rm e steel design aashto

RM Bridge Professional Engineering Software for Bridges of all Types

RM Bridge V8i

June 2013

COMPOSITE BRIDGE- STEEL DESIGN AASHTO LRFD

RM Bridge

C o m p o s i t e B r i d g e - S t e e l D e s i g n A A S H T O L R F D

Bentley Systems Austria

Copyright

This document is integral part of the program package RM Bridge. Duplication and dissemi-

nation is only allowed with explicit permission of Bentley Systems or authorised agents.

2012, Bentley Systems, Incorporated. All Rights Reserved

RM Bridge Contents

Composite Bridge- Steel Design AASHTO LRFD I


Contents

1 Introduction ..................................................................................................................... 1-1

1.1 Background .............................................................................................................. 1-1

1.2 General Description ................................................................................................. 1-1

2 Structural Data ................................................................................................................. 2-2

2.1 General Layout ........................................................................................................ 2-2

2.2 Numbering Scheme ................................................................................................. 2-3

2.3 Support Conditions .................................................................................................. 2-4

2.4 Main Girders ............................................................................................................ 2-5

2.4.1 Definition of the Main Girder Segments ............................................................. 2-6

2.5 Cross Frames and Stiffeners .................................................................................... 2-7

2.6 Shear Studs ............................................................................................................ 2-10

2.7 Materials ................................................................................................................ 2-11

3 Construction Schedule and Loading .............................................................................. 3-12

3.1 Element Activation by Stages ............................................................................... 3-12

3.2 Design Loads ......................................................................................................... 3-14

3.2.1 Dead Load.......................................................................................................... 3-14

3.2.2 Live loads .......................................................................................................... 3-14

3.2.3 Braking Load ..................................................................................................... 3-15

3.2.4 Wind Loads ....................................................................................................... 3-15

3.2.5 Thermal Forces .................................................................................................. 3-16

3.3 Load Combinations ............................................................................................... 3-17

4 Analysis results .............................................................................................................. 4-19

5 Steel Design Checks ...................................................................................................... 5-23

5.1 General................................................................................................................... 5-23

5.1.1 Design Calculation Actions ............................................................................... 5-23

5.1.2 Relevant additional input parameters ................................................................ 5-23

5.2 Slender parts .......................................................................................................... 5-23

5.2.1 Definition of Slender parts ................................................................................ 5-24

RM Bridge Contents

Composite Bridge- Steel Design AASHTO LRFD II


5.2.2 Slender parts in the current example ................................................................. 5-25

5.3 Buckling lengths .................................................................................................... 5-26

5.3.1 Definition of Buckling Lengths ......................................................................... 5-26

5.3.2 Buckling Lengths in the current example .......................................................... 5-27

5.4 Design Resistances (without considering locked-in stressing).............................. 5-27

5.4.1 General............................................................................................................... 5-27

5.4.2 Main girders Typical sections......................................................................... 5-28

5.4.3 RM Bridge Results ............................................................................................ 5-32

5.4.4 Assessments ........................................................................................................ 5-34

5.5 Capacity Factors ...................................................................................................... 5-34

5.5.1 Definitions ........................................................................................................... 5-34

5.5.2 Resulting Capacity factors ................................................................................. 5-35

5.6 Consideration of locked-in stresses ....................................................................... 5-35

5.7 Rating factor .......................................................................................................... 5-40

RM Bridge Introduction

Composite Bridge- Steel Design AASHTO LRFD 1-1


1 Introduction

1.1 Background

This training and demonstration example is used to show the application of RmBridge on a

composite bridge with concrete slab and welded I-girders as main girders. This example is

also used as a verification example for the RM Bridge functionality for steel design in accord-

ance with AASHTO LRFD Bridge Design Specifications.

1.2 General Description

The bridge is a continuous road bridge with 3 spans and 2 welded I-shaped main girders. The

roadway has 2 traffic lanes with 3.5 m width and lateral strips of 2 m on each side.

The analyses comprise Static analysis for loads covered in Section 6 of the AASHTO LRFD

Bridge Design Specifications; the design of I-section flexural members is covered within Ar-

ticle 6.10, fundamental section property calculations for flexural members used in RM analy-

sis are found in Appendix D.

Figure 1-1: General view of the RM model

RM Bridge Structural Data



2 Structural Data

The bridge is a continuous road bridge with 3 spans and 2 welded I-shaped main girders. The

roadway has 2 traffic lanes with 3.5 m width, and lateral strips of 2 m on each side.

Figure 2-1 : Schematic view of the cross-section

Summary of cross-section data:

Total slab width 12.0 m

Spacing of main girders 7.0 m

Overhang left and right 2.5 m

Effective depth of concrete slab 0.307 m

Effective haunch depth 0.109 m

Depth of steel girders 2.8 m

Upper flange width 1.0 m

Lower flange width 1.2 m

2.1 General Layout

The structure is modelled as a grillage with two axes in the longitudinal direction and four

axes in the transverse direction (one for each of the cross-members at the beginning and the

end of the system (A1, A2) as well as over the piers (P1, P2)). Each of these 6 axes has its

own associated segment.




Figure 2-2: Span distribution

The longitudinal overhang at begin and end of the bridge is assumed 0.8 m.

The model has been prepared with the wizard functionality of RM Bridge, which allows for an

easy and straightforward definition of the structure. However, model preparation could also

be done directly in the standard RM Bridge GUI.

In plan the structure is straight and abutments and piers are orthogonal to the longitudinal di-

rection of the superstructure. The piers are drop cap piers with bearings under each main gird-

er of the superstructure.

Default pier dimensions of the wizard have been used without consideration of actual feasibil-

ity, as the focus of this example is just on superstructure design and not on substructure de-

sign.

Longitudinal fixation is assumed at the left abutment, bearings over the piers and the right

abutment are assumed free to move in longitudinal direction.

2.2 Numbering Scheme

The bridge wizard automatically creates nodes and elements of the structural system and the

respective node and element numbers.

Due to modeling the structure as a girder grid we have two main girders, left (MG1) and right

(MG2). Both main girders are composite girders, where structural elements are assigned to the

individual cross-section parts as well as to the full composite section.

The actual refinement of the calculation model is automatically done by the wizard. Default

(and minimum) subdivision is 24 per span, i.e. with considering the left and right overhang

the first and the last span will have 25 elements, and the intermediate spans will have 24 ele-

ments with equal length.

If there are additional points of interest in the system, this regular subdivision will be auto-

matically adapted. The wizard considers every point, where the cross-section of a main girder

changes, as additional point of interest. I.e. points, where a parameter of the cross-section

changes (e.g. web thickness or flange thickness) the program automatically places a subdivi-




sion point. It depends on the distance of such a point from the regular subdivision points

whether a new point is inserted or the nearest regular point is moved into this position.

Note that the program does not check the actual change of a cross-section parameter, but just

whether there is a constraint point in the variation diagram. I.e. the user may enforce the pro-

gram to create a subdivision point at a certain position by assigning a Variation to one param-

eter (e.g. the web width) and specifying the value in this position no matter whether the value

before or behind this point is the same.

Note also that the program does not automatically create additional subdivision points at posi-

tions of cross-frames, bracings or stiffeners. Those are always eccentrically connected to the

nearest subdivision point on the main girder. If the user wants to have subdivision points at

the positions of cross-frames, he must place at this position a variation constraint point as ex-

plained above.

In our example we have in the first and last span a cross-frame distance of 7.5 m which is 1/8

of the the span length. I.e. cross-frame positions automatically coincide with regular subdivis-

tion points. However, in the center span we have cross-frame distances of 8.0 m (1/10 of the

span length). Therefore, in order to have subdivision points in these positions, we defined

respective variation constraint points in the variation of the web thickness (see variation

tw_S02 in the wizard). As a consequence, we have in the center span 30 elements in longitu-

dinal direction instead of 24.

Table 2-1: Numbering scheme

Item Span 1 Span 2 Span3

Node numbers (MG1) 101-125 201-230 301-325

Element numbers (MG1, steel) 10101-10125 10201-10230 10301-10325

Element numbers (MG1, concrete) 20101-20125 20201-20230 20301-20325

Element numbers (MG1, composite) 101-125 201-230 301-325

Node numbers (MG2) 401-425 501-530 601-625

Element numbers (MG2, steel) 10401-10425 10501-15230 10601-10625

Element numbers (MG1, concrete) 20401-20425 20501-20530 20601-20625

Element numbers (MG1, composite) 401-425 501-530 601-625

Abutments/Piers (left) 80001, 80002 80003-80025 80027-80049

Abutments/Piers (right) 80003-80025 80027-80049 80051, 80052

2.3 Support Conditions

The following table defines the support conditions in reference to the local coordinate system

of the spring elements (alpha1 = 90 degrees), i.e. X = vertical, Y = longitudinal, Z = trans-

verse direction. Actual stiffness of bearings and foundation is not considered and spring con-

stant 1e+008 indicates a rigid support.

Table 2-2: Support conditions

Axis Part/Soil Elem Type C-X C-Y C-Z C-MX C-MY C-MZ

Abut-

ment 1

1

2

80001

80002

Spring

Spring

1e+008 1e+008 1e+008

1e+008 1e+008 1e+008

Pier 1 1

2

Soil

80009

80010

80012

Spring

Spring

Spring

1e+008 1e+008

1e+008

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008




Soil

Soil

80017

80022

Spring

Spring

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008

Pier 2 1

2

Soil

Soil

Soil

80033

80034

80036

80041

80046

Spring

Spring

Spring

Spring

Spring

1e+008 1e+008

1e+008

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008

1e+008 1e+008 1e+008 1e+008 1e+008 1e+008

Abut-

ment 2

1

2

80051

80052

Spring

Spring

1e+008 1e+008

1e+008

2.4 Main Girders

Every main girder has a constant depth of 2800 mm and the variations in thickness of the up-

per and lower flanges are found towards the inside of the girder. The lower flange is 1200 mm

wide whereas the upper flange is 1000 mm wide.

Figure 2-3: Structural steel distribution for Upper and Lower main girder flanges




Figure 2-4: Structural steel distribution of the main girder web

2.4.1 Definition of the Main Girder Segments

Separate segments are created by the wizard for each span and each main girder

(w1_Span01.01, w1_Span01.02, w1_Span02.01, w1_Span02.02, w1_Span03.01,

w1_Span03.02). Creating the model in the RM Bridge Modeler would of course also allow

working with 2 segments reaching over all spans. In the first and last span the segments are

subdivided into 25 elements with typical element length of 2.5 m. In the center span we have

30 elements with a typical length of 2.667 m, but some variation of the element length (2.0 m,

3.0 m) to meet the relevant points where cross-frames are connected or the cross-section var-

ies.

The main girder segment numbering systems are given in chapter 2.2 (Numbering Scheme). A

cross section must be assigned to every segment point. Cross-section w1_Deck is assigned to

the span part of the first main girder and the same w1_Deck for the second main girder.

Figure 2-5: Segmentation of the 3rd

span




Figure 2-6: w1_Deck cross-section

2.5 Cross Frames and Stiffeners

Steel cross frames are arranged over the piers and in the spans. Over the piers we have a

welded I girder with height of 1.5 m and 30 cm wide flanges. Cross frames in span are rolled I

beams IPE-600.

Figure 2-7: Cross frame used in the span Figure 2-8: Transversal view of theIPE 600

profile




Figure 2-9: Cross frame used over the piers Figure 2-10: Transversal view of the I-

welded profile

Figure 2-11: Cross frame arrangement over Span 2

Figure 2-12: Cross frame arrangement over the first and also third span




At each cross frame position stiffeners are present on both sides of the main girder.

Figure 2-13: T-welded profile used for transverse stiffneres

Diaphragm elements are numbered as follows:

Over the left abutment Element 50001

Over the first pier Element 50091

Over the second pier Element 50191

Over the right abutment E lement 50261

Cross frames in span have a spacing of 7.5 m in the first and last span, respectively 8 m in the

central span. The numbering is:

Left Span Elements 50001 to 50081 step 10

Central Span Elements 50091 to 50181 step 10

Right Span Elements 50191 to 50261 step 10

Slab reinforcement:

For both reinforcing steel layers, the transverse reinforcing bars are placed outside the longi-

tudinal reinforcing bars, on the side of the slab free surface.

Transverse reinforcing steel

At mid-span of the slab (between the main steel girders) o High bond bars with diameter = 20 mm, spacing s = 170 mm in upper layer o High bond bars with diameter = 25 mm, spacing s = 170 mm in lower layer

In the slab sections supported by the main steel girders o High bond bars with diameter = 20 mm, spacing s = 170 mm in upper layer o High bond bars with diameter = 25 mm, spacing s = 170 mm in lower layer

Longitudinal reinforcing steel

In span o High bond bars with diameter = 16 mm, spacing s = 130 mm in upper and

lower layers (i.e. in total s = 0, 92% of the concrete section)

In intermediate support regions: o High bond bars with diameter = 20 mm, spacing s = 130 mm in upper layer o High bond bars with diameter = 16 mm, spacing s = 130 mm in lower layer o (i.e. in total s = 1, 19% of the concrete section)




Figure 2-14: Location of mid-span and support sections for longitudinal reinforcement

Figure 2-15: Green lines representing longitudinal reinforcement in w1_deck Cross section

2.6 Shear Studs

Special shear stud spring elements are available for composite cross-sections in RM Bridge

Analysis (Figure 2-16). These shear stud elements must be defined as spring elements by the

user connecting the same structural nodes as the associated composite elements. Their num-

ber, by default, must be the number of the elements formed by the first cross-section part plus

30000. For these elements no other information needs to be defined; the warnings regarding

the missing spring stiffness during calculation can be ignored. These shear stud elements do

not contribute to the structural stiffness of the system. However, the change in normal force

per length within this element is stored and can be accessed during post-processing. During

result superposition, results for these elements are added together as for the other structural

elements in the system ensuring, that the true minimum and maximum values for the shear

force are computed. For the present example spring elements: 30101-30125; 30201-30230;

30301-30325; 30401-30425; 30501-30530; 30601-30625 are automatically generated by the

program.




Figure 2-16: Composite and shear stud elements with element numbers

The spring elements modelling the shear studs can be input under Structure Elements El-ement Types and Nodes.

Figure 2-17: Composite and shear stud elements with element numbers

2.7 Materials

Reinforcement: AASHTO_LRFD_RGr75 o Yield Strength: 5.171e+05 kN/m2 o Modulus of Elasticity: 200E+06 kN/m2

Concrete: AASHTO_LRFD_C35MPa o Compressive Strength: 3.497E+04kN/m2 o Modulus of Elasticity: 3.127E+07 kN/m2

Structural AASHTO_LRFD_STGr50 o Yield Strength: 3.447E+05 kN/m2 o Modulus of Elasticity: 2.0000E+08 kN/m2

RM Bridge Construction Schedule and Loading



3 Construction Schedule and Loading

Stage-wise erection is only related to subsequent erection of superstructure, bearings, steel

construction and concrete slab, but there are assumed that all spans are erected simultaneously

(erection of the whole steel construction in one stage, pouring the whole slab in one stage).

3.1 Element Activation by Stages

Each construction stage is related to a certain active system, which may contain all elements

of the model or just a part of them. The activation of new elements is done in Schedule >

Stages > Activation. Elements, which already have been activated in previous construction

stages remain active until they are explicitly deactivated, and must not be specified again in a

subsequent stage. An appropriate indication is given by the program in the case that a previ-

ously activated element is again specified. If the user then selects the option , the

element will be removed from the previous construction stage and added in the current stage.

The activation of the elements in the different stages is shown below.

Stage SubS

Activation of earth springs and pier elements:

80003-80008; 80012-80015; 80017-80020; 80022-80025; 80027-80032; 80036-

80039; 80041-80044; 80046-80049.

Stage Abutment

Activation of left and right bearings

80001-80002; 80009-80010; 80033-80034; 80051-80052.

Stage Girder

Activation of steel girders including cross-frames, bracings and stiffeners

Main girders: 10101-10125; 10201-10230; 10301-10325; 10401-10425; 10501-

10530; 10601-10625

Cross-frames: 50001-50261

Lateral bracings: 60001-60351

Vertical Stiffeners: 70001-70261; 70401-70661




Figure 3-1: Active structure after installing main and secondary steel members

Stage Slab

Activate concrete elements, shear studs and composite elements

Composite elements: 101-125; 201-230; 301-325; 401-425; 501-530; 601-625

Concrete slab elements: 20101-20125; 20201-20230; 20301-20325; 20401-20425;

20501-20530; 20601-20625

Shear studs: 30101-30125; 30201-30230; 30301-30325; 30401-30425; 30501-

30530; 30601-30625

Further Stages

All further stages in the schedule dont contain new activations but are just defined to group the different categories of actions.




3.2 Design Loads

3.2.1 Dead Load

Self-weight (concrete): 23.56 kN/m3

Self-weight (steel): 76.97 kN/m3

Additional dead load (asphalt, traffic barriers...): 3.0 kN/m2 over roadway surface 3.13 kN/m on each side

3.2.2 Live loads

Traffic loading consists in defining Lane placement, Dynamic load allowance, Design Vehic-

ular Live load and Pedestrian load.

When the position of the load trains is between two girders then the program automatically

calculates the distribution to the both girders. The same is done for the other side when miror

option is selected

Figure 3-2: Traffic loading on the bridge

Dynamic load allowance in accordance to AASTHO 3.6.2 table 3.6.2.1-1.The factor to be

applied to the static load shall be taken as (1+IM /100).

Joints - Deck Joints for all Limit States with IM= 75 %.

Fracture - Fatigue and Fracture Limit State with IM=15 %.

Standard - All other Limit States with IM=33 %.

Design Vehicular Live load in accordance to AASTHO 3.6.1.2, designated HL-93, and shall

consist of a combination of the design truck or design tandem and design lane load.

Design Truck -specified in figure 3.6.1.2.2-1 of AASHTO code.




Design Tandem consists of two 110-kN axles spaced at 1.2 m from centre.

Design lane load is equal to 9.3 kN/m per lane (3.1 kN/m2) and emulates a caravan of trucks.

3.2.3 Braking Load

The braking load is calculated according to AASHTO 3.6.5

The load is considered to be applied uniformly distributed in longitudinal direction along the

roadway axis acting at the finished roadway level and in case of grillage modeling distributed

proportionally to all applicable main girders.

There is no influence line evaluation made for the braking load, but the whole braking load is

applied in one loadcase w1_brake as distributed load over the whole roadway surface. The

total line load intensity is calculated and then distributed to the different girders.

Nominal load per lane 109.994 kN

Nominal line load per lane 0.546 kN/m (Calculated as Nominal Load per Lane/bridge length (with begin and end excess

length).

Multiple presence factor 1 (In accordance with AASHTO table 3.6.1.1.2-1)

Total line load 1.091 kN/m (Calculated as Nominal Load per Lane*Number of lanes *Multiple presence fac-

tor/bridge length)

Height of application 1.8m above cross-section surface

3.2.4 Wind Loads

Figure 3-3: Wind loading on the bridge

Wind loading is defined in accordance with AASHTO 3.8.1. The LRFD Specification pro-

vides wind loads as a function of base design wind velocity, VB equal to 160 km/h.




Wind pressure on strucures (WS)

Applied to the surface area of the superstructure as seen in elevation, according to AASHTO

3.8.1.2.1-1 for beams.

Base pressure(Pd) 2.4 kN/m2

Height(h) 4.116 m

Wind pressure on vehicles (WL)

When vehicles are present, the design wind pressure shall be applied to both structure and

vehicles. Wind pressure on vehicles is represented by an interruptible, moving force.

Line load(ll) 2.46 kN/m

Eccentricity(ecc) 1.8 m

Vertical Wind Pressure (W-up)

In absence of live loads, an upward load of 9.6 10-4 MPa is multiplied by the width of the

superstructure and applied at the windward quarter point simultaneously with the horizontal

wind loads applied perpendicular to the length of the bridge.

Upward wind

Pd-up 0.96 kN/m2

Ecc up 3 m

Downward wind

Pd-down 0 kN/m2

Ecc up 3 m

3.2.5 Thermal Forces

Uniform temperature load:

The default value of the initial temperature is considered by T0=12 C, Te,min=-12 , Te,max=27

TN,neg = Te,min T0 -24

TN,pos = Te,max T0 +15

RM calculates 2 load cases w1_T-const1 (TN,pos) and w1_T-const2 (TN,neg). Both load cases are based on a load set with unit load 1.0 C, which is factorized by the relevant T value.

Temperature gradient:

According to AASHTO 3.12.3-1 there are four Temperature zones which provide a linear

relationship for the temperature gradient in steel and concrete and allow you to change the

temperature of the top and bottom independly: T1=23o C , T2=6

o C, T3 shall be taken 0

0 C.

Negative temperature gradient factor: -0.3 negative temperatures values shall be obtained by

multiplying the values by this factor.

Vertical temperature gradients in concrete and steel superstrucures




A-top 0.1

A 0.3

A-bootom 0

3.3 Load Combinations

RM Bridge offers the possibility of defining a combination table describing the rules for au-

tomatic load case superposition and creation of result envelopes. Templates for automatic

generation of this combination table are available for many design codes. Also, the wizards

automatically generate the relevant combination table for the selected design code. The com-

bination table for Eurocode as used in this example is shown below in Figure 3-4. It is a very

comprehensive table, but only few generated envelopes are used in this example.

Figure 3-4: Combination table for AASHTO

Abstract of predefined Load Combinations:

Combination I and II - "permanent loads"

Comb.I: t=0

Comb.II: t=oo




SERVICE - Combinations III to VII

Comb.III: SERVICE I (incl. Live load)

Comb.IV: SERVICE I (excl. Live load)

Comb.V: SERVICE II

Comb.VI: SERVICE III

Comb.VII: SERVICE IV

Comb.VIII: SERVICE I - deflection (incl. live load)

Comb.IX: SERVICE I - deflection (excl. live load)

STRENGTH - Combinations XI to XV

Comb.XI: STRENGTH I

Comb.XII: STRENGTH II

Comb.XIII: STRENGTH III

Comb.XIV: STRENGTH IV

Comb.XV: STRENGTH V

EXTREME - Combinations XVI to XVII

Comb.XVI: EXTREME I (earthquake) Comb.XVII: EXTREME II (collision by vessels)

Wind and Braking loadings are not mentioned in the Setra documentation, but for complete-

ness of the generated model they are treated here.

RM Bridge Analysis results



4 Analysis results

Figures below illustrate a few results of internal forces and moments coming from the global

analysis of the deck in the design example.

All diagrams below are related to the first main girder MG1. Due to the symmetry conditions

there is no difference between the 2 girders and assessing just 1 of them is sufficient.

Bending moments: Figure 4-1 below shows the extreme bending moments of the main girder

due to traffic. The comparison with the Setra results is shown in Figure 4-2. We see that the

minimum moment due to traffic is -15779 kNm compared to (15720+6190=21910) kNm from the Setra document. In fact traffic load prescription in Eurocode are much higher than in

AASHTO LRFD and the ratio between 21910 and 15779 approximately corresponds to the

ratio between the design traffic load intensities to be used in the different codes.

Referring now to the ultimate state design moments presented in Figure 4-3, we see that max-

imum hogging moments are about 102425 kNm and the maximum positive moment in the

center is about 45510 kNm. Here we see that the difference is smaller than for traffic loads,

this is likely caused by the fact that Setra used stiffness reduction in the pier region to cater

for caracking of the concrete slab. The reported values in the Setra document are shown in

Figure 4-4.

Figure 4-1: Moments for traffic loads RM results




Figure 4-2: Moments for traffic loads (UDL and TS) - Setra document

Figure 4-3: Moments of final ULS and characteristic SLS combinations RM results




Figure 4-4: Moments of final ULS (comb. 11) and characteristic SLS (comb.6) combinations - Setra document

Shear forces (Figure 4-5 and Figure 4-6): The maximum value of the shear-force over the

piers is some +7080/-7020 kN. When we compare this with the results given in the Setra doc-

ument we see maxima of some 7450 kN, what is again caused by the lower traffic load.

Figure 4-5: Shear forces for ULS and characteristic SLS combinations RM results




Figure 4-6: Shear forces for ULS (comb. 11) and characteristic SLS (comb. 6) combinations Setra document

Displacements: We can observe that the largest value of the vertical displacement is situated

at mid span of the second span with an approximate value of 125 mm caused by Ultimate

Limit State actions.

Figure 4-7: Vertical displacement (Vy) from ULS actions

RM Bridge Steel Design Checks



5 Steel Design Checks

5.1 General

5.1.1 Design Calculation Actions

Steel design checks in RM Bridge are performed in 2 steps:

1. Calculation of design resistances (Schedule action UltRes) 2. Actual proof check using interaction formulas (Schedule action ResChk)

The relevant design resistances can be stored in superposition files like normal impact enve-

lopes. This allows viewing them in the GUI in the same way than viewing structural analysis

results, with the full functionality of graphic presentation.

Plotting the resistances into the same diagram together with the relevant ULS combination

allows for direct graphical assessment of the results as shown in Figure 5-3 and Figure 5-4.

Note that the calculation of basic resistances without consideration of locked-in force effects

is based on the presumption of sufficient stress redistribution capacity by plasticization. I.e. in

theory this is only allowed for class 1 and 2 cross-sections. These resistances must be com-

pared with so called Joined forces, i.e. fictitious internal forces on the composite section which are equivalent to the combined effect of forces acting on the steel girders only (self

weight, wet concrete) and forces acting on the composite section (SDL, traffic, ).

RM Bridge also allows taking locked-in forced into account by specifying the load case con-

taining the relevant forces acting on the steel part only. In that case the capacity factor is re-

lated to the additional forces acting on the composite section. These results are described in

chapter 5.6, Consideration of locked-in stresses.

5.1.2 Relevant additional input parameters

Two additional input parameter sets must be specified to be able to perform steel checks:

1. The definition of Slender cross section parts to check for local buckling phenome-na in the cross section plane (buckling of cross-section plates), and

2. The definition of Characteristic lengths (buckling lengths) for buckling phenome-na in longitudinal direction of the members.

5.2 Slender parts

The definition of slender cross-section parts (SP) is required to consider local buckling phe-

nomena due to compression forces. These slender parts are defined as lines between two

points of the cross-section, with the thickness t as additional parameter. These slender parts

are used for the cross-section classification as described in the next section.

The characteristic slenderness value used for classification is the width to thickness ratio, de-

fined as c/t in Eurocode or slenderness parameter in AASHTO code. The thickness is com-monly denoted t, often with reference to the type of the part (tw for web, tf for flange). Differ-




ent rules are given in the different design codes for defining the relevant width of slender

parts.

5.2.1 Definition of Slender parts

In the RmBridge database Slender parts are defined as Reference Sets of the cross-section. These reference sets have the type Steel slender part. The definition of these refer-ence sets may be done either in the RmBridge Modeler during graphic definition of the sec-

tion, or in the RmBridge Analysis GUI in the function for cross-section definition and modifi-

cation (Properties > Cross-sections > Reference Sets).

One slender part is defined as a line segment with a start point and an end point. As long as

the material is the same, an arbitrary number of such slender parts (line segments) may be

arranged in one common reference set. In case of hybrid sections (e.g. steel grade of the web

lower than grade of flanges), slender parts of the cross-section parts with different material

have to be defined in different reference sets.

Figure 5-1: Slender parts definition

One slender part is defined as a line segment with a start point and an end point. As long as

the material is the same, an arbitrary number of such slender parts (line segments) may be

arranged in one common reference set. In case of hybrid sections (e.g. steel grade of the web

lower than grade of flanges), slender parts of the cross-section parts with different material

have to be defined in different reference sets.

In addition to the slender parts themselves the reference set may contain stress points to be

used for calculating the minimum elastic section modulus. This is just required if other than

start and end points govern the calculation of the minimum section modulus, because start and

end points of the slender parts are automatically checked whether they become decisive.

The individual slender parts consist each of a start point of the type POINT and an end point of the type LINETO. In slender parts with free ends (outstand flanges or ribs) the free point must essentially be the end point (i.e. the slender part must be a line from the restraint point to

the free point). For slender parts with restraints at both sides (webs) the sequence of the 2

points is arbitrary, however, we recommend to use a unique definition throughout the project

(e.g. bottom-up for vertical lines which is also the wizard convention).




The subtype of the individual slender parts in a reference set is defined as a flag assigned to

the start point. The following subtypes are allowed:

W Web Webs of I Girders, Channels or Box Girders ( 2A)

F Flange Outstand Flanges of I Girders, T-Girders, Channels, etc. ( 1A)

B Box Flanges of box girders (restraint on both sides) ( 2B)

R Rib Outstand rib e.g. stems of T girders, ribs or stiffeners ( 1B)

Like the subtype, the effective thickness of the slender part is also a parameter assigned to the

start point. For calculating the slenderness of the part the program calculates the length of the

line between the start and end point and divides it by the effective thickness.

5.2.2 Slender parts in the current example

In our example we use SlenderF and SlenderW as reference sets in definition of the main

girders, and SlenderF and SlenderR in the definition of secondary members (cross frames and

stiffeners).

Figure 5-2: Slender parts definition in the Cross section.




5.3 Buckling lengths

The characteristic length for local buckling of main girders is in general defined by the rele-

vant distance of transverse stiffeners. The characteristic length for lateral-torsional buckling is

normally the distance between cross-frames or diaphragms. Buckling due to normal force is

not relevant for the main girder; nevertheless reasonable values for the respective buckling

lengths have been defined (automatically created by the wizard).

5.3.1 Definition of Buckling Lengths

As a theoretical and accurate calculation of these characteristic lengths is impossible, they are

directly defined for the different beams elements in the GUI in Structure > Elements > Buck-

ling lengths. Separate values can be defined for the start point and the end point of each ele-

ment.

The characteristic length for local buckling of main girders is in general defined by the rele-

vant distance of transverse stiffeners. The characteristic length for lateral-torsional buckling is

normally the distance between cross-frames or diaphragms.

The RmBridge wizard functionality automatically creates this table of characteristic lengths in

accordance with above habits with the following constitutive law for standard I girder compo-

site bridges:

Steel main girders (constructability check):

L-rz Span length respectively overhang length at begin and end

L-ry Cross frame distance

L-rx Cross-frame distance

L-loc Distance of transverse stiffeners

L-lt Distance of transverse stiffeners

Composite main girders (ULS check):

L-rz Span length respectively overhang length at begin and end

L-ry Zero

L-rx Zero

L-loc Distance of transverse stiffeners

L-lt Distance of transverse stiffeners

Cross-frame members and diaphragms

L-rz = L-ry = Lrx = L-loc = L-lt = nominal member length

These characteristic lengths may also be directly defined in the GUI in Structure > Elements

> Buckling lengths. It is also possible to define separate values start points and end points of

the different elements. The following defaults are valid if not all lengths are specified:

No buckling lengths L-rz, L-ry, L-rx defined: the program assumes that there is no flexural and no torsional-flexural buckling hazard

Only L-rz defined: the program assumes L-ry and L-rx the same (one com-mon beam buckling length)

No L-loc defined: the program assumes that there are no transverse stiffeners




No L-lt defined: the program assumes there is no lateral-torsional buckling hazard

Profile type information can be defined in Rm first in Modeler in the Cross-Section window

by clicking on the arrow button of Parts.In the part definition window the respective part has to be edited.There is a drop-down menu Profile where the respective type has to be se-lected.

In the Analyzer this data is stored in the menu Properties/Cross-Section/Parts->edit part in

bottomwindow->option Part-class.

5.3.2 Buckling Lengths in the current example

Table 5-1

Elements L-rx L-ry L-rz L-loc L-lt

101 0.8 0.8 0.8 0.8 0.8

102-125 7.5 7.5 60.0 7.5 7.5

201-230 8.0 8.0 80.0 8.0 8.0

301-324 7.5 7.5 60.0 7.5 7.5

325 0.8 0.8 0.8 0.8 0.8

401 0.8 0.8 0.8 0.8 0.8

402-425 7.5 7.5 60.0 7.5 7.5

501-530 8.0 8.0 80.0 8.0 8.0

601-624 7.5 7.5 60.0 7.5 7.5

625 0.8 0.8 0.8 0.8 0.8

10101 0.8 0.8 0.8 0.8 0.8

10102-10125 7.5 7.5 60.0 7.5 7.5

10201-10230 8.0 8.0 80.0 8.0 8.0

10301-10324 7.5 7.5 60.0 7.5 7.5

10325 0.8 0.8 0.8 0.8 0.8

10401 0.8 0.8 0.8 0.8 0.8

10402-10425 7.5 7.5 60.0 7.5 7.5

10501-10530 8.0 8.0 80.0 8.0 8.0

10601-10624 7.5 7.5 60.0 7.5 7.5

10625 0.8 0.8 0.8 0.8 0.8

5.4 Design Resistances (without considering locked-in stressing)

5.4.1 General

In RM Bridge design resistances for slender steel and composite sections are calculated in the

schedule action UltRes. The calculated resistance values are written into a listfile and an Ex-

cel sheet, and also stored in a superposition file in order to allow for subsequently using

standard result presentation techniques for graphic presentation of design resistances.

In composite sections where we may have locked-in stresses due to stage-wise assembly of

the whole section, the resistances may either be calculated without considering locked-in




stresses or by specifying the relevant locked-in stressing state (load case) as additional resistances (forces which can be applied on the composite section in addition to the locked-in

forces in the individual elements).

In order to distinguish between the 2 situations in composite elements we speak of total resistances if locked-in stresses are not considered and of additional resistances if they are considered. The total resistances must be compared with the joined ULS forces, i.e. we as-sume that in the ultimate state the locked-in stresses will be redistributed to the composite

section. Note that the total resistances are not correct for slender cross-section, because lo-cal buckling failure will occur before redistribution due to plasticization can take place.

5.4.2 Main girders Typical sections

RM Bridge calculates the resistances for all element start and end points with the respective

switch in the element table set to Yes. This allows presenting diagrams along the bridge as shown in Figure 5-3: Bending resistances and ULS bending moments along the main gird-

erand Figure 5-4: Shear resistances and ULS shear forces along the main girder. Only re-

sistances for bending moments Mz and shear forces My are shown here, because these are the

design relevant quantities.

For comparison a hand-calculation is made for 1 typical section:

the cross-section over the piers (element 10125), and

5.4.2.1 Hand calculation for a Cross Section over Pier1: element 10125:w1_Deck:005:2

Classification compression and bending(ANSI/AISC 360-05, Table B4.1)

Table 5-2

c t c/t y1 y2

Web 2.540 0.026 97.690 -3.086 -0.546

flanges_top 0.5 0.120 4.167 -0.476 -0.476

flanges_bot 0.6 0.120 5 -3.156 -3.156

ey_el ey_pl

Eccenter -1.913 -2.278

Specific values E = 200E6; Yield strength compression fyc = -344778;

Yield strength tension fyt=344738 => fyc

E 24.086; kc =

twh /

4= 0.405

Compression




Table 5-3

c/t case P r class

Web 97.690 10 1.12* =26.978 1.49* =35.88 SL

flanges_top 4.167 4 0.38* = 9.15 0.64* *kc =9.81 C

flanges_bot 5 4 0.38* = 9.15 0.64* *kc =9.81 C

Bending +z

flanges: already in compact class

web: sign=+1 ; dx1p = ( y1 ey_pl )*(sign) = 1.903 > 0 => compression ( web partly in compression)

dx2p = (y2 ey_pl)*(sign) = -0.637 < 0 => tension (whole web in tension would be compact)

Type 2A, welded, flexure => case 11: hc = ey_el; hp = ey_pl; My = 121827.423 ; Mpl =

134818.468

P = 2)09.0/*54.0(

*/

MyMp

hphc = 3.316* =78.52; r =5.70 * =137.2

c / t = hc / tw = 73.577 => class compact

Bending -z

web: sign=-1 ; 0.637 > 0 => compression ( web partly in compression)

type 2A, welded, flexure => case 11: hc = ey_el ; hp = ey_pl ;

My = -121827.423;

Mpl = -134818.468 (see calculation below in bending resistance)

see bending +z => class compact

Tensile / Compressive Resistance( AASHTO LRFD 6.8.2.1-1)

Ax = 0.3308 = At = Ac; fyt = 344738; fyc = -344738; y = 0.950; c = 0,900

Nt = At * fyt * y = 0.3308 * 344738 * 0.950 = 108337.364 tensile resistance

Web is in class SL => normally reduction of web, but preliminary we dont reduce webs

Nc = Ac * fyc * c = 0.3308 * -344738 * 0.900 = -102635.4 compressive resistance

Bending resistance +z

Cross section is in class compact, so we calculate the plastic values:




Wpl = 0.391075; ey_pl = -2.278 and ey_el = -1,913

fnc= Rb * Rh * fy = 344738 => (webload shedding 6.10.7.2.2-1)

Mpl = Wpl * f * fnc = +-134818.413

Shear Resistance in y direction for cross section (AASHTO LRFD 6.10.9.1-1)

fy = 344738 (authoritative yield ) ; Ay_Shear = 0.071; v = 1.000

(AASHTO LRFD 6.10.9.3.2-2) Vp = Ay_Shear * fy / 3 * v = 14131.455 plastic

shear resistance

(AASHTO LRFD 6.10.9.3.2)

d0 = inf. => unstiffened; k = 5.000; D = 2.540; tw = 0.026; E = 200E6; fy = 344738

1.12 * fy

kE*= 1.12 * 53.858 = 62.703; 1.40 * 53.858 = 78.379; D / tw = 97.692 => 97.692 >

78.379 =>

C = 1.57 * tw / D *(E * k / Fy) = 1.57 * 97.692 * 53.858 = 0.477 reduction factor

Vn = Vp * C = 6740.704 design nominal shear resistance

Shear Resistance in y direction for beam (AASHTO LRFD 6.10.9.3.2)

Vpl_rd = 13732.276 design

plastic shear resistance

L-loc is defined => d0 = 7.5

d0< 3 * D => 7.5 stiffened => C = 1.389 reduction factor

Vn = Vp * C = 9386.4 design nominal shear strength

Flexural and torsional - flexural buckling (AASHTO LRFD 6.9.4.1)

Table 5-4

x y z

Moment of Inertia I 0.001234 0.027284 0.507905

Buckling length L 7.500 7.500 60.000

Radius of Gyration r 1.272 0.287 1.239




Elastic Slenderness 0.006 0.11925 0.4095

Reduction factor 0.997 0.952 0.84351

Nominal Resistance Pn = Nc *

-102327.4938 -97708.9 -86573.986254

Ax = 0.3308; K = 1.000; Nc = -102635.4 Design compression resistance

rx = Ax

IzIy = 1.272 ; ry =

Ax

Iy = 0.287 ; rz =

Ax

Iz = 1.239

Nb= *

Nc = -86573.986 Design buckling resistance

Lateral-torsional buckling

Iy = 0.027284; Iz = 0.507905 => Iz > Iy => relevant direction is z ( Mz is considered)

Table 5-5

Top (+Mz) Bottom (-Mz)

Design bending resistance

Mz

134818.468 -94372.928

Buckling length Lb ( = L-lt ) 8.000 8.000

Compression web Dc 1.367 1.173

Compression flange bfc 1 1.2

Radius of gyration rt

(6.10.8.2.3-9)

0.2754 0.334

Lim. unbraced length Lp

(6.10.8.2.3-4)

6.632 8.063

Lim. unbraced length Lr

(6.10.8.2.3-5)

24.904 30.276

Reduction factor Fnc

(6.10.8.2.3-1,2)

0.9857 1.000

Design LTB resistance Mb 132898.15 -94372.928

tfc = 0.120 ; tw = 0.026, Ltop = 0.5 ; Lbot = 0.6

Compression web Dc: ey = -1.913; y1 = -3.086; y2 = -0.546




dx1e = (y1 ey) * sign = -1.173 resp. +1.173

dx2e = (y2 ey) * sign = 1.367 resp. -1.367

Mz+: dx > 0: Dc = 1.367

Mz- : dx > 0: Dc = 1.173

Compression flange bfc: ey = -1.913; y1 = -0.476; y2 = -0.476 and y1 = -3.156; y2 = -3.156

Top : dx1e = ( y1 ey ) * sign = 1.437 resp. -1.437

dx2e = (y2 ey) * sign = 1.437 resp. -1.437

Bot : dx1e = ( y1 ey ) * sign = -1.243 resp. +1.243

dx2e = (y2 ey) * sign = -1.243 resp. +1.243

Mz+: dx1e > 0: bfc = Ltop * 2 = 1

Mz- : dx1e > 0: bfc = Lbot * 2 = 1.2

rt = bfc / ))**3/()*(1(*12 tfcbfctwDc

Lp = 1.0 * rt *fyc

E

Lr = * rt *fyr

E; with fyr = 0.7 * fyc = 234500 => for Mz+: Lp Lb Lr and for Mz- :

Lb Lp

=>Mz+ reduction: Fnc = Cb * [ 1 ( 1 fyr / fyc ) * (Lb Lp ) / ( Lr Lp ) ] ; with Cb = 1.000

=>Mz- no reduction

5.4.3 RM Bridge Results

The following table shows a summary of the calculated bending resistance values for the

composite section over pier 1 (begin of element 10125) to be compared with the above hand-

calculated values. The full development of resistances along the bridge is shown in the subse-

quent Figure 5-3: Bending resistances and ULS bending moments along the main girder and

Figure 5-4: Shear resistances and ULS shear forces along the main girder.

The table contains the relevant resistance, if the effective cross-section has been changed for

accounting for local buckling hazard. For lateral torsional buckling only the negative moment




is relevant (bottom flange in compression) as the top flange is laterally fixed by the concrete

plate. I.e. lateral torsional buckling needs not be considered in the centre span.

Table 5-6: Element resistence table

Elem N+ My+ Mz+ N- My- Mz- Mx Qy Qz

10125 108324.2 9707.5 132898.2 -86564.3 -9707.5 -134818.5 0.0 9386.5 42702

125 114497.3 273903.2 188693.9 -142964 -99085.1 -147920.3 0.0 9386.5 42702.3

Figure 5-3: Bending resistances and ULS bending moments along the main girder




Figure 5-4: Shear resistances and ULS shear forces along the main girder

5.4.4 Assessments

Figure 5-3 shows that the bending resistance is sufficient throughout the whole girder length.

Resistance values are in the relevant points typically 30-50 % higher than required.

Figure 5-4 shows that over the piers the relevant design shear force exceeds the shear capacity

by a small amount.

5.5 Capacity Factors

5.5.1 Definitions

Results of the verification process which will be greater than 1.0 when the generalized re-

sistance is less than the generalized impact.

The definition and calculation of these capacity factors is based on the respective formulas

required for verification of mixed impact and given in the design codes:

AASHTO allows a less conservative approach and the capacity factors for combined actions

are defined accordingly dependent on the factor CN: (CN




5.5.2 Resulting Capacity factors

Figure 5-5: Girder 1 composite section capacity factors

5.6 Consideration of locked-in stresses

Calculation of resistances due to lockedin stress

w1_Deck:007, Elements 102 and 10102

Table 5-7

LC SUM-SW as locked-in stress N / Mx My / Mz Qy / Qz

10102 (single steel) -28.04/ 80.64 -18.50/ -48.79 -1134.12 / 23.52

102 (joined composite) -28.15/ -274.78 -20.39/ -83.47 -1198.21/ 4.00

Class Mz-, N SL

Composite CS Resistance BucklingResistance Residual Resistance

Mz+ 67025.202 67025.202 67025.202

Mz- -54742.296 Calculated via fy_eff Calculated via fy_eff

Qy 1970.152 1970.152 -2414.703/ +4801.972

Nc -105917.562 Calculated via fy_eff Calculatedvia fy_eff

Nt 48870.682 Calculated via fy_eff Calculated via fy_eff




Nc_remaining calculated via fy_eff

Relevant stresspoint: SlenderF: FB01B:2 (SLP06)

y_steel = ey_steel y_stpt = -1.896 + 3.196 = 0.5; z_steel = ez_steel z_stpt = 0 0.6 = 0.6

fyc = -344738 ; E = 2.0E8 ; Iz_steel = 0.19730; Iy_steel = 0.009095 ; Aeff_steel = 0.096,

Ac_comp = 0.341379

chi_steel = 0.789517

eps = N_steel / E / Aeff_steel + Mz_steel / E / Iz_steel * y_steel + My_steel / E / Iy_steel *

z_steel = -0.00000923

The procedure in non-compact sections is directly calculating the Residual Resistance with reduced (or increased) yield limits. I.e. in every investigated stress-point the locked-in longi-

tudinal stress is subtracted from the yield limit, and the residual elastic resistance is calculated

in the standard manner with using this reduced stress limit instead of the yield stress.

=>fy_eff = fyc * chi_steel E * eps = -287653.329+ 1938.300 = -285715.329

Nc_comp = fyc * Ac_comp = -117686.314

Nc_b_comp = fy_eff * Ac_comp = -97537.213

Nt_remaining calculated via fy_eff

Relevant stresspoint: SlenderF: FB01B:2 (SLP02)

y_steel = ey_steel y_stpt = -1.896 + 0.436 = -1.460; z_steel = ez_steel z_stpt = 0 0.5 = -0.5

fyt = 344738 ; E = 2.0E8 ; Iz_steel = 0.19730; Iy_steel =0.009095 ; Aeff_steel = 0.096,

At_comp = 0.1492

chi_steel = 1.000 (no buckling hazard for tension)


z_steel = 0.000005485

=>fy_eff = fyt * chi_steel E * eps = 344738 1151.800 = 343586.2

Nt_comp = fyt * At_comp = 51434.9096

Nt_b_comp = fy_eff * At_comp = 51263.06104




Mz-_remaining calculated via fy_eff

Relevant stresspoint: SlenderF: FB01B:2 (SLP06);

y_steel = ey_steel y_stpt = -1.896 + 3.196 = 1.3; z_steel = ez_steel z_stpt = 0 + 0.6 = 0.6

fy = +/-344738; E_comp = 2.0E8 ; Iz_steel = 0.1973 ; Ax_steel = 0.13716

chi_steel = 1.000; y_steel > 0 => compression => fy = -344738


z_steel = -0.00000878

The procedure in non-compact sections is directly calculating the Residual Resistance with reduced (or increased) yield limits. I.e. in every investigated stress-point the locked-in longi-

tudinal stress is subtracted from the yield limit, and the residual elastic resistance is calculated

in the standard manner with using this reduced stress limit instead of the yield stress.

=>fy_eff = fy * chi_steel E * eps = -344738+ 1843.38 = -342894.62

y_comp = ey_eff_comp_iter1 y_stpt = -1.664+ 3.196 = 1.532

kappa = fy_eff / E / y_comp = -0.001035548

Izeff_comp_iter1 = 0.395175

Mz-_comp = kappa0 * E_comp * Izeff_comp_iter1 = -52848.115

Figure 5-9: Normal force resistance due to locked in stresses on composite section




Tension force capacity is not influenced by locked in stress as you can see in the above Fig-

ure.

Figure 5-10: Bending moment resistance due to locked in stresses on composite section

Bending capacity is increased when the primary state has a deloading effect but decreased

when it has the same sign. When we look at the hogging moment over the piers we see that

the residual resistance for negative moment is lower than the total resistance, due to the

locked-in moment being negative. On the contrary, the resistance against positive moments is

increased.

When we look at the end of element 125 we see that we have a locked in bending moment of -

31133 kNm. We find that value as joined result value of the load case SUM-SW in the results

GUI.

The residual capacity in this point is -116787 kNm (envelope uresprimLC.sup in the exam-

ple). Those two added together will give a similar value to the maximum design bending re-

sistance without locked-in forces of -147920 kNm as shown in Figure 5-3. Similar checks

have been done for the entire bridge length but not documented here.




Figure 5-11: Shear resistances due to locked in stresses on composite section

A shear resistence check for end of element 125 gives us a Qy from SUM-SW locked in state

of 2439 kN and adding this with the residual resistance of 6946 kN will get a resistance of

9385 kN which is similar to the resistence without locked in state.

Figure 5-12: Capacity factors for residual resistences




If we look at the capacity factors we see, that the factors are lower than those calculated for

total loading situation. The reason for that is that in the joined load approach the locked-in

part is also multiplied by the relevant load factor for self weight (1.25 respectively 1.5),

whereas in the approach with separate consideration of locked-in forces this part is not in-

creased with the safety factor.

Various result plots were added in the Steel design check schedule to have a better compari-

son with Setra document and for locked-in stress presentation values. For the last one a super-

position file was created: uresprimLC.sup that uses the internally generated load case SUM-

SW for defining the lock-in state. Afterwards 3 new RM sets were made (PrimLC_MZ for

bending moment; PrimLC_N for tension force; PrimLC_Qy for shear force) defined on ele-

ments representing the entire bridge length of Girder1. Result of SUM-SW Load case (join) to

be added plus normal results from envelopes uresPrimLC.sup and w1_SteelRes.sup that will

show min/max values in the final diagram. In the last stage DgmSets having the same name as

the RM sets are added in the schedule that will show the needed results.

Similar approach is made in the case of DgmSet: UDL-TS; ULS-SLS-MZ; ULS-SLS-Qy;

displ_Vy, first the corresponding Rmset is created and then added in the schedule.

5.7 Rating factor

Using RateF schedule action we can find the rating factor at a certain point which is showed

in the plot file from the created RM-set (Lrate for our example)

Element 102 Begin

D= Dead Load Effect from W1_Comb01.sup: Max Nx- Nx Begin = 1514.417 kN

Min Nx- Nx Begin = -1490.361 kN

L=Live Load Effect from W1_Comb02.sup: Max Nx- Nx Begin =1730.422 kN

Min Nx- Nx Begin =-1722.294 kN

A1 = Factor for Dead Loads =1.1

A2 = Factor for Live Loads =1.2

I = Impact factor (Dynamic Load Allo wence) = 1.3

C=Capacity =Result: w1_SteelRes 102 Begin: +NxRd= 48870.682 kN

-NxRd=-83623.672 kN

RF (MaxNx) =

=

= 9.883829

RF (MinNx) =

=

= 17.247




Figure 5-12: Load rating for element 102

Element 113 Begin

D= Dead Load Effect from W1_Comb01.sup: Max Nx- Nx Begin = 696.004 kN

Min Nx- Nx Begin = -757.487 kN

L=Live Load Effect from W1_Comb02.sup: Max Nx- Nx Begin =784.382 kN

Min Nx- Nx Begin =-856.584 kN

A1 = Factor for Dead Loads =1.1

A2 = Factor for Live Loads =1.2

I = Impact factor (Dynamic Load Allowence) = 1.3

C=Capacity =Result: w1_SteelRes 113 Begin: +NxRd= 48870.682 kN

-NxRd=-83623.672 kN

RF (MaxNx) =

=

= 22.22

RF (MinNx) =

=

= 35.018




Figure 5-13: Load rating for element 113

rm e steel design aashto

Documents

types rm bridge v8i

d e s i g n

program package rm bridge

design loads

s h t o

dead load

braking load

load combinations