rm e prestressing basic part2 aashto imp
DESCRIPTION
bridge design softwareTRANSCRIPT
RM Bridge Professional Engineering Software for Bridges of all Types
RM Bridge V8i
March 2011
TRAINING PRESTRESSING BASIC
ANALYZER – PART 2: AASHTO [IMP. UNITS]
RM Bridge
Training Prestressing Basic - ANALYZER - Part 2: AASHTO [IMPERIAL UNITS] 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 ............................................................................ 4-9
4.3 Traffic Loads ................................................................................................ 4-11
4.4 Traffic Calculation ....................................................................................... 4-12
4.4.1 Calculation of influence lines .................................................................. 4-12
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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
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Training Prestressing Basic - ANALYZER - Part 2: AASHTO [IMPERIAL UNITS] 1-1
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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 for longitudinal bending.
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1.2.2.1 Load train 1 – Lane
1.2.2.2 Load train 2 – Truck
1.2.2.3 Load train 3 – Tandem
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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:
(32 kip + 32 kip + 8 kip)x0.25 = 18 kip
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:
18kip x 3(lanes) x 0.85 (mult. presence) / 455ft (length of bridge) = 0.1 kip/ft
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 30 ft,
design wind velocity is assumed to be 100mph. Therefore, the wind pressure is as fol-
lows:
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= 0.05 kip/ft
2
Wind pressure will be applied to the concrete box, and it is also assumed to act on a
barrier that is 3 ft tall.
Wind load on the live load according to AASHTO 3.8.1.3 is also applied.
Wind on Live Load: 0.1 kip/ft (6 ft 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 68oF.
According to AASHTO 3.12.2.1 the temperature range for uniform temperature diffe-
rence will be 0.0oF to 80
oF (table 3.12.2.1-1). For an initial temperature of 68
oF this
gives:
- Uniform temperature postitive = 12oF
- Uniform temperature negative = -68oF
Thermal Coefficient: 6 x 10e-6 per °F
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:
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Temperature Gradient
Point Positive (oF) Negative (
oF)
T1 41 -12.3
T2 11 3.3
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
0.5 inches at each abutment and pier axis
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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 - -
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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:
|σc| 0.6 · |f’c| = 0.6 x 6ksi = 3.6ksi
Concrete tensile stresses are limited to:
|σt| 0.0948 |f’c| 0.2ksi = 0.0948 = 0.232ksi 0.2ksi
Concrete stresses after losses
Concrete compressive stresses for prestressing and permanent loads are limited to:
|σc| 0.45 · |f’c| = 0.45 x 6ksi = 2.7ksi
Concrete tensile stresses are limited to:
|σt| 0.19 |f’c| = 0.19 = 0.465ksi
According to AASHTO 5.9.3
Initial stress in the tendons
σp 0.90 · fpy = 0.90 x 245 ksi = 220ksi.
Stress in tendons at service limit state after losses
σp 0.80 · fpy = 0.80 x 245ksi = 196ksi
1.4.2 Ultimate limit state
Accordingly to AASHTO LRFD 2007 Section 5.
Design checks to be made:
Bending and axial force
Shear
Torsion
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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 1
Settlement
of pier 1
Settlement
of pier 2
Settlement
of abut-
ment 2
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 [ft] 0 0 0 0
Vy [ft] 0.0417 0.0417 0.0417 0.0417
Vz [ft] 0 0 0 0
Direc-
tion Global Global Global Global
Rx
[Rad] 0 0 0 0
Ry [ft] 0 0 0 0
Rz [ft] 0 0 0 0
Where Begin Begin Begin Begin
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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
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Define Load Sets
for Uniform Tem-
perature Loads
CONSTR.SCHED. Name TU-P
Loading Initial
stress/strain
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 6e-6 6e-6 6e-6
DT-G
[°F] 12 12 12
DT- Y
[°F] 0 0 0
H-Y [ft] 0 0 0
DT- Z
[°F] 0 0 0
H-Z [ft] 0 0 0
Name TU-N
Loading Initial
stress/strain
Initial
stress/strain
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 6e-6 6e-6 6e-6
DT-G
[°F] -68 -68 -68
DT- Y
[°F] 0 0 0
H-Y [ft] 0 0 0
DT- Z
[°F] 0 0 0
H-Z [ft] 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.
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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 [k/ft] 0 0
Qy [k/ft] 0 0
Qz [k/ft] 0.05 0.15
Direction Local Local
Eccentricity Local Local+Y
Elem-Ecc
Ey [ft] 0 1.5
Ez [ft] 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/m2) 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.
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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 [k/ft2] 0 0
Qy [k/ft2] 0 0
Qz [k/ft2] 0.05 0.05
Direction Local Local
Eccentricity Local Local
Ey [ft] 0 0
Ez [ft] 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 6 ft 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 [k/ft] 0
Qy [k/ft] 0
Qz [k/ft] 0.1
Direction Local
Eccentricity Local+Y
Elem-Ecc
Ey [ft] 6
Ez [ft] 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).
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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 [k/ft] 0.1
Qy [k/ft] 0
Qz [k/ft] 0
Direction Local
Eccentricity Local+Y
Elem-Ecc
Ey [ft] 6
Ez [ft] 0
Load applica-
tion Real length
Definition Load/Unit
length
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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 support
settlement
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-A3 Settle-A4
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.
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Type LC/Enve
lope action
LC/Enve
lope action
LC/Enve
lope action
LC/Enve
lope action
LC/Enve
lope action
Action SupInit SupAndLc 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
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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
doesn’t have to be defined because it will be automatically added. This doesn’t 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
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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/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
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
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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/Envelop
e action
LC/Envelop
e 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
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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.
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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/12, where w is the clear roadway width:
w = 42ft – 2(1.5ft barriers) = 39ft
number of design lanes = 39ft/12 = 3.25 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 12’-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 load train. 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
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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.
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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
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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 = +12 ft ez = 0.0 ft ez = -12 ft
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 [ft] 0 0 0
ez [ft] +12 +0.0 -12
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
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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 [k/ft] -0.64 - - -
Load Definitions Free Length Free - - -
F [k] - -32 -32 -8
AASHTO - - - -
Load Trains l-from [ft] - 14 14 0
l-to [ft] - 30 0 0
Bottom Table l-step [ft] - 1.6 0 0
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LTrain 3 4 5
Q [k/ft] - - - - - - - - - - -
Free
Length - - - - - - - - - - -
F [k] -25 -25 -32 -32 -8 -32 -32 -8 -32 -32 -8
AASHTO - - - - - - - - -
l-from [ft] 4 - 14 14 50 14 14 0 30 14 0
l-to [ft] 0 - 0 0 0 0 0 0 0 0 0
l-step[ft] 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 = -32 kip (negative
y-direction) and a variable length between 14ft and 30ft to the next force. The next input
for the first load train consist only of a concentrated load F = -32 kip.
Using the same principle, load train numbers 2 through 5 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
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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
Insert the following definitions in the bottom table after the influence line calculation
actions:
Type LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe 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
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Type LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
Action SupInit SupInit SupInit SupInit SupInit SupInit
Inp1 - - - - - -
Inp2 - - - - - -
Inp3 - - - - - -
Out1
L2-
Dbl_Truck.su
p
L2-Lane.sup L3-Truck.sup L3-
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)
Calculation
(Static)
Calculation
(Static)
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
L1-Lane.sup L2-Truck.sup L2-
Tandem.sup
Out2 * * * * * *
Delta-T 0 0 0 0 0 0
Type Calculation
(Static)
Calculation
(Static)
Calculation
(Static)
Calculation
(Static)
Calculation
(Static)
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
L2-Lane.sup L3-Truck.sup L3-
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.
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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/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e 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/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
Action SupInit SupORSup SupORSup SupORSup SupANDSup
Inp1 - L2.sup L2.sup L2.sup L2.sup
Inp2 - L2-Truck.sup L2-
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
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Type LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
Action SupInit SupORSup SupORSup SupORSup SupANDSup
Inp1 - L3.sup L3.sup L3.sup L3.sup
Inp2 - L3-Truck.sup L3-
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/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe action
LC/Envelo
pe 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/Envelop
e action
LC/Envelop
e action
LC/Envelop
e 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
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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/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
action
LC/Env
elope
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.
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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
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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 - -
Comb IV 1 1 1 1 - 1 - -
Comb V 1 1 1 1.2 - 1.2 - -
Comb VI 1 1 1 1.2 - 1.2 - -
Comb VII 1 1 1 1 - 1 - -
Comb VIII 1 1 1 1 - 0.5 - -
Comb IX 1 1 1 1 - 0.5 - -
LC/Envelo
pe live.sup brake.up WS.sup WL.sup TU.sup
Comb SupAndSup SupAndSup SupAndSup SupAndSup SupAndSup
Type F-fav. F-
unfav. F-fav.
F-
unfav. F-fav.
F-
unfav. F-fav.
F-
unfav. F-fav.
F-
unfav.
Comb I - - - - - - - - - -
Comb II - - - - - - - - - -
Comb III - 1 - 1 - 0.3 - 1 - 1
Comb IV - - - - - 0.3 - 1 - 1
Comb V - 1 - 1 - - - 1 - 1.2
Comb VI - - - - - - - 1 - 1.2
Comb VII - 0.8 - 0.8 - - - - - 1
Comb VIII - 1.75 - 1.75 - - - - - 0.5
Comb IX - - - - - - - - - 0.5
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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 - 1
Comb IV - 1 - 1
Comb V - 0.5 - 1
Comb VI - 1 - 1
Comb VII - 0.5 - 1
Comb VIII - - - 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
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Insertion of the
Calculation Ac-
tions to the Con-
struction Stage
Combos
Schedule Type LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e 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/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e action
LC/Envelop
e 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
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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 0.6∙f’c and the compression stresses under load com-
binations 2-7 (Perm-t-inf.sup and Serviceability limit states) should not exceed 0.45∙f’c.
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).
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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 0.6∙f’c, and the stress limit number 2 corresponds to 0.45∙f’c. For stress limit
1, the tensile stress is limited to 0.0948 , which corresponds to a limit of
0.2ksi. For stress limit 2, the tensile stress is limited to 0.19 = 0.465ksi. After in-
putting 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.
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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:
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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.
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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/Envelop
e action
LC/Envelop
e 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 Check actions
(SUP)
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
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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.
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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∙∑Φ. In our case with arrangements of 3 tendons at same level (paral-
lel; side by side) with 3.14 in. diameter the reduction is (0.25∙2∙3∙3.14 =) 4.71 in.
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 (in):4.71;
b-end (in):4.71.
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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
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the traffic loads relevant for fatigue. The difference between maximum and minimum is
taken as a relevant stress range value Δf.
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.
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11 Lesson 21: Lists and Plots
The different possibilities of post processing (RM-Sets and Plot Containers) 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.