RM E Prestressing Basic Part2 AASHTO

RM Bridge Professional Engineering Software for Bridges of all Types

RM Bridge V8i

March 2014

TRAINING PRESTRESSING BASIC

ANALYZER PART 2: AASHTO

RM Bridge

Training Prestressing Basic - ANALYZER - Part 2: AASHTO I

Bentley Systems Austria

Content

1 General ................................................................................................................... 1-1

1.1 Design Code ................................................................................................... 1-1

1.2 Design Loadings: ........................................................................................... 1-1

1.2.1 Permanent actions and Creep & Shrinkage ............................................... 1-1

1.2.2 Live Load ................................................................................................... 1-1

1.2.3 Braking Loads ............................................................................................ 1-3

1.2.4 Wind Loads ................................................................................................ 1-3

1.2.5 Thermal Forces .......................................................................................... 1-4

1.2.6 Creep and Shrinkage .................................................................................. 1-5

1.2.7 Pier settlement ............................................................................................ 1-5

1.3 Load combinations ......................................................................................... 1-6

1.4 Design checks ................................................................................................ 1-7

1.4.1 Servicebility limit state .............................................................................. 1-7

1.4.2 Ultimate limit state ..................................................................................... 1-7

2 Lesson 13: Definition of Additional Loads ........................................................... 2-1

2.1 Definition of Settlement Load Cases ............................................................. 2-1

2.2 Definition of Temperature Load Case ........................................................... 2-2

2.3 Definition of Wind Load Case ....................................................................... 2-4

2.4 Definition of Braking Forces ......................................................................... 2-6

3 Lesson 14: Calculation and Superposition of Additional Loads ........................... 3-1

3.1 Calculation and superposition of Settlement loads ........................................ 3-1

3.2 Calculation and superposition of temperature loads ...................................... 3-3

3.3 Calculation and superposition of wind loads ................................................. 3-4

3.4 Calculation and superposition of braking loads ............................................. 3-5

4 Lesson 15: Traffic Loads ....................................................................................... 4-7

4.1 Traffic Definition ........................................................................................... 4-7

4.2 Definition of Traffic Lanes .......................................................................... 4-10

4.3 Traffic Loads ................................................................................................ 4-11

4.4 Traffic Calculation ....................................................................................... 4-12

4.4.1 Calculation of influence lines .................................................................. 4-12

RM Bridge

Training Prestressing Basic - ANALYZER - Part 2: AASHTO II


4.4.2 Combining Influence Lines with Load Trains ......................................... 4-13

4.5 Traffic Superposition ................................................................................... 4-15

5 Lesson 16: Load Combinations ............................................................................. 5-1

5.1 Definition of the Load Combination .............................................................. 5-1

5.2 Calculation of the load combinations ............................................................ 5-3

6 Lesson 17: Fiber Stress Check ............................................................................... 6-1

7 Reinforced concrete checks General ................................................................... 7-3

8 Lesson 18: Ultimate Load Capacity Check ........................................................... 8-1

9 Lesson 19: Shear Capacity Check ......................................................................... 9-1

10 Lesson 20: Fatigue Check .................................................................................... 10-2

11 Lesson 21: Lists and Plots ................................................................................... 11-4

RM Bridge General

Training Prestressing Basic - ANALYZER - Part 2: AASHTO 1-1


1 General

1.1 Design Code

This example is designed in accordance with AASHTO LRFD 2007.

1.2 Design Loadings:

1.2.1 Permanent actions and Creep & Shrinkage

See Prestressing Basic Training Analyzer Part 1; Chapter 1.7.

1.2.2 Live Load

Traffic loads will be in accordance with AASHTO 3.6.1 and 3.6.2. Centrifugal force is

not considered in this example. Three lanes will be considered, and multiple presence

factors will be applied as required.

A simplification is made which assumes that the axial load trains stay at a fixed location

transversely within the notional lane. Varying the load positions in the transverse direc-

tion would have no effect on the longitudinal bending moment and shear force for cal-

culations on the global one-beam system*. In order to produce the worst case torsional

moments, all of the load trains could be shifted to one side of their respective notional

lanes.

During the live load superposition, the dynamic impact factor 1.33 will be applied

where necessary according to AASHTO 3.6.2. Also for the negative bending region, a

factor of 90% will be applied to the double truck load train.

The optional live load deflection evaluation is not checked in this example.

The following figures show the necessary load trains for HL-93 loading. A more de-

tailed description of how they will be superimposed is presented in Section 4.1.

*This is not true of a grillage model where position of the load train transversely within the

notional lane must be considered.

RM Bridge General



1.2.2.1 Load train 1 Truck

1.2.2.2 Load train 2 Tandem

1.2.2.3 Load train 3 Lane

RM Bridge General



1.2.2.4 Load train 4 Double Truck

1.2.2.5 Load train 5 Fatigue Truck

1.2.3 Braking Loads

Braking load will be calculated in accordance with AASHTO 3.6.4, and is taken as the

greater of:

- 25% of the axle weights of the design truck or tandem

- 5% of the design truck/tandem plus the lane load

In this example, 25% of the design truck is the governing condition:

(142kN + 142kN + 35kN)x0.25 = 79.75k

It is assumed that all three lanes are loaded and multiple presence factors are applied.

Because the lanes are symmetric about the centerline of the bridge, the braking load will

be applied as a single uniform line load located 1.8m above the surface of the deck. The

load will have the following magnitude:

79.75 x 3(lanes) x 0.85 (mult. presence) / 140 (length of bridge) = 1.45 kN/m

1.2.4 Wind Loads

AASHTO 3.8.1.2 will be used to determine the wind pressure to be applied on the struc-

ture. In the absence of information about the wind velocity for a bridge taller than

9.14m (30 ft), design wind velocity is assumed to be 161km/h (100mph). Therefore, the

wind pressure is as follows:

RM Bridge General



= 2.394 kN/m2

Wind pressure will be applied to the concrete box, and it is also assumed to act on a

barrier that is 0.9m tall.

Wind load on the live load according to AASHTO 3.8.1.3 is also applied.

Wind on Live Load: 1.459 kN/m (1.83 m above the deck)

1.2.5 Thermal Forces

Uniform temperature and temperature gradient loads will be applied to the structure.

The initial temperature is assumed to be 10oC.

According to AASHTO 3.12.2.1 the temperature range for uniform temperature diffe-

rence will be +27.67oC and -17.78

oC (table 3.12.2.1-1). For an initial temperature of

10oC this gives:

- Uniform temperature postitive = 16.67oC - Uniform temperature negative = -27.78oC

Thermal Coefficient: 10.8 x 10e-6 per C

The non-linear temperature gradient is done according to AASHTO 3.12.3. The struc-

ture is assumed to be in temperature zone 3, thus the values for T1 and T2 are given in

table 3.12.3-1. T3 is assumed to be zero, and the multiplier for negative temperature

gradient is 0.3. The table and sketch below show the temperature points and their loca-

tions.

Temperature Points:

RM Bridge General



Temperature Gradient

Point Positive (oC) Negative (

oC)

T1 23 -6.9

T2 6.1 -1.8

T3 0 0

This information was input in the modeler in the form of reference sets TempPlus and TempMinus which will be called up in the stage actions for calculating the tempera-ture gradient. To review this curve, go to the modeler and double click on the cross

section for the main girder. Open the Reference Sets dialogue box, highlight either

TempPlus or TempMinus and click the Curve button.

1.2.6 Creep and Shrinkage

Time dependent effects calculated in accordance with LRFD.

1.2.7 Pier settlement

1 cm at each abutment and pier axis

RM Bridge General



1.3 Load combinations

Service Limit States

Load Case/Envelope

Perm. Load t=0

Perm. Load

t= Service 1a

Service 1b

Service 1c

Service 1d

Service 3

Self Weight DC 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Superimposed Dead Loads DC 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Prestressing PS 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Creep and Shrinkage CR+SH 1.00 1.00 1.00 1.00

1.00 / 1.20

1.00 / 1.20 1.00

T= Creep and Shrinkage CR+SH - 1.00 1.00 1.00 1.20 1.20 1.00

Live Load LL - - 1.00 - 1.00 - 0.80

Braking BR - - 1.00 - 1.00 - 0.80

Wind on the Structure WS - - 0.30 0.30 - - -

Wind on the Live Load WL - - 1.00 1.00 1.00 1.00 -

Uniform Tempera-ture TU - - 1.00 1.00 1.20 1.20 1.00

Temperature Gra-dient TG - - 0.50 1.00 0.50 1.00 0.50

Settlement SE - - 1.00 1.00 1.00 1.00 1.00

Earthquake EQ - - - - - - -

Strength Limit States Load Case/Envelope Strength 1 Strength 4

Self Weight DC 0.90 / 1.25 0.90 / 1.25

Superimposed Dead Loads DC 0.65 / 1.50 0.65 / 1.50

Prestressing PS 1.00 1.00

Creep and Shrinkage CR+SH 1.00 1.00

T= Creep and Shrink-age CR+SH 0.50 0.50

Live Load LL 1.75 -

Braking BR 1.75 -

Wind on the Structure WS - -

Wind on the Live Load WL - -

Uniform Temperature TU 0.50 0.50

Temperature Gradient TG - -

Settlement SE 1.00 -

Earthquake EQ - -

RM Bridge General



1.4 Design checks

According to AASHTO LRFD 2007 Section 5

1.4.1 Servicebility limit state

1.4.1.1 Stresses

According to AASHTO 5.9.4

Concrete stresses before losses

Concrete compressive stresses are limited to:

|c| 0.6 |fc| = 0.6 x 45MPa = 27MPa

Concrete tensile stresses are limited to:

|t| 0.25 |fc| 1.38MPa = 0.25 = 1.67MPa 1.38MPa

Concrete stresses after losses

Concrete compressive stresses for prestressing and permanent loads are limited to:

|c| 0.45 |fc| = 0.45 x 45MPa = 20.25MPa

Concrete tensile stresses are limited to:

|t| 0.5 |fc| = 0.5 = 3.35MPa

According to AASHTO 5.9.3

Initial stress in the tendons

p 0.90 fpy = 0.90 x 1674MPa = 1507MPa.

Stress in tendons at service limit state after losses

p 0.80 fpy = 0.80 x 1674MPa = 1340 MPa

1.4.2 Ultimate limit state

Accordingly to AASHTO LRFD 2007 Section 5.

Design checks to be made:

Bending and axial force Shear Torsion

RM Bridge Lesson 13: Definition of Additional Loads



2 Lesson 13: Definition of Additional Loads

2.1 Definition of Settlement Load Cases

The settlement of foundations will be done for each axis. 4 separate load cases will be

created. Later the superposition of those load cases will be done to get the most unfa-

vorable case.

Definition of

Load Cases

Schedule Name Settle-A1 Settle-A2 Settle-A3 Settle-A4

Type Permanent Permanent Permanent Permanent

Load Definition

Load

Manag-

er

- - - -

De-

scriptio

n

Settlement

of abut-

ment axis 1

Settlement

of abut-

ment axis 2

Settlement

of abut-

ment axis 3

Settlement

of abut-

ment axis 4

Load Case

Top Table

Definition of

Settlement

Load Cases

Schedule Num-

ber Settle-A1 Settle-A2 Settle-A3 Settle-A4

Load-

ing

Actions on the

elements

ends

Actions on the

elements

ends

Actions on the

elements

ends

Actions on the

elements

ends

Load Definition Type

Element

end dis-

placements

Element

end dis-

placements

Element

end dis-

placements

Element

end dis-

placements

From 1100 1200 1300 1400

Load Case To 1100 1200 1300 1400

Step 1 1 1 1

Bottom Table Vx [m] 0 0 0 0

Vy [m] 0.01 0.01 0.01 0.01

Vz [m] 0 0 0 0

Direc-

tion Global Global Global Global

Rx

[Rad] 0 0 0 0

Ry [m] 0 0 0 0

Rz [m] 0 0 0 0

Where Begin Begin Begin Begin




2.2 Definition of Temperature Load Case

All temperature loads, the positive and negative uniform and gradients, will be defined

in separated load cases. To get the most unfavorable case the load cases will be super-

posed. Temperature gradients only need to have a load set created. Uniform tempera-

ture loads do not require a load set, but do require more input in the load case.

Definition of Load

Sets

CONSTR.SCHED. Load-

ing

Add to load case

Add to load case

Name TG-P TG-N

LOAD

DEFINIT. LCnr. TG-P TG-N

Temperature

gradient - Posi-

tive

Temperature

gradient - neg-

ative

LSET

Top table

Definition of

Load Cases

Schedule Name TU-P TU-N

Type Non-

Permanent

Non-

Permanent

Load Definition

Load

Manag-

er

- -

De-

scriptio

n

Uniform

Tempera-

ture Load -

Positive

Uniform

Tempera-

ture Load -

Negative

Load Case

Top Table




Define Load Sets

for Uniform Tem-

perature Loads

CONSTR.SCHED. Name TU-P

Loading Initial

stress/strain

Initial stress/strain


LOAD

DEFINIT. Type

Tempera-

ture load

Tempera-

ture load

Tempera-

ture load

From 101 1201 1301

LCASE To 135 1204 1304

Step 1 1 1

Bottom table Alfa 1.08e-5 1.08e-5 1.08e-5

DT-G

[C] 16.67 16.67 16.67

DT- Y

[C] 0 0 0

H-Y [m] 0 0 0

DT- Z

[C] 0 0 0

H-Z [m] 0 0 0

Name TU-N

Loading Initial

stress/strain



Type Tempera-

ture load

Tempera-

ture load

Tempera-

ture load

From 101 1201 1301

To 135 1204 1304

Step 1 1 1

Alfa 1.08e-5 1.08e-5 1.08e-5

DT-G

[C] -27.78 -27.78 -27.78

DT- Y

[C] 0 0 0

H-Y [m] 0 0 0

DT- Z

[C] 0 0 0

H-Z [m] 0 0 0

* If the input for Alpha is defined as 0, the value for the

temperature expansion coefficient is taken from the materi-

al definitions.

The load sets for the temperature gradient Plus and Minus will automatically be cal-culated by using the Module TEMPVAR.




2.3 Definition of Wind Load Case

Insert Load Set

CONSTR.SCHED. Name WL WS

Duration Type Non-permanent Non-permanent

LOAD

DEFINIT. Const. Factor 1 1

Description Wind on live

load

Wind on struc-

ture

LCASE

Top table

Define Load Sets

for Winds on the

Structure

CONSTR.SCHED. Name WS

Loading Uniform load Uniform load

LOAD

DEFINIT. Type

Uniform eccen-

tric element

load

Uniform eccen-

tric element

load

From 101 101

LCASE To 135 135

Step 1 1

Bottom table Qx [kN/m] 0 0

Qy [kN/m] 0 0

Qz [kN/m] 2.394 2.155

Direction Local Local

Eccentricity Local Local+Y Elem-Ecc

Ey [m] 0 0.45

Ez [m] 0 0

Load applica-

tion Real length Real length

Definition Load mult. by CS depth

Load/Unit length

The load case for wind on the structure consists of two load definitions. The first one

defines the wind load directly on superstructure box, and the second one defines the

wind load on the barrier.

The variation of the wind load on the superstructure due to the variable height can be

defined with the option Load multiply with cross-section depth where the wind pres-sure (kN/m

2) is defined. The program then internally calculates the uniform wind load

and applies it on the elements (the load is applied to the centre of gravity, and the actual

application point of the load is neglected).

For the wind load acting on the barrier, the wind pressure has to be first multiplied with

the barrier height (assumed 0.9m) and then defined as uniform load. Load application is

0.45 meters above the road surface and has to be defined accordingly. This can be done

with local Y element eccentricity (this represents the distance from the element centre

of gravity to the node) and an additional eccentricity 1 m above the road way relative to

the node.




Name WS

Loading Uniform load Uniform load

Type

Uniform eccen-

tric element

load

Uniform eccen-

tric element

load

From 1201 1301

To 1204 1304

Step 1 1

Qx [kN/m] 0 0

Qy [kN/m] 0 0

Qz [kN/m] 2.394 2.394

Direction Local Local Eccentricity Local Local

Ey [m] 0 0

Ez [m] 0 0

Load applica-

tion Real length Real length

Definition Load mult. by CS depth

Load mult. by CS depth

Wind load is also applied to the substructure.

Wind on the live load is applied as a uniform load at 1.459m above the surface of the

deck.

Define Load Sets

for Winds on Live

Loads

CONSTR.SCHED. Name WL

Loading Uniform load

LOAD

DEFINIT. Type

Uniform eccen-

tric element

load

From 101

LCASE To 135

Step 1

Bottom table Qx [kN/m] 0

Qy [kN/m] 0

Qz [kN/m] 1.459

Direction Local

Eccentricity Local+Y Elem-Ecc

Ey [m] 1.83

Ez [m] 0

Load applica-

tion Real length

Definition Load/Unit

length

To consider wind from both sides it possible to define the same load case with a differ-

ent sign. Another possibility is to define the loads with load sets and to use these load

sets for both direction (once with positive and once with negative factor).




Within this example the third option will be used where this will be achieved with the

superposition of the above created load cases. This is done with the corresponding su-

perposition rule (AndX, AddX or OrX) which superposes the effects once with a posi-

tive sign and once with a negative sign.

2.4 Definition of Braking Forces

The braking load will be applied as a uniform load in the longitudinal (x) direction

along the whole bridge length. Both application directions will be considered using the

same principle as the wind load by superposing the load case with corresponding su-perposition rule.

Definition of

Load Cases

Schedule Name BR

Type Non-

permanent

Load Definition Load Manager -

Description Braking forces

Load Case

Top Table

Definition of

Load Cases for

Braking Forces

Schedule Name Braking

Loading Uniform

Load

Load Definition Type

Uniform eccen-

tric element

load

From 101

Load Case To 135

Step 1

Bottom Table Qx [kN/m] 1.45 [kN/m]

Qy [kN/m] 0

Qz [kN/m] 0

Direction Local X/L 0

Eccentricity Local+Y Elem-Ecc

Ey [m] 1.83

Ez [m] 0

Load applica-

tion Real length

Definition Load/Unit

length

RM Bridge Lesson 14: Calculation and Superposition of Additional Loads



3 Lesson 14: Calculation and Superposition of Additional Loads

The arrangement of the subsequent Construction stages can be made freely. They are actually not real construction stages because there will be no elements activated or time

dependent calculations made. They will be only recalculation stages. However, it is

recommended to group them with some logical principle.

Each type of additional load will be grouped together this means that for each a calcu-lation stage will be generated where the loads will be calculated and superposed into

one envelope. In this envelope the minimum and maximum results will be saved. The

same envelope will be used for the load combinations.

3.1 Calculation and superposition of Settlement loads

Definition of the

Required Con-

struction Stage

Schedule Name Settlement

Description

Calculation and super-

position of pier settle-

ment

Stages

Schedule Actions

Top Table

Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

Settlement

Schedule Type

Calcu-lations

(Static)

Calcu-lations

(Static)

Calcu-lations

(Static)

Calcu-lations

(Static)

Action Calc Calc Calc Calc

Stages Inp1 Settle-A1 Settle-A2 Settle-A1 Settle-A2

Inp2 - - - -

Inp3 - - - -

Schedule Actions Out1 - - - -

Out2 * * * *

Bottom Table Delta-

T 0 0 0 0

First all settlement load cases are calculated with the Calc action. Only now can these

load cases be superposed this will be done with following actions.

If in the output field a star is defined (*) the created list file will have the default name LC Name.lst (e.g.: Settle-A1.lst). The name of the list file can be changed by defining the name of it in the corresponding output window.




Type LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupAddLc SupAndLc SupAndLc SupAndLc

Inp1 - Settle-A1 Settle-A2 Settle-A3 Settle-A4

Inp2 - - - - -

Inp3 - - - - -

Out1 Settle.sup - - - -

Out2 - - - - -

Delta-T 0 0 0 0 0

With the LC/Envelope action SupInit (Superposition file Initialization) an envelope file

with name defined in Output-1 will be generated. All envelope files have, unlike load

cases, an extension *.sup.

In each envelope the maximum and minimum values/results for six internal forces (Nx,

Qy, Qz, Mx, My, and Mz) and six deformations (Vx, Vy, Vz, Rx, Ry, and Rz) are saved

for each element (e.g.: MinNx, MaxNx, MinRz, MaxRz). As it can be seen this is a 12*12 result matrix. There is always a leading result component

(e.g.: Max and Min for Mz MinMz and MaxMz) and other values that are corre-sponding values (MinMz:Qy).

Therefore, in addition to the result component (e.g.: Qy or Mz), the leading (superposi-

tion) component (e.g.: MinQy or MaxMz) has to be defined when presenting envelope

results. If we want to see the maximum or minimum bending moments around the z axis

of an envelope the definition is as follows: MinMz:Mz for minimum bending moments

and MaxMz:Mz for maximum bending moments. To see the corresponding shear forces

the definition is: MinMz:Qy and MaxMz:Qy.

There are different ways of superposing certain load cases/envelopes superposition rules. Depending on the chosen rule the end results can be different. Therefore the en-

gineer has to chose with which rule the superposition has to be done. All superposition

rules are explained in the table below.

Rule Description Application Example

LcAdd

SupAdd

Unconditional adding/superposing here the val-ues/results are added/superposed without checking if the

new result is favorable or unfavorable compared to the

existing result.

Permanent loads (self weight,

pre-stressing, etc.)

Traffic etc.

SupAnd Conditional adding/superposing here the values are added/superposed only if the new result is unfavorable

compared to the existing value.

To get the most unfavorable

situation.

Traffic etc.

SupOr Substitution if unfavorable using this rule the values are compared to each other, and if the value to be added

is unfavorable it will replace the existing one. In other

cases the existing value will remain.

Exclusive loads (different tem-

perature loads, etc.)

SupAndX Both have the same functionality as their basic rules Wind loads and Braking loads




SupOrX (SupAnd and SurOr). The difference is that the values to

be added are superposed once with positive factor (+1)

and once time with negative factor (-1).

which are defined only from one

side.

Depending on the file to be added, load case or envelope, there are different actions SupAndLc or SupAndSup.

For further and more detailed information about the superposition rules see the RM

Bridge Analysis User Guide, Section 7.2.5.

In this particular example (Settlement of each axis) the values are conditionally super-

posed with the actions SupAndLc (to the Settle envelope a load case will be added with

the rule And conditional adding). This means that individual result components (Nx, Qy, Mz) are added only if the respective maximum or minimum result value be-comes unfavorable.

Note: By the definition of the envelope file (Output 1) using the SupInit action the extension

doesnt have to be defined because it will be automatically added. This doesnt apply for all other superposition actions it is necessary to write the extension (or selection from the drop down menu).

Selecting the envelope from the drop down menu is possible only if the envelope already

exists (that it was created/initialized). To avoid a complete recalculation, the action for

creating the envelope can be started separately by clicking the Run Action button on the

right side between the top and bottom table. By clicking on it a new window opens where

the Run Action button has to be clicked and the currently selected action will be performed.

Using this principle the created envelope can be selected from the drop down menu.

For easier and faster definition the action can be copied and modified. The input can also

be defined by the copy-paste function.

3.2 Calculation and superposition of temperature loads

Definition of the

Required Con-

struction Stage

Schedule Name Temperature

Description

Temperature loads

(Calculation and Su-

perposition)

Stages

Schedule Actions

Top Table




Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

Temperature

Schedule Type

Calcu-lations

(Static)

Calcu-lations

(Static)

Calcu-lations

(Static)

Calcu-lations

(Static)

Action Calc Calc TempVar Calc

Stages Inp1 TU-P TU-N TempPlus TG-P

Inp2 - - - -

Inp3 - - - -

Schedule Actions Out1 - - TG-P -

Out2 * * * *

Bottom Table Delta-

T 0 0 0 0

First the temperature load cases are calculated. This must be done before they can be

superposed.

Type

Calcu-lations

(Static)

Calcu-lations

(Static)

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

Action TempVar Calc SupInit SupORLc SupORLc SupInit SupORLc SupORLc

Inp1 TempMin

us TG-N - TU.sup TU.sup - TG.sup TG.sup

Inp2 - - - TU-P.sup TU-N.sup - TG-P.sup TG-N.sup

Inp3 - -

Out1 TG-N - TU.sup TG.sup

Out2 * * - - - - - -

Delta-T 0 0 0 0 0 0 0 0

Both positive and negative load cases for the uniform and gradient temperature load are

superposed with the Or rule into separated envelopes.

Using that principle we get two envelopes one for the uniform temperature loads and another one for the gradient temperature loads where the maximum and minimum val-

ues from each temperature load type are saved.

3.3 Calculation and superposition of wind loads

Definition of the

Required Con-

struction Stage

Schedule Name Wind

Description Wind loads (Calcula-

tion and Superposition)

Stages

Schedule Actions

Top Table




Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

Wind

Schedule Type Calcula-

tions (Static)

Calcula-tions (Static)

Action Calc Calc

Stages Inp1 WS WL

Inp2 - -

Inp3 - -

Schedule Actions Out1 - -

Out2 * *

Bottom Table Delta-

T 0 0

The load cases for wind on the structure and wind on the live load are calculated first.

Afterwards both wind loads will be superposed into separate envelopes with the AndX

rule the load case is once added with the positive factor and then with negative factor (-1.0) when it produces unfavorable results.

Type LC/Envelope

action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupAndX

Lc SupInit

SupAndX

Lc

Inp1 - WS.sup - WL.sup

Inp2 - WS - WL

Inp3 -

Out1 WS.sup - WL.sup -

Out2 - - - -

Delta-T 0 0 0 0

3.4 Calculation and superposition of braking loads

Definition of the

Required Con-

struction Stage

Schedule Name Braking

Description

Braking loads (Calcu-

lation and Superposi-

tion)

Stages

Schedule Actions

Top Table

Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

Wind

Schedule Type Calculations

(Static)

LC/Envelope action

LC/Envelope action

Acion Calc SupInit SupAndXLc

Stages Inp1 BR - brake.sup

Inp2 - - BR

Inp3 - - -

Schedule Actions Out1 - brake.sup -

Out2 * - -

Bottom Table Delta-

T 0 0 0




The same principle that was used for the wind load applies also for braking load first the load case is calculated and then superposed to an envelope with the AndX rule.

Note: It would be possible to define the braking load as live load. For that a traffic lane and load

train (e.g.: concentrated load) have to be defined and calculated. The principle of calcula-

tion of live load is defined in next section.

RM Bridge Lesson 15: Traffic Loads



4 Lesson 15: Traffic Loads

4.1 Traffic Definition

The traffic load definition for this simple example is in accordance with AASHTO.

HL-93 loading will be applied with three lanes. A dynamic impact factor of 1.33 will

be applied where it is applicable, and multiple lanes loaded will be checked with the

appropriate dynamic impact factors.

According to Article 3.6.1.1.1 the number of design lanes should be the integer part of

w/3.6m, where w is the clear roadway width:

w = 13m 2(0.4m barriers) = 12.2m number of design lanes = 12.2m/3.6m = 3.39 or 3 design lanes.

As mentioned in Section 1.2.2 of this document, some simplifications and assumptions

are made in order to present the fundamentals of defining and calculating live loads in

RM. The principles presented here can be applied in the same manner on a more pre-

cise live load scenario. The following assumptions and simplifications have been made:

The three design lanes will be placed symmetrically about the centerline of the roadway.

In each design lane the centerline of the truck, tandem, and lane load remain at a fixed

position transversely. In this example it is assumed that each of the load trains remains

in the middle of the 3.6m-wide design lane. The following picture shows how the lanes

and load trains will be set up:

The first step in setting up the live loading is to define influence lines. In the program

they are called "lanes" (which is how they will be referred to from here on out), but it is

more appropriate to think of them as the centerline of a vehicle. Any number of lanes

can be defined on a bridge.

The next step is to define the load trains. There are 4 load trains for the HL-93 loading

used in this example: Truck, Tandem, Double Truck, and Design Lane. They can be

seen in Section 1.1.2.

Finally, the load trains need to be combined with the lanes. In RM, the influence lines

are calculated first without any consideration of a particular load train. Using this ap-

proach, any load train can be combined with an influence line to create an envelope of




results. Then another load train can be combined with that same influence line to create

another envelope of results.

The approach taken here is to first determine the worst case loading for each lane indi-

vidually from the different load trains. According to HL-93, the loading can be either

the Truck or the Tandem or the Double Truck (in negative flexure), and the Design

Lane. Worst case loading envelopes for each individual lane are determined. Then en-

velopes are created for different combinations of multiple lanes loaded. Finally, the

worst case overall traffic load is determined by checking envelopes of different numbers

of lanes loaded with multiple presence factors applied. The figure below shows this

process.




Z

Z

Z

Three lanes loaded:

L1L2L3.sup

Two lanes loaded:

L1L2.sup L1L3.sup L2L3.sup

One lane loaded:

L1.sup L2.sup L3.sup




4.2 Definition of Traffic Lanes

Traffic lanes are defined under Menu Schedule Load definition Traffic Lanes. Lanes to be defined were explained in section 1.2.2.

Definition of

Lanes

Schedule Number 1 2 3

Output-

File - - -

Load Definition Info-File - - -

Descrip-

tion

ez = +3.6

m ez = 0.0 m

ez = -3.6

m

Traffic Lanes

Top Table

A traffic lane is defined through an element series (normally all elements of the super-

structure). Information about the load direction and position (eccentricity) is required

for each element at least at one point. Normally it is done at two points on the ele-ment begin and element end. These points can be generated very easily using different

macros.

In this example Macro 2 will be used for generation of all traffic lanes (vertical load

with eccentricity).

Note: The basic direction (x,y,z longitudinal, vertical, transversal) of the live load is defined via the lane definition different macros. The load intensity and orientation (positive or negative) is defined via the definition of the load train.

In case of grillage models the transversal elements can be loaded directly (Macro3) or the

load is distributed from the transversal to the longitudinal girders (Macro4).

For more detailed information about traffic lanes please see RM Analysis user guide sec-

tion 7.2.9.

The procedure of creation of the Traffic Lanes can be different than shown here the lane can be created (upper table) and immediately defined (bottom table)

Definition of the

Lanes by Mac-

ros

Schedule Lane 1 2 3

Macro Macro2 Macro2 Macro2

Load Definitions Eccentri-

city Ygl Ygl Ygl

El-from 101 101 101

Traffic Lanes El-fo 135 135 135

El-step 1 1 1

Bottom Table ey [m] 0 0 0

ez [m] +3.6 +0.0 -3.6

Phi 1.00 1.00 1.00

Ndiv 1 1 1




The lane eccentricities are defined in the local coordinate system of the element (EYel

and EZel). Lane eccentricities (ey and ez) can be referenced to the node by using the

local vertical and transversal eccentricities. For a vertical load, only the transversal load

eccentricity has an effect.

The input sequence is as follows:

Select the lane to be defined in the upper table and click on the insert after button in the

bottom table. A window with macros opens and Macro2 has to be chosen. In the newly

opened window click again on the insert after button and make the input as is shown in

the table above. With this the definition of one influence line is finished. The same has

to be repeated for all other lanes also.

The macro creates the information in the bottom table where for each element there are

4 definitions two at the element begin (x/l = 0.00001) and two at the element end (x/l = 0.99999). One defines the position of the lane relative to the element (eccentricities),

and the other defines the load position (which is the same as the lane position) and di-

rection. This information allows the program to calculate influence lines.

4.3 Traffic Loads

Load Trains are defined under menu Schedule Load definition Load Trains. Load trains to be defined were explained in Section 1.1.2.

Input the Load

Trains

CONSTR.SCHED. Name 1 2 3 4 5

Fact-min 1 1 1 1 1

LOAD

DEFINIT. Fact-max 1 1 1 1 1

Location - - - - -

LTRAIN Descrip-

tion

Design

Lane Truck Tandem

Double

Truck

Fatigue

Truck

Top table

Definition of

Load Train

Properties

Schedule LTrain 1 2

Q -9.34 - - -

Load Definitions Free Length Free - - -

F - -142 -142 -35

AASHTO - - - -

Load Trains l-from - 4.3 4.3 0

l-to - 9 0 0

Bottom Table l-step - 1 0 0




LTrain 3 4 5

Q - - - - - - - - - - -

Free

Length - - - - - - - - - - -

F -110 -110 -142 -142 -35 -142 -142 -35 -142 -142 -35

AASHTO - - - - - - - - -

l-from 1.2 - 4.3 4.3 15.25 4.3 4.3 0 9 4.3 0

l-to 0 - 0 0 0 0 0 0 0 0 0

l-step 0 - 0 0 0 0 0 0 0 0 0

A certain load train is defined by a load and length to the next load. Therefore the first

input for load train 2 is defined by a concentrated load F = -142 kN (negative

y-direction) and a variable length between 4.3m and 9m to the next force. The next in-

put for the first load train consist only of a concentrated load F = -142 kN.

Using the same principle, load train numbers 2 and 3 have to be defined.

The load trains for uniformly distributed loads (load train number 1) are defined as is

shown in the table above. The length of the uniformly distributed load is set to free the program will automatically calculate the unfavorable position and length and load the

structure with it.

The input fields on the right side of the window for the definition of the load trains are

for two dimensional definitions of the load trains and are irrelevant for the one-beam

model. This input is generally used for FEM models (it can also be used for grillage

models).

Pre-defined load train definitions according to AASHTO can be imported via Extras Traffic Load Macros Live Load Macro for AASHTO (ASD and LRFD).

4.4 Traffic Calculation

4.4.1 Calculation of influence lines

Definition of the

Required Con-

struction Stage

Schedule Name TrafficCalc

Description Traffic Calculations

Stages

Schedule Actions

Top Table




Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

InflCalc

Schedule Type

Calcu-lation

(Static)

Calcu-lation

(Static)

Calcu-lation

(Static)

Action Infl Infl Infl

Stages Inp1 1 2 3

Inp2 - - -

Inp3 - - -

Schedule Actions Out1 - - -

Out2 * * *

Bottom Table Delta-T 0 0 0

First the influence lines for the defined Traffic Lanes are calculated with the Infl action.

The results of the calculations are saved to list files and also to binary files which can be

graphically presented under Results Influence Lines Corresponding influence line.

Note: The graphical presentation is possible only if the influence lines were actually calculated.

4.4.2 Combining Influence Lines with Load Trains

Definition of the

Required Con-

struction Stage

Schedule Name TrafficCalc

Description Traffic Calculations

Stages

Schedule Actions

Top Table

The definitions in the bottom table are as follows:




Type LC/Envelo

pe action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupInit SupInit SupInit SupInit SupInit

Inp1 - - - - - -

Inp2 - - - - - -

Inp3 - - - - - -

Out1 L1-Truck.sup L1-

Tandem.sup

L1-

Dbl_Truck.su

p

L1-Lane.sup L2-Truck.sup L2-

Tandem.sup

Out2 - - - - * *

Delta-T 0 0 0 0 0 0

Type LC/Envelo

pe action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupInit SupInit SupInit SupInit SupInit

Inp1 - - - - - -

Inp2 - - - - - -

Inp3 - - - - - -

Out1

L2-

Dbl_Truck.su

p


Tandem.sup

L3-

Dbl_Truck.su

p

L3-Lane.sup

Out2 - - - - * *

Delta-T 0 0 0 0 0 0

Here the envelopes are created/initialized, which is necessary for the evaluation of load

trains and traffic lanes. It is highly recommended to use a systematic number-

ing/naming. In this example the envelopes are named with the numbers of the lanes and

trains that will be combined with each other.

When the influence lines are calculated and the envelopes initialized the load trains can

be combined with the traffic lanes.

Type Calculation

(Static)

Calculation (Static)





Action LiveL LiveL LiveL LiveL LiveL LiveL

Inp1 1 1 1 1 2 2

Inp2 2 3 4 1 2 3

Inp3 - - - - - -

Out1 L1-Truck.sup L1-

Tandem.sup

L1-

Dbl_Truck.su

p


Tandem.sup

Out2 * * * * * *

Delta-T 0 0 0 0 0 0




Type Calculation

(Static)






Action LiveL LiveL LiveL LiveL LiveL LiveL

Inp1 2 2 3 3 3 3

Inp2 4 1 2 3 4 1

Inp3 - - - - - -

Out1

L2-

Dbl_Truck.su

p


Tandem.sup

L3-

Dbl_Truck.su

p

L3-Lane.sup

Out2 * * * * * *

Delta-T 0 0 0 0 0 0

The action LiveL combines the chosen load train (Input2) with the selected traffic lane

(Iput1). The results of the calculation are saved not only into the previously generated

envelope (Output1) file but also to a list file.

4.5 Traffic Superposition

Definition of the

Required Con-

struction Stage

Schedule Name TrafficSup

Description Superposition of

Traffic Loads

Stages

Schedule Actions

Top Table

The definitions in the bottom table are as follows:

Type LC/Envelop

e action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupORSup SupORSup SupORSup SupANDSup

Inp1 - L1.sup L1.sup L1.sup L1.sup

Inp2 - L1-Truck.sup L1-

Tandem.sup

L1-

Dbl_Truck.su

p

L1-Lane.sup

Inp3 - 1.33 1.33 1.197 1.0

Out1 L1.sup - - - -

Out2 - - - - -

Delta-T 0 0 0 0 0




Type LC/Envelop

e action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action




Tandem.sup

L2-

Dbl_Truck.su

p

L2-Lane.sup

Inp3 - 1.33 1.33 1.197 1.0

Out1 L2.sup - - - -

Out2 - - - - -

Delta-T 0 0 0 0 0

Type LC/Envelop

e action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action




Tandem.sup

L3-

Dbl_Truck.su

p

L3-Lane.sup

Inp3 - 1.33 1.33 1.197 1.0

Out1 L3.sup - - - -

Out2 - - - - -

Delta-T 0 0 0 0 0

Now there are envelopes file for the worst case load train in each one of the lanes. First,

the Truck, Tandem or Double Truck was used (whichever produced worst case results

for each element), and then the Design Lane load was added to that. Dynamic impact

factors were applied here, and the 90% reduction factor for the Double Truck was taken

into consideration. The resulting envelopes are L1.sup, L2.sup, and L3.sup.

The next step is to create envelope files for the condition when more than one lane is

loaded. There are 3 unique conditions when 2 lanes are loaded and one condition when

3 lanes are loaded. These conditions along with their envelope file names in RM can be

seen in Section 4.1.

Type LC/Envelo

pe action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Action SupInit SupANDSup SupInit SupANDSup SupInit SupANDSup

Inp1 L1.sup L1L2.sup L1.sup L1L3.sup L2.sup L2L3.sup

Inp2 - L2.sup - L3.sup - L3.sup

Inp3 - - - - - -

Out1 L1L2.sup - L1L3.sup - L2L3.sup -

Out2 - - - - - -

Delta-T 0 0 0 0 0 0




Ac-

tion

LC/Envelope action

LC/Envelope action

LC/Envelope action

Type SupInit SupANDSup SupANDSup

Inp1 L1.sup L1L2L3.sup L1L2L3.sup

Inp2 - L2.sup L3.sup

Inp3 - - -

Out1 L1L2L3.sup - -

Out2 - - -

Delta-

T 0 0 0

All intermediate envelopes have now been created for different lanes loaded. The last

step is to check and see which condition of lanes loaded produces the worst case results

when multiple presence factors are applied. The final envelope for live load results will

be called live.sup.

Type

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

LC/Envelope

action

Action SupInit SupORSu

p

SupORSu

p

SupORSu

p

SupORSu

p

SupORSu

p

SupORSu

p

SupORSu

p

Inp1 - live.sup live.sup live.sup live.sup live.sup live.sup live.sup

Inp2 - L1.sup L2.sup L3.sup L1L2.sup L1L3.sup L2L3.sup L1L2L3.s

up

Inp3 - 1.2 1.2 1.2 1.0 1.0 1.0 0.85

Out1 live.sup - - - - - - -

Out2 - - - - - - - -

Delta-T 0 0 0 0 0 0 0 0

This completes the definition of the live load.

RM Bridge Lesson 16: Load Combinations



5 Lesson 16: Load Combinations

5.1 Definition of the Load Combination

The results of the calculated loads are saved into load cases or envelopes. They can now

be used for the definition of the Load Combinations. The definition of load combina-

tions is done under menu Schedule Load definition Combination table.

It is possible to define up to 48 different combinations. Using the buttons on the top left

side allows you to change between different pages 6 load combination definitions per page.

The first column represents the load cases and/or envelopes to be combined into a cer-

tain combination. In the second column the rule of the superposition for each load case

and/or envelope is defined. Afterwards there are 2 columns for each combination that

represent the favorable and unfavorable factors.

The input of the combinations is not combination oriented but instead is load case ori-

ented. This means simply that the input is done for each load case separately where

favorable and unfavorable factors have to be defined for all combinations.

The load combinations to be defined are explained in section 1.3 and are again dis-

played in the table below.

COMBINATION

LC/Envelope Rule 1 2 3 4 5 6 7 8 9

SW-SUM AddLc 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.90/ 1.25

.90/ 1.25

SDL-SUM AddLc 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.65/ 1.50

0.65/ 1.50

PT-SUM AddLc 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

CS-SUM AddLc 1.00 1.00 1.00 1.00

1.00/ 1.20

1.00/ 1.20

1.00 1.00 1.00

CS-INF AndLc - - 1.00 1.00 1.20 1.20 1.00 0.50 0.50

CS-INF AddLc 1.00 - - - - - - -

live.sup AndSup - - 1.00 - 1.00 - 0.80 1.75 -

Brake.sup AndSup - - 1.00 - 1.00 - 0.80 1.75 -

WS.sup AndSup - - 0.30 0.30 - - - - -

WL.sup AndSup - - 1.00 1.00 1.00 1.00 - - -

TU.sup AndSup - - 1.00 1.00 1.20 1.20 1.00 0.50 0.50

TG.sup AndSup - - 0.50 1.00 0.50 1.00 0.50 - -

settle.sup AndSup - - 1.00 1.00 1.00 1.00 1.00 1.00 -

Perm

. Loads t=

0

Perm

. Load t

=

Serv

ice 1

a

Serv

ice 1

b

Serv

ice 1

c

Serv

ice 1

d

Serv

ice 3

Str

ength

1

Ste

ngth

4




Definition of

Load Case

Combina-

tions

Schedule LC/Envelop

e SW-SUM SDL-SUM

Comb SupAddLc SupAddLc

Load Definitions Type F-fav. F-

unfav. F-fav.

F-

unfav.

Comb I 1 1 1 1

Combination Table Comb II 1 1 1 1

Comb III 1 1 1 1

Top Table Comb IV 1 1 1 1

Comb V 1 1 1 1

Comb VI 1 1 1 1

Comb VII 1 1 1 1

Comb VIII 0.9 1.25 0.65 1.50

Comb IX 0.9 1.25 0.65 1.50

LC/Envelope PT-SUM CS-SUM CS-INF CS-INF

Comb SupAddLc SupAddLc SupAndLc SupAddLc

Type F-fav. F-

unfav. F-fav.

F-

unfav. F-fav.

F-

unfav. F-fav.

F-

unfav.

Comb I 1 1 1 1 - - - -

Comb II 1 1 1 1 - - 1 1

Comb III 1 1 1 1 1 1 - -

Comb IV 1 1 1 1 1 1 - -

Comb V 1 1 1 1.2 1.2 1.2 - -

Comb VI 1 1 1 1.2 1.2 1.2 - -

Comb VII 1 1 1 1 1 1 - -

Comb VIII 1 1 1 1 0.5 0.5 - -

Comb IX 1 1 1 1 0.5 0.5 - -

LC/Envelo

pe live.sup brake.up WS.sup WL.sup TU.sup

Comb SupAndSup SupAndSup SupAndSup SupAndSup

Type F-fav. F-

unfav. F-fav.

F-

unfav. F-fav. F-fav. F-fav.

F-

unfav.

F-

unfav.

F-

unfav.

Comb I - - - - - - - - - -

Comb II - - - - - - - - - -

Comb III 1 1 1 1 0.3 0.3 1 1 1 1

Comb IV - - - - 0.3 0.3 1 1 1 1

Comb V 1 1 1 1 - - 1 1 1.2 1.2

Comb VI - - - - - - 1 1 1.2 1.2

Comb VII 0.8 0.8 0.8 0.8 - - - - 1 1

Comb VIII 1.75 1.75 1.75 1.75 - - - - 0.5 0.5

Comb IX - - - - - - - - 0.5 0.5




LC/Envelo

pe TG.sup settle.sup

Comb SupAndSup SupAndSup

Type F-fav. F-

unfav. F-fav.

F-

unfav.

Comb I - - - -

Comb II - - - -

Comb III 0.5 0.5 1 1

Comb IV 1 1 1 1

Comb V 0.5 0.5 1 1

Comb VI 1 1 1 1

Comb VII 0.5 0.5 1 1

Comb VIII - - 1 1

Comb IX - - - -

5.2 Calculation of the load combinations

Up to now the load combinations have only been defined and have not yet been calcu-

lated. To calculate them a schedule action has to be defined SupComb. With this ac-tion all defined load cases and envelopes with their corresponding superposition rule

and defined favorable and unfavorable factors are superposed into the final (combina-

tion) envelope.

For a better overview a separated calculation stage will be created where all 9 combi-nations will be calculated.

Definition of the

Required Con-

struction Stage

Schedule Name Combos

Description Load Combination

calculation

Stages

Schedule Actions

Top Table




Insertion of the

Calculation Ac-

tions to the Con-

struction Stage

Combos

Schedule Type LC/Envelop

e action

LC/Envelope action

LC/Envelope action

Acion SupComb SupComb SupComb

Stages Inp1 1 2 3

Inp2 - - -

Inp3 - - -

Schedule Actions Out1 Perm-t-0.sup Perm-t-inf.sup SLS-1a.sup

Out2 - - -

Bottom Table Delta-

T 0 0 0

Type LC/Envelop

e action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

LC/Envelope action

Acion SupComb SupComb SupComb SupComb SupComb SupComb

Inp1 4 5 6 7 8 9

Inp2 - - - - - -

Inp3 - - - - - -

Out1 SLS-1b.sup SLS-1c.sup SLS-1d.sup SLS-3.sup ULS-1.sup ULS-4.sup

Out2 - - - - - -

Delta-

T 0 0 0 0 0 0

RM Bridge Lesson 17: Fiber Stress Check



6 Lesson 17: Fiber Stress Check

Definition of the

Required Con-

struction Stage

Schedule Name SLS

Description

SLS-Fibre Stress

Check

Stages

Activation

Top Table

Insertion to the construction schedules:

Definition of

the Fibre

Stress Check

actions

Schedule Ac-

tion

Check

ac-

tions(SUP)

Check

ac-

tions(SUP)

Check

ac-

tions(SUP)

Check

ac-

tions(SUP)

Type FibSup FibSup FibSup FibSup

Stages Inp1 Perm-t-

0.sup

Perm-t-

inf.sup SLS-1a.sup SLS-1b.sup

Inp2 1 2 2 2

Schedule Action Out1 - - - -

Out2 * * * *

Bottom Table Delta-

T 0 0 0 0

Ac-

tion

Check

ac-

tions(SUP)

Check

ac-

tions(SUP)

Check

ac-

tions(SUP)

Type FibSup FibSup FibSup

Inp1 SLS-1c.sup SLS-1d.sup SLS-3.sup

Inp2 2 2 2

Out1 - - -

Out2 * * *

Delta-

T 0 0 0

The compressive stresses in concrete have to be checked to see if they exceed some

limit under a certain combination. The compression stresses due to load combination 1

(Perm-t-0.sup) should not exceed 0.6fc and the compression stresses under load com-binations 2-7 (Perm-t-inf.sup and Serviceability limit states) should not exceed 0.45fc.

The schedule actions for various checks are separated into different menus for load cas-

es and for envelopes Check actions (LC) and Check actions (SUP).

RM Bridge Lesson 17: Fiber Stress Check



The schedule action for checking the stresses in predefined fibers is Fib. The suffix de-

fines for what the check is done for load case (FibLc) or for envelope (FibSup).

The first input field (Input-1) defines for which load case or for which envelope the

check will be done.

Next input field defines the stress limit. The input is a number which references the

stress limit defined in the material data (Properties Material data Corresponding material; stress limits are defined in the small table in the bottom right corner).

If the stress limits are not defined the stress check cannot be done. To define the stress

limits for a material the insert after button has to be chosen (it is on the bottom right

side above the stress limit table). The stress limit number is automatically assigned (se-

rial number), and two other inputs represent the maximum (tension-positive) and mini-

mum (compression-negative) allowed stress limit.

In this case the stress limits have to be defined defined. The stress limit number 1 corre-

sponds to 0.6fc, and the stress limit number 2 corresponds to 0.45fc. For stress limit

1, the tensile stress is limited to 0.25 , which corresponds to a limit of

1.38MPa. For stress limit 2, the tensile stress is limited to 0.5 = 3.35MPa. After inputting these limits, the material properties should looks as follows:

The check determines the minimum and maximum stresses under the defined load

case/envelope in all stress check points defined in the cross-sections and compares them

with stress limits. Results are saved into a list file (Output-2). Those exceeding the lim-

its (if there are any) are saved into the list file (values marked with #), and a warning is

displayed after completion of the calculation.

The same check can also be done graphically. It can be seen at which places the re-

quirements are not satisfied. This is done by creating a diagram via RMSet. On this dia-

gram certain stresses in certain fibers are plotted along with stress limits.

RM Bridge Reinforced concrete checks General



7 Reinforced concrete checks General

The results of different design check actions are reinforcement areas that are saved into

their corresponding Attribute-Sets. They can be seen under menu Structure Ele-ments Checks for each element.

In the upper table the element is selected and in the bottom table the results can be seen

by selecting one of the corresponding Attribute Set.

Some Attribute Sets have more than one result component (e.g.: Attribute Set for Shear-

Longitudinal reinforcement which has two result components one for the top and an-other for the bottom reinforcement).

The calculated reinforcement areas are stored and displayed under the A2 reinforcement

area. The A1 reinforcement area represents an input where a predefined reinforcement

area (e.g.: minimum reinforcement) can be defined (double click on the Attribute Set or

select it and click on the modify button). It is possible to define that this reinforcement

area is fixed or variable. If it is set to fixed, then the program will not increase the val-

ues even if it is necessary according to a certain design check. In the other case the rein-

forcement area will be increased by the necessary reinforcement area calculated by a

certain design check.

The reinforcement areas can be displayed also graphically via RM-Sets. The corre-

sponding elements and attribute sets have to be defined. In addition the results can be

presented numerically by creating an excel sheet or a list file.

It is also possible to specify for which elements certain design checks should not be

done (double click on an element in the upper table and check the OFF button next to a

certain design check). By default all design checks are ON for all elements. The pro-

gram distinguishes between beam elements and other elements (spring elements, stiff-

ness elements, tendons, etc.). In addition it is also possible to make a detailed list file

(export) for each design check.

In principal the reinforcement area calculated by previous design actions (depending on

the schedule sequence defined in under schedule actions) is taken into account in the

subsequent design actions.

The data of the calculated reinforcement area (A2) remains as an existing reinforcement

area even when a new recalculation of the project is run (it is also exported into TCL

files). Therefore it is necessary to initialize (delete) the A2 reinforcement areas (calcu-

lated areas) before the first design action. This is done with the ReinIni action (Rein-

forcement Initialization) where the A2 reinforcement area of a certain or all Attribute

sets is set to 0 for all elements.

For clarification and clear overview a new (calculation) stage will be created:

RM Bridge Reinforced concrete checks General



Definition of the

Required Con-

struction Stage

Schedule Name ReinIni

Description Reinforcement initiali-

zation

Stages

Schedule Actions

Top Table

Initialization of

the A2 Reinforcement

areas

Schedule Action Check

actions(SUP)

Type RenIni

Stages Inp1 -

Inp2 -

Schedule Action Out1 -

Out2 -

Bottom Table Delta-T 0

The action ReinIni is located in the menu for load case check actions (Check Actions

(LC)). It is also found in the envelope check actions (Check Actions (SUP)).

If the first input (Input-1) remains empty (or a * is defined) all Attribute-Sets will be initialized. To initialize a certain Attribute-Set, it has to be selected from the drop down

menu at the input field.

RM Bridge Lesson 18: Ultimate Load Capacity Check



8 Lesson 18: Ultimate Load Capacity Check

Definition of the

Required Con-

struction Stage

Schedule Name Ult-ULS

Description ULS- Ultimate Load

Carrying Capacity

Stages

Schedule Actions

Top Table

Definition of the

Ultimate Load

Carrying Capacity

Schedule Action LC/Envelop

e action

LC/Envelope action

LC/Envelope action

Type SupInit SupOrSup SupOrSup

Stages Inp1 - ULS.sup ULS.sup

Inp2 - ULS-1.sup ULS-4.sup

Inp3 - - -

Schedule Actions Out1 ULS.sup - -

Out2 - - -

Bottom Table Delta-T 0 0 0

Action Nachweis-

Aktionen

LC/Envelope action

Check actions (SUP)

Type UltSup SupInit UltSup

Inp1 ULS.sup - ULS.sup

Inp2 Rein * - UltMz *

Inp3 - - -

Out1 - Ult-ULS.sup Ult-ULS.sup

Out2 * - *

Delta-T 0 0 0

For the ULS check the unfavorable effects of load combinations 8 and 9 (Strength limit

states 1 and 4) have to be considered. Therefore these combinations are superposed into

the final ULS.sup envelope with the Or rule (substitute if unfavorable).

The first check action performs the design check by selection of the Rein option (Rein-

forcement design). With this input the necessary reinforcement will be calculated and

added to the corresponding Attribute-Set. The reinforcement amount can be displayed

as was already explained (diagram creation via RM-Set). In addition, the results are

exported/saved also to a list file. Also for this check a detailed list can be made (at same

principle as already explained).

In next steps first an envelope file (Ult-ULS.sup) is initialized. Into this envelope the

results of the following ultimate load capacity check (UltSup check action with option

Ultimate load check for UltMz) are saved. This action calculates the maximum capacity

RM Bridge Lesson 18: Ultimate Load Capacity Check



of the bending moment Mz of the cross-section (structure respectively). For this calcula-

tion both other internal force components for the ultimate load check (Nx and My) are

fixed, and only the bending moment Mz is increased until the maximum capacity of the

bending moment is reached. The iteration process varies the strain planes which are

based on the stress-strain diagram of the corresponding element (concrete, reinforce-

ment steel and pre-stressing steel). These diagrams are defined under material proper-

ties. Also these results are saved to a list file.

For pre-stressed structures the initial strain load case has to be defined to correctly con-

sider the initial strain of the pre-stressing steel caused by the primary state of pre-

stressing (V*e) when evaluating the stress-strain diagram. This state is saved in the

summation load case of pre-stressing (PT-SUM).

To consider the initial strain of creep and shrinkage and relaxation also, the total sum-

mation load case (STG-SUM) should be defined as the initial strain load case.

Furthermore, it is possible to consider the initial strain state from the envelope (load

case respectively) used for the design check. To do so, a * has to be defined, instead of certain load case in the corresponding input field. This option considers also the fac-

tored initial strain of time effects. However, this is not allowed if the envelope includes

factored pre-stressing load cases and time effects and is not relevant in this form for

consideration of initial strain (see combination factors for combination used for crack

check).

If no initial strain load case is defined, then the load case defined in the recalc pad is

used as initial strain load case. If no load case is defined in the recalc pad, then the ini-

tial strain is not considered.

For more information about the ultimate load check and design of reinforced concrete

with or without pre-stressing see RM Analysis User Guide section 15.3 and 15.4.

A very instructive graphical comparison between demand moments (ULS.sup) and ul-

timate moments (Ult-SUL.sup) is done in the corresponding example.

RM Bridge Lesson 19: Shear Capacity Check



9 Lesson 19: Shear Capacity Check Definition of the

Required Con-

struction Stage

Schedule Name ULS-Shear

Description Shear capacity

check

Stages

Schedule Actions

Top Table

Definition of the

Shear Capacity

Check

Schedule Action Check actions

(SUP)

Type ShearSup

Stages Inp1 ULS.sup

Inp2 PT-SUM

Inp3 -

Schedule Actions Out1 -

Out2 *

Bottom Table Delta-

T 0

To perform a check for shear force and torsion (Shear check) for an envelope, the check

action ShearSup has to be used (ShearLc for load cases). The envelope for the ULS

checks was already generated and can be used. Also for this check an initial strain load

case has to be defined.

The results are, same as for all other checks, saved to the corresponding Attribute-Set as

well as to a normal or extended list file.

If the tendon geometry is not defined in a detailed manner (the tendons are grouped to-

gether into one tendon geometry), the nominal web thickness is not calculated automati-

cally. Therefore the reduction of the web thickness has to be defined manually. This

reduction is defined via the parameters b-beg and b-end (reduction at element begin and

end) under menu Structure Elements Checks. These two parameters are refer-enced to elements and via this to the assigned cross-sections. In case of multiple webs,

the defined values will be subdivided on the individual webs taking into account the

number and width of the web (the thinnest web will have the smallest reduction and

vice versa for thickest web).

For grouted tendons the reduction of the web thickness according to AASHTO 5.8.2.9

is defined as 0.25. In our case with arrangements of 3 tendons at same level (paral-lel; side by side) with 8 cm diameter the reduction is (0.25230.08 =) 0.12 m.

To define the reduction change, go to the top table under Structure Elements Checks and double click (or modify) one of the superstructure elements (elements from 101 to 135). Define as follows: El-from:101; El-to:135; El-step:1; b-beg (m):0.12;

b-end (m):0.12.

RM Bridge Lesson 20: Fatigue Check



10 Lesson 20: Fatigue Check

Definition of the

Required Con-

struction Stage

Schedule Name ULS- Fatigue

Description Fatigue check

Stages

Activation

Top Table

Definition of the

Fatigue Check

Schedule Action

LC/Envelope

action

Calcula-tion (Static)

Type SupInit LiveL

Stages Inp1 - 2

Inp2 - 5

Inp3 - -

Schedule Actions Out1 Fatigue.sup Fatigue.sup

Out2 *

Bottom Table Delta-T 0 0

Action LC/Envelope

action

LC/Envelope action

Check actions (SUP)

Check actions (SUP)

Type SupInit SupInit FatigSup FatigSup

Inp1 Fatigue.sup Fatigue.sup FLS-1.sup FLS-2.sup

Inp2 1.38 0.69 - -

Inp3 - - - -

Out1 FLS-1.sup FLS-2.sup - -

Out2 * *

Delta-T 0 0 0 0

For the fatigue limit state, first a live load evaluation is done with the fatigue truck (load

train number 5). Next, the fatigue limit state combinations FLS-1 and FLS-2 are creat-

ed by applying factors to the live load envelope. According to AASHTO 3.6.1.4 a fac-

tor of 0.8 will be applied because there are 3 lanes. According to AASHTO 3.6.2 the

dynamic impact factor will be 1.15. The factors for FLS-1 and FLS-2 are computed as

follows:

- FLS-1: 0.8*1.15*1.5 = 1.38

- FLS-2: 0.8*1.15*0.75 = 0.69

The action FatigSup performs a fatigue check only for a superposition file (envelope).

This is because only envelope can contain the maximum/minimum internal forces for

RM Bridge Lesson 20: Fatigue Check



the traffic loads relevant for fatigue. The difference between maximum and minimum is

taken as a relevant stress range value f.

The results are saved to the list file which contains the stress difference for each element

in all stress check points, longitudinal reinforcement and tendons. These stress ranges

can then be checked against the limits set forth in AASHTO 5.5.3.

RM Bridge Lesson 21: Lists and Plots



11 Lesson 21: Lists and Plots

The different possibilities of post processing (RM-Sets and Plot Conatiners) were

shown already in section 11 of Part1. In the corresponding example there are multiple

Rm-Sets and Plots for presentation of internal forces, stresses and reinforcement areas

defined and created/plotted in schedule actions. This definition can be seen directly in

the program.

In addition a new stage is created (last stage) in which additional predefined plot actions

(Schedule Stages Schedule actins; Bottom table List/Plot actions) are defined for plotting: working diagrams, creep and shrinkage diagrams, cross-sections, tendon

geometry, tendon scheme, tendon positions in cross-sections, stressing actions, load

trains, influence lines, etc. Also these definitions can be seen directly in the program.

1 General1.1 Design Code1.2 Design Loadings:1.2.1 Permanent actions and Creep & Shrinkage1.2.2 Live Load1.2.2.1 Load train 1 Truck1.2.2.2 Load train 2 Tandem1.2.2.3 Load train 3 Lane1.2.2.4 Load train 4 Double Truck1.2.2.5 Load train 5 Fatigue Truck

1.2.3 Braking Loads1.2.4 Wind Loads1.2.5 Thermal Forces1.2.6 Creep and Shrinkage1.2.7 Pier settlement

1.3 Load combinations1.4 Design checks1.4.1 Servicebility limit state1.4.1.1 Stresses

1.4.2 Ultimate limit state

2 Lesson 13: Definition of Additional Loads2.1 Definition of Settlement Load Cases2.2 Definition of Temperature Load Case2.3 Definition of Wind Load Case2.4 Definition of Braking Forces

3 Lesson 14: Calculation and Superposition of Additional Loads3.1 Calculation and superposition of Settlement loads3.2 Calculation and superposition of temperature loads3.3 Calculation and superposition of wind loads3.4 Calculation and superposition of braking loads

4 Lesson 15: Traffic Loads4.1 Traffic Definition4.2 Definition of Traffic Lanes4.3 Traffic Loads4.4 Traffic Calculation4.4.1 Calculation of influence lines4.4.2 Combining Influence Lines with Load Trains

4.5 Traffic Superposition

5 Lesson 16: Load Combinations5.1 Definition of the Load Combination5.2 Calculation of the load combinations

6 Lesson 17: Fiber Stress Check7 Reinforced concrete checks General8 Lesson 18: Ultimate Load Capacity Check9 Lesson 19: Shear Capacity Check10 Lesson 20: Fatigue Check11 Lesson 21: Lists and Plots

Documents

RM E Prestressing Basic Part2 AASHTO