60 120

125 60 15 2

2

339,300

FL DLP psf

psf

lbs

,

150 60 120

2

180,000

FL LLP psf

lbs

, 68 60 120

15 125 60 2

2 2

256,050

RL DLP psf

psf

lbs

,

130 60 120

2

108,000

RL LLP psf

lbs

Roof Floor


May 18-20 35

AISC APPENDIX 7 - DIRECT ANALYSIS

Design Analysis Requirements

,n in planeP computed using 1.0in planeK

Out of plane strength defined in usual manner.

Column Nominal Strength

Analysis must incorporate geometric nonlinearity: P P and

• AISC amplification factors allowed if reduced stiffness is used;

2

1

10.85

nt H

BP

HL

Interstory drift, , and axial force demands computed using;H

* 0.8 bEI EI 4 1 0.50r r rb

y y y

P P P

P P P

1

1

1

m

r

e

CB

P

P

and construction/erection imperfections.


May 18-20 36

AISC APPENDIX 7 (continued)

Design Analysis Requirements (continued)

P • effects can be omitted when; 1 1.00B

0.15r eLP P

• Story out-of-plumb imperfections must be included through notional loading;

0.002i iN Y

Out-of-plumbness can be directly inserted into the analytical model (1/500).

• If second-order amplification is less than 50% notional loads need only need only be applied with gravity load combinations.

• Computer software capable of conducting geometrically nonlinear analysis is allowed.


May 18-20 37

AISC APPENDIX 1 - INELASTIC ANALYSIS AND DESIGN

Material Limitations:

The yield strength of members shall not exceed 65 ksi.

Local Buckling:

2.753.76 1

0.90r

w y y

Ph E

t F P

1.12 2.33 1.490.90

r

w y y y

Ph E E

t F P F

• Flanges;

0.1250.9

r

y

P

P

0.1250.9

r

y

P

P

• Webs in Combined flexure and axial compression;

0.382

f

f y

b E

t F


May 18-20 38


Stability and Nonlinear Geometric Effects

• First order (mechanism) analysis can be used provided second-order effects are considered. Second order inelastic analysis is permitted.

• Sufficient rotational ductility in columns preserved through limiting axial load levels;

0.90 0.75 0.675r y g yP F A P

Lateral-Torsional Buckling

4.71b

y

L E

r F

1

2

0.12 0.076b

y y

L M E

r M F

(targeted for column members)

(targeted for beam and beam-column members)


May 18-20 39


Axial Capacity, Moment Capacity and Combined Forces

0.90r c nP P P 0.90 0.9 1.6r c p yM M M M

81

0.9 9 0.9r r

n p

P M

P M

1

2 0.9 0.9r r

n p

P M

P M

0.9r

p

M

M

0.9r

n

P

P

0.900.9

r

p

M

M

0.200.9

r

n

P

P


May 18-20 40

BEAM DESIGN - STRENGTH

217

1 1 0.5

144.7

ssu

b n reqM

MM

k ft

Roof Beams Floor Beams

1

2

1.4 12.08 16.9

1.2 12.08 1.6 4.5 21.7

u

u

P k

P k

1

2

1.4 16.95 23.7

1.2 16.95 1.6 7.5 32.3

u

u

P k

P k

32.3 10 323ssuM k k ft 21.7 10 217ss

uM k k ft

323

1 1 0.5

215.3

ssu

b n reqM

MM

k ft

10bL (negative bending)

Assume connection strength at 50% of the plastic moment capacity: 0.50M

At the strength limit state, beams are bent in reverse curvature and ratio ofend moments is 0.50.

min

10 121.31

0.12 0.076 0.5 580yr

min

1.49yr

Try W14x30 Try W16x36177b n pM M k ft

min

1.52yr

240b n pM M k ft


May 18-20 41

10

BEAM DESIGN - SERVICEABILITY (continued)


12.08 4.5 16.6P k 16.95 7.5 24.4P k

0.42CL tot

Assume that beam connection stiffness results in PR behavior:

10.91

21

mb

EI

k L

429,000 448

10360

360,889

zmb

ksi inEIk

Lk in rad

429,000 291

10360

234,417

zmb

ksi inEIk

Lk in rad

10.83

21

mb

EI

k L

W14x30 W16x36

120a 120a

7.50.42 0.13

24.4CL LL

0.16CL tot

4.50.16 0.04

16.6CL LL

Check total, DL and LL deflections at mid-span.

12.080.16 0.12

16.6CL DL

16.950.42 0.29

24.4CL DL


May 18-20 42

BEAM DESIGN - SERVICEABILITY (continued)


12.08 4.5 16.6P k 16.95 7.5 24.4P k

10.91

21

mb

EI

k L

10.83

21

mb

EI

k L

W14x30 W16x36

120a 120a

3

2

8(24.4)(120) (0.83)180.0

(360) (12)eM k ft

Ensure end moments are less than connection yield moment at service loads.

0.5 177 88 134M pM NG 0.5 240 120 180M pM NG

3

2

8(16.6)(120) (0.91)134.3

(360) (12)eM k ft

connection yield moments may be exceeded at service

Revise to W16x40 Revise to W21x55

1.35 1.31yr 1.57 1.31yr

473b n pM M k ft 274b n pM M k ft


May 18-20 43

SIZING FOR TARGET MECHANISMS (continued)

Interior 2nd Story Column Exterior 2nd Story Column

Interior 1st Story Column Exterior 1st Story Column

2 max14.2 21.7 35.9uP k

1 max22.9 32.3 55.2uP k

2 max3 21.7 65.1uP k

2 max11.8 16.8 28.6uP k

1 max3 32.3 96.9uP k

2 max3 16.8 50.4uP k

,2274cap col

M k ft

,1 ,2

473cap capcol colM M k ft

,1 ,2236cap capcol col

M M k ft

15yK L min

1.96yr

,2137cap col

M k ft

Gravity loading combinations will be used (axial load in columns greatest).

W8x40

W12x58

W12x58

W8x40


May 18-20 44

COLUMN DESIGN - Out-of-Plane Buckling

Interior Column: Exterior Column:

W12x58 W8x40

1.4 DL

1.2 1.6 0.5 rDL LL LL

1.2 0.5 1.6 rDL LL LL 14.2 21.7

18.8 24.0 78.7

uP

k

Only first-story columns and gravity load combinations will be checked at this point.

1.4 DL

3 21.7

3 24.0 137.1

uP

k

1.2 1.6 0.5 rDL LL LL

12.4 16.9

19.7 23.7 72.7

uP

k

3 16.9

3 23.7 121.8

uP

k

1.0 15minor uK L ft

11.8 16.8

22.9 32.3 83.8

uP

k

3 16.8

3 32.3 147.3

uP

k

1.2 0.5 1.6 rDL LL LL

299 84c nP k k OK 527 147c nyP k k OK

W12x58 W8x40


May 18-20 45

COLUMN DESIGN - Cross-Section Stability Checks

Interior Column: Exterior Column:W12x58 W8x40

1.2 1.6 0.5 rDL LL LL 1.2 1.6 0.5 rDL LL LL

11.8 16.8 22.9 32.3 83.8uP k 3 16.8 3 32.3 147.3uP k

585y g yP A F k 850y g yP A F k

7.21 9.152

f

f

b

t 7.82 9.15

2f

f

b

t

27.0 29.94 2.10 57.8u

w y

Ph

t P

840.14 0.675

585u

y

P

P

1470.17 0.675

850u

y

P

P

17.6 29.94 2.10 58.7u

w y

Ph

t P

W12x58 W8x40


May 18-20 46

kR

RcI

bI1h

2h

eV

eV

2L

cI

2L 2L

kR

kR

iV

iV1 2

i

h hR V

L

RcI

cI

bI bI1h

2h

kRcI

eV

eV

bI

1 2i

h hR V

L

2L

cI 1h

2h

FLOOR-LEVEL SUBASSEMBLAGES


May 18-20 47

COLUMN DESIGN - Out-of-Plane Buckling

Interior Column: Exterior Column:

W10x45 W8x35

1.4 DL

1.2 1.6 0.5 rDL LL LL

1.2 0.5 1.6 rDL LL LL 14.2 21.7

18.8 24.0 78.7

uP

k

Only first-story columns and gravity load combinations will be checked at this point.

1.4 DL

3 21.7

3 24.0 137.1

uP

k

1.2 1.6 0.5 rDL LL LL

12.4 16.9

19.7 23.7 72.7

uP

k

3 16.9

3 23.7 121.8

uP

k

1.0 15minor uK L ft

11.8 16.8

22.9 32.3 83.8

uP

k

3 16.8

3 32.3 147.3

uP

k

1.2 0.5 1.6 rDL LL LL

260 84c nP k k OK 332 147c nP k k OK

W10x45 W8x35


May 18-20 48

COLUMN DESIGN - Cross-Section Stability and LTB Checks

Interior Column: Exterior Column:W10x45 W8x35

1.2 1.6 0.5 rDL LL LL 1.2 1.6 0.5 rDL LL LL

11.8 16.8 22.9 32.3 83.8uP k 3 16.8 3 32.3 147.3uP k

515y g yP A F k 665y g yP A F k

8.1 9.152

f

f

b

t 6.47 9.15

2f

f

b

t

22.5 29.94 2.10 56.29r

w y

h P

t P

840.16 0.675

515r

y

P

P

1470.22 0.675

665r

y

P

P

20.5 29.94 2.10 57.99r

w y

h P

t P

W10x45 W8x35

min

1801.59 2.03

113.43yr min

1801.59 2.01

113.43yr


May 18-20 49

LOADING COMBINATIONS

1.4 256.1 358.5RuLP k

1.4 339.3 475.0FuLP k

Leaning Columns

1.4 DL

Floor Beam Loads

1.4 16.9 23.7FuIP k

1.4 14.1 19.7FuEP k

Roof Beam Loads

1.4 12.1 16.9RuIP k

1.4 8.85 12.4RuEP k

Notional Loading (applied laterally)

0.002 2 12.4 11 16.9 358.5

0.002 2 19.7 11 23.7 475.0 2.69

FuN

k

0.002 2 12.4 11 16.9 358.5 1.14RuN k


May 18-20 50

LOADING COMBINATIONS (continued)

1.2 1.6 0.5 rDL LL LL

Leaning Columns

Floor Beam LoadsRoof Beam Loads


1.2 16.9 1.6 7.5 32.3FuIP k

1.2 14.1 1.6 3.75 22.9FuEP k

1.2 12.1 0.5 4.5 16.8RuIP k

1.2 8.85 0.5 2.25 11.8RuEP k

1.2 256.1 0.5 108.0 361.3RuLP k

1.2 339.3 1.6 180.0 695.2FuLP k

0.002 2 11.8 11 16.8 361.3

0.002 2 22.9 11 32.3 695.2 3.33

FuN

k

0.002 2 11.8 11 16.8 361.3 1.14RuN k


May 18-20 51


1.2 0.5 1.6 rDL LL LL

Leaning Columns



1.2 16.9 0.5 7.5 24.0FuIP k

1.2 14.1 0.5 3.75 18.8FuEP k

1.2 12.1 1.6 4.5 21.7RuIP k

1.2 8.85 1.6 2.25 14.2RuEP k

1.2 256.1 1.6 108.0 480.1RuLP k

1.2 339.3 0.5 180.0 497.2FuLP k

0.002 2 11.8 11 16.8 361.3

0.002 2 18.8 11 24.0 497.2 3.09

FuN

k

0.002 2 14.2 11 21.7 480.1 1.49RuN k


May 18-20 52


1.2 0.5 1.6rDL LL LL WL

Factored Wind Loading

1.6 6.75 10.8RuH k

1.6 13.5 21.6FuH k

Leaning Columns



Second-order effects will be "small" and thus, no notional loading.

1.2 12.1 0.5 4.5 16.8RuIP k

1.2 8.85 0.5 2.25 11.8RuEP k

1.2 16.9 0.5 7.5 24.0FuIP k

1.2 14.1 0.5 3.75 18.8FuEP k

1.2 339.3 0.5 180.0 497.2FuLP k

1.2 256.1 0.5 108.0 361.3RuLP k


May 18-20 53

R

R

bI

eV

kR

bI

con

b

kR

cI

c

bI cI

cI

kR

21 2

6e

bb

V L h h

EI

31 2

12e

cc

V h h

EI

21 2econ

k

V h h

R

FLOOR-LEVEL - EXTERIOR

eV

eV

eV

eVeVR

1h

2h


May 18-20 54

bI

iV

kR

bI

con

b

kR

cI

c

bI cI

cI

kR

21 2

12i

bb

V L h h

EI

31 2

12i

cc

V h h

EI

21 2

2i

conk

V h h

R

FLOOR-LEVEL - INTERIOR

iV

R

R

1h

2h


May 18-20 55

21 21 2

12

6i

ii

b c k

V EK

L h h Eh h

I I R

Exterior Sub-AssemblyInterior Sub-Assembly

21 21 2

6

6

2

ee

e

b c k

V EK

L h h Eh h

I I R

STORY STIFFNESS

Concrete floor diaphragm provides displacement compatibility. Thisleads to relationship between interior and exterior shear;

1 2 1 26 6

2 2i

eb c k b c k

L h h L h hV E EV

I I R I I R

i e

Portal frame assumptions regarding shear distribution met when;

1 2 1 2

2 2i

eb c b c

V L h h L h hV

I I I I

2006 asce/sei structures congress st. louis, mo may 18-20 1 manual and inelastic-analysis based...

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