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for midas CivilDESIGN GUIDE

CAN/CSA S6-14

Prestressed Concrete Girder Design

Steel Composite I-Girder Design

Steel Composite Box Girder Design

Developers and distributors assume no responsibility for the use of MIDAS Family Program (midas Civil, midas FEA, midas FX+, midas Gen, midas Drawing, midas SDS, midas

“MIDAS package”) or for the accuracy or validity of any results obtained from the MIDAS package.

Developers and distributors shall not be liable for loss of

caused directly or indirectly by the MIDAS package, when used for any purpose or use, due to any defect or

fully understand the bases of the program and become familiar with the users manuals. The user shall also inde-pendently verify the results produced by the program.

DISCLAIMER

analysis and design system. The guide aims to provide

features and to provide relevant references to the clauses in the Design standards.

The design guide covers prestressed concrete girder, steel composite I-girder and steel composite box girder as per CAN/CSA S6-14.

It is recommended that you read this guide and review corresponding tutorials, which are found on our web site,

the program’s main menu.

girder design to CAN/CSA S6-14.

design to CAN/CSA S6-14.

design to CAN/CSA S6-14.

Organization

features and to provide relevant references to the clauses in the Design standards.

The design guide covers prestressed concrete girder, steel composite I-girder and steel composite box girder as per CAN/CSA S6-14.

It is recommended that you read this guide and review corresponding

help available in the program’s main menu.

Foreword

Steel Composite I - Girder Design (CAN/CSA-S6-14)Chapter 2. 471. CAN/CSA S6-14 Steel Composite I-Girder 49

51

51

1. Composite I Girder

2. Shear Connector

4. Horizontally curved Box girders

72

86

88

94

Modeling and Design Variables1. Modeling Design Variables 55

Contents

Prestressed Concrete Girder Design (CAN/CSA-S6-14) 01Strength Limit States1. Flexural resistance

2. Shear resistance

3. Torsion resistance

03

14

21

Serviceability Limit States

3. Tensile stress for Prestressing tendons

5. Principal stress at service loads (Excluding torsional shear stress)

6. Principal stress at service loads

26

31

34

37

39

40

7. Check crack 42

Steel Composite Design Result97

100

101

103

104

105

7. Total Checking 106

Steel Composite Design Result163

166

167

169

170

171

7. Total Checking 172

Steel Composite Box Girder Design (CAN/CSA S6-14)Chapter 3. 1071. CAN/CSA S6-14 Steel Composite Box Girder 109

111

111

1. Composite Box Girder

2. Shear Connector

4. Horizontally curved Box girders

Box Girder

132

148

150

158

Modeling and Design Variables1. Modeling Design Variables 115

Prestressed ConcreteGirder Design

CAN/CSA S6 -14

Chapter 1.

Prestressed Concrete Girder Design

Serviceability Limit States

Tensile stress for Prestressing tendons

Principal stress at service loads

Check crack

Chapter 1. Prestressed Concrete Girder Design : CSA-S6-14

Strength Limit State

3Chapter 1. Prestressed Concrete Girder Design

1. Flexural resistance For the flexural resistance design limit, Mf ≤Mr shall be satisfied where Mf : factored moment at a section

Mr : factored flexural resistance of a section in bending

1.1 Material resistance factors

[Fig.1. 1] Material resistance factors

In CSA, regardless of applied members, resistant forces are calculated with the corresponding material resistance factors.

1.2 Calculate neutral axis depth. (by Iteration approach) Neutral axis is iteratively calculated by the following steps.

Assume neutral axis depth, c

Calculate Cc (Concrete)

Calculate Ts, Cs (Reinforcement)

Calculate Tps (Tendon)

Cc+Cs-(Ts+Tps)=0?

Get neutral axis depth, c

YES

NO

(1)

(2)

(3)

(4)

Initial c = H/2 (H=Section Height)

[Fig.1. 2] Flow chart to calculate neutral axis depth, c

CAN/CSA-S6-14 (8.4.6)

4 Design Guide for midas Civil

(1) Calculate force of concrete, Cc. midas Civil assumes a rectangular stress distribution in the stress and strain relationship of concrete. Note that the maximum strain is assumed εcu = 0.0035

[Fig.1. 3] Flow chart to calculate neutral axis depth, c

1 'c c c cC f A (1.1)

where

1 0.85 0.0015 ' 0.67cf

c : Material resistance factors for concrete

'cf : Specified compressive strength of concrete

cA : Concrete area of compressive zone 1( )ab c b

1 0.97 0.0025 ' 0.67cf c : Distance from the extreme compression fiber to the neutral axis. b : Width f’c value applied in calculation is inputted as shown below.

PSC>PSC Design Data> PSC Design Material…

[Fig.1. 4] PSC Design Material

Concrete and reinforcement data are entered in the PSC Design Materials dialog box. Selection of design standard and the type of concrete to be used determine the Specified Compressive Strength, which is the f’c value in PSC design.

CAN/CSA-S6-14 (8.8.3)

Concrete Material Property

Reinforcement Material Property

5 Chapter 1. Prestressed Concrete Girder Design

Similarly for concrete, selection of design standard and the type of steel to be used determine the yield stress for longitudinal reinforcements and shear reinforcements, and these values are used in PSC design. Input tendon profile data for PSC design in the dialog box below.

Load>Temp./Prestress>Section Manager >Tendon Profile

Tendon data can be entered in the 2D or 3D coordinate system. Tendon position which is placed at the farthest position from the extreme compression fiber will be used to calculate the strain.

Input longitudinal reinforcement data for PSC design in the dialog box below.

Properties>Section Manager>Reinforcements

[Fig.1. 6] Input Longitudinal reinforcement

Once reinforcement is entered at the PSC section, the rebar which is placed at the farthest position from the extreme compression fiber will be used to calculate the strain. In short, the rebar at the bottom most is used under the sagging moment while the rebar at the top most is used under the hogging moment.

Entered rebar data

Rebar coordinate at section

[Fig.1. 5] Tendon Profile


(2) Calculate force of reinforcement, Ts, Cs.

, ' 's s s s s s s sT A f C A f (1.2)

where Φs : Material resistance factor for steel As, As’ : the cross sectional area of tensile and compressive reinforcements. fs , fs’: the stress of tensile and compressive reinforcements.

In order to calculate the tensile stress of reinforcements at a section, strain of the reinforcements is first obtained based on the strain compatibility condition. The corresponding stresses are then computed by the stress-strain relationship. The equations are shown below. Strain

cut

s xxd , cu

cs x

dx' (1.3)

where εs : the strain of tensile reinforcement. εs’ : the strain of compressive reinforcement.

εcu : the ultimate compressive strain in the concrete. (εcu = 0.0035) x : the neutral axis depth. dt : distance from the extreme compression fiber to the rebar at the bottom most dc : distance from the extreme compression fiber to the rebar at the top most

Stress

Once the yield stress is reached, the yield stress is applied for stress in steel. εs x Es is, otherwise, used.

( )( )

s s s ys

y s y

E f ff

f f f,

' ( ' )'

( ' )s s s y

sy s y

E f ff

f f f (1.4)

where Es : Elastic modulus of steel Fy : Yield stress of steel

(3) Calculate force of tendon, Tps.

ps p p psT A f (1.5)

where Φp : Material resistance factors for tendon Ap : the cross sectional area of tendon fps : the stress of tendon.


Tendon-related data can be entered in the Tendon Property dialog box.

Load>Temp./Prestress>Section Manager>Tendon Property

[Fig.1. 7] Tendon Property Dialog

Tendon Type

Select one among Pre-Tension, Post-Tension, and External Tension. Internal(Pre-Tension) : Tendon is tension-stressed prior to the placement of concrete and unloaded after the concrete has hardened. This introduces compression through adhesive bonds between concrete and tendon. Internal(Post-Tension) : Compression is introduced by tensioning tendons after concrete has hardened. The tendons are wedged after achieving a desired level of stress. External : Tendons are placed external to concrete members and stressed

Bond Type

Bonded : This defines a perfect bond between concrete and tendon. The case of Internal(Pre-Tension) defines the Bond Type as Bonded. Unbonded : In this case, tendon is not well bonded with concrete, allowing relative movements to the concrete. The case of External defines the bond Type as Unbonded.

Bond type can be classified as shown in Table1.1 below, depending on the Tendon Type. [Table1. 1] Bond Type Depending on Tendon Type

Tendon Type Bond Type

Internal (Pre-tension) Bonded

Internal (Post-tension) Bonded

Unbonded

External Unbonded Total Tendon Area

Enter the area of Tendon (Ap).

Select the number of tendon cable and the size o f its diameter via button.

fpu, fpy Enter the ultimate strength fpu and yield strength fpy of the prestressing steel.

Stress fps differs depending on the Bond Type. For the case of the Bonded Type, depending on the ratio c/dp, fps is calculated differently as well.

CAN/CSA-S6-14 (8.8.4.2)

Total Tendon Area

fpu fpy

Bond Type

Tendon Type


[Table1. 2] calculation method of fps Bond Type Classification Tensile stress

Bonded Type c/dp ≤0.5 Bonded Type fps c/dp >0.5 Strain compatibility

Unbonded Type - Unbonded Type fps

Where c: Distance between the neutral axis and the compressive face

dp : Distance from the extreme compression fiber to the centroid of the prestressing tendons

fps in Bonded Type

1ps pu pp

cf f k

d (1.6)

where Kp : 0.3 for low-relaxation strands 0.4 for smooth high-strength bars 0.5 for deformed high-strength bars fpu : Specified tensile strength of tendon (MPa)

Tendon Type can be assigned as shown in a red box below.

PSC> Design Parameter> Parameters…

[Fig.1. 8] PSC Design Parameter Dialog – Tendon Type

For clarification, notations used in a Civil dialog and in Design Code are summarized in Table1.3. [Table1. 3] Tendon Type

Civil Dialog Design Code

Low Relaxation Tendons Low Relaxation Strand

Stress Relieved Tendons smooth high-strength Bar

Prestressing Bar deformed high-strength Bar


fps in Unbonded Type

ps sef f (1.7)

where fse : effective stress in prestress steel after losses fps by Strain compatibility

When bending strength is calculated using strain compatibility condition, Stress-strain equation of Tendon is used.

When εp ≤ 0.008 : fps = Epεp When εp > 0.008 :

(Grade 1760 Strands) 0.4331749 0.980.00614ps pu

p

f f (1.8)

(Grade 1860 Strands) 0.5171848 0.98

0.0065ps pup

f f

(4) Check if a resultant force is Zero.

Until equilibrium between compressive forces (C=Cc+Cs) and tensile forces(T=Ts+Tps) is satisfied within a certain level of convergence criterion, iterative calculations are performed by changing the c value. Convergence criterion is applied as shown in the following equation • Convergence condition :

1.0 0.001 ( )CTolerance

T (1.9)

1.3 Calculate moment resistance (Mr) Once the neutral axis is computed, the axial forces obtained in 1.2.1(1)~(3) are multiplied by the distance from their individual acting point to the neutral axis. These obtained moments are summed to obtain the total moment resistance Mr.

'r c c s s s s ps piM C a C a T a T a (1.10)

where ac, as, as’, api : the distance from neutral axis depth, c to concrete, reinforcement rebar, tendon.

As

As

Ap

Cs

Cc

Ts

Tps

0.85f c

ac

a s a p

a c a s'

[Fig.1. 9] Forces and distances from neutral axis depth for Mn

CAN/CSA-S6-00 (C 8.8.3.2)


If tendon is located above the neutral axis, the moment due to this tendon will generate a negative moment and it will be subtracted in the equation.

' ''ps pir c c s s s s ps piM C a C a T a T a T a

(1.8)

1.4 Minimum Reinforcement

Process to check the minimum reinforcement is the following. 1. Mr≥4/3Mf is checked,

If Mr≥4/3Mf , the minimum reinforcement ratio needs to be checked 2. Calculate cracked moment Mcr 3. if Mr≥1.2Mcr , the minimum reinforcement is satisfied.

Cracked moment( Mcr) Civil applies a below equation for a cracked moment.

( )cr cr cpe cM f f S (1.9)

Where, in midas Civil

fcr : 0.4 'cf

Sc : modulus of section on the tension side fcpe : Compressive stress of the section in elastic state due to effective prestress.

Equation used in the program is shown below.

ps e ps e pcpe

g

A f A f ef

A S (1.13)

where

ef : Effective prestress forces in tendon reinforcement

pe : Distance from the neutral axis to the centroid of tendon reinforcement

psA : Area of tendon reinforcement

gA : Gross cross-sectional area

S

: Section modulus on the compression side

1.5 Maximum Reinforcement If c/d ≤0.5, it is considered that the requirement for the maximum reinforcement is satisfied. where c = Distance from the neutral axis to the extreme compression fiber d = Distance from the extreme compression fiber to the center of tension force. Equation used in program is shown below.

ps ps p s s s

ps ps s s

A f d A f dd

A f A f (1.10)

Where, dp : Distance from the extreme compression fiber to the centriod of tensile tendon ds : Distance from the extreme compression fiber to the centriod of tensile reinforcement

CAN/CSA-S6-14 (8.8.4.3)

CAN/CSA-S6-14 (8.4.1.8.1)

CAN/CSA-S6-14 (8.8.4.4)

CAN/CSA-S6-14 (8.8.4.5)


1.6 Check Component of Flexural Resistance If c/dp > 0.5, it is considered that the calculated flexural resistance can be ignored. The users can check the results with the table. There is the calculated value for c/dp, and if c/dp > 0.5, it will be shown with dash(-).

The tendon stress (fps) will be calculated by fps equation of Bonded type, depending on the value for c/dp.

1.7 Check moment resistance

The user needs to select load combination cases to be used to check the strength limit with respect to bending moments as shown in Figure1.10.

Results>Load combinations>Concrete Design tab

[Fig.1. 10] Load Combinations dialog

Load combinations for PSC design can be entered within the Concrete Design tab of the Load Combination dialog. For load combinations with Strength/Stress defined in the Active column, bending strength is checked in terms of positive and negative bending moments. In addition, these load combinations are applied to check strength limits for shear and twist. For load combinations with Serviceability defined in the Active column, serviceability limits are checked. There are two cases to be considered in the verification of moment

▪ When not required to satisfy minimum reinforcement requirements Mr≥Mu and (c/d≤0.5) need to be satisfied.

▪ When required to satisfy minimum reinforcement requirements Mr≥Mu, Mr≥Mcr and (c/d≤0.5) need to be satisfied.

Active: Strength/Stress

Active: Serviceability


1.8 Moment resistance verification

1.8.1 by Result Tables The results can be checked as shown in the table below.

Design>PSC Design>PSC Design Result Tables>Check Flexural Strength…

[Fig.1. 11] Result table for moment resistance

Elem : Element number Part : Check location (I-End, J-End) of each element. Positive/Negative : Positive moment, negative moment. LCom Name : Load combination name. Type : Displays the set of member forces corresponding to moving load case or settlement load case for which the maximum stresses are produced. CHK : Flexural strength check for element Mf : factored moment Mcr : Cracked Moment Mr : factored flexural resistance Ratio : Mf/ Mr, (less than 1, ok) min(4/3Mf, 1.2Mcr)/Mr : verification of minimum reinforcement ratio(less than 1, ok) C/D : verification of maximum reinforcement ratio (less than 0.5, ok) c/dp : Component of Flexural Resistance CHK(less than 0.5, ok)


1.8.2 by Excel Report Detailed verification results with the basis of calculation can be checked in an excel report as shown in Figure 1.12.

Design>PSC Design>PSC Design Calculation…

[Fig.1. 12] Excel Report for moment resistance


2 Shear resistance Pure shear without the effects of torsion is verified with the following equation. (for shear with the effects of torsion, refer to 1.3 Torsion resistance) Limit state of Shear resistance needs to satisfy Vf ≤Vr. Where Vf = factored Shear force

Vr = factored Shear resistance

2.1 Parameters for shear

2.1.1 Effective web width(bv) Effective web width (bv) is taken as web thickness. For PSC multi-cell girder, web thickness can be automatically taken as a summation of thickness for all webs. Also this value can be entered by the user directly as shown in the figure below.

Property > Section Property > Section >PSC

[Fig.1. 13] Effective web width

1) When the user directly enters values for web thickness Apply the minimum value among the entered web thickness values. 2) When “Auto” option is selected Apply the minimum web thickness among t1, t2, and t3. These values are automatically taken as

a summation of thickness for both webs at the stress point, Z1, Z2, and Z3.

2.1.2 Effective shear depth (dv) Effective shear depth is considered as follows.

min 0.9 , 0.72vd d h (1.11)

CAN/CSA-S6-14 (8.9.1.5)


where

ps ps p s s s

ps ps s s

A f d A f dd

A f A f

dp : Distance from the extreme compression fiber to the centroid of tendon reinforcements ds : Distance from the extreme compression fiber to the centroid of tensile reinforcements

2.1.3 Longitudinal strain (εx)

Longitudinal strain εx is computed with the following equation.

/ 0.52( )

f v f p f ps fpox

s s p ps

M d V V N A f

E A E A (1.12)

where Vf and Mf are positive Mf ≥ (Vf-Vp)dv Nf is posive for tension and negative for compression fpo is 0.7fpu for the bonded type, and is equal to fpe for the unbounded type εx is bounded inbetween : 0 0.003x As and Aps are the area of tensile reinforcements and tendon reinforcements, respectively

2.2 The factored shear resistance, Vn Vn is determined as the lesser of the results from Equations 1.15 and 1.16.

r c s pV V V V

(1.13)

'0.25r c c v v pV f b d V

(1.14)

Where Φc : Material resistance factors for concrete Vc : factored shear resistance by concrete Vs : factored shear resistance by shear reinforcement Vp : shear resistance component in the direction of the applied shear of the effective prestressing

force.

In midas Civil, shear resistance due to prestressing force, Vp, includes primary prestress force. The secondary effects from prestressing shall be included in the design shear force obtained from the load combinations.

2.3 The factored shear resistance by concrete, Vc

2.3.1 Determination β and Φ by general method

Design for shear allows to use two methods (Simplified method and General method) to calculate β and Φ. In midas Civil, the general method is applied.

0.4 13001 1500 1000x zeS

(1.15)

(29 7000 ) 0.882500

zex

S (1.20)

CAN/CSA-S6-14 (8.9.3.3)

CAN/CSA-S6-14 (8.9.3.7)


where

,min300 ( )ze v vS mm A A

,min

35 0.85 ( )15

zz v v

g

SS A A

a

Sz : dv (refer to clause 8.9.3.6) ag : 25.4mm (f’c ≤ 60Mpa)

0mm (f’c ≥ 70Mpa) 60~70 by linear interpolation (60MPa < f’c < 70Mpa) * 25.4mm is taken as an equivalent value of 1inch used in AASHTO standard.

[Fig.1. 14] θ and dv for shear

2.3.2 Vc

2.5c c cr v vV f b d (1.21)

where min(0.4 ' , 3.2 )cr cf f MPa

2.4 The factored shear resistance by transverse reinforcement, Vs

The angle of inclination of transverse reinforcements is considered in the calculation of the factored shear resistance by transverse reinforcement, Vs.

(cot cot )sins v y vs

A f dV

s (1.16)

where α = Enter the angle of transverse reinforcement as shown in Fig1.14 s = Enter the spacing as shown in Fig1.14

CAN/CSA-S6-14 (8.9.3.4)

CAN/CSA-S6-14 (8.9.3.5)


Properties>Section Manager>Reinforcements

[Fig.1. 15] Diagonal Reinforcement

Transverse reinforcement data are entered as follows. - Pitch : spacing of transverse reinforcements - Angle : angle of inclination of transverse reinforcements - Aw : total area of all transverse reinforcements in the web

2.5 Minimum amount of transverse reinforcement

,min 0.15 vv cr

y

b sA f

f (1.17)

Where,

0.4 'cr cf f

Compare the calculated Av,min with the Aw shown in Fig.1.15. If Av,min > Aw, which means the requirement is not satisfied, a message “NG” (not good) is printed in the report.

2.6 Maximum spacing for transverse reinforcement (smax)

The maximum spacing of transverse reinforcement can be checked according to the following steps:

1. Below equation is checked.

0.20 0.5f c cr v v p pV f b d V

(1.24)

Where,

min(0.4 ' , 3.2 )cr cf f MPa

2. If the above equation is applicable, then transverse reinforcements are required and the maximum spacing(smax) needs to be computed.

3. Compare the calculated smax with the entered s. If s > smax, which means the requirement is not satisfied, a message “NG” (not good) is printed in the report.

CAN/CSA-S6-14 (8.9.1.2)

CAN/CSA-S6-14 (8.9.1.3)

Transverse reinforcement

data


The maximum spacing(smax) for transverse reinforcements is computed with the following equation.

max min(0.33 ,300 ) (0.1 ' )v c c v v p fs d mm f b d V V (1.25)

min(0.75 ,600 ) (0.1 ' )v c c v v p fd mm f b d V V

2.7 Longitudinal reinforcement Check

Flexural Tension Side

It is verified if tensile reinforcements and tendons are capable enough to resist applied

tension induced by bending moment and shear forces.

0.5 ( 0.5 )cotflt f f s p

v

MF N V V V

d (1.26)

t p ps ps s s sF A f A f

(1.18)

If Ft ≥ Flt , OK

Flexural Compression Side

It is verified if compressive reinforcements are capable enough to resist applied

compression induced by bending moment and shear forces.

0.5 ( 0.5 )cot flc f f s p

v

MF N V V V

d (1.19)

' 'c s s sF A f (1.20)

If Fc ≥ Flc , OK

CAN/CSA-S6-14 (8.9.3.11)

CAN/CSA-S6-14 (8.9.3.12)


2.8 Interface shear Check midas Civil checks if the shear-friction reinforcement of the girder can resist against the shear force generated between the girder and the slab for the composite section.

PSC > PSC Design > Interface Shear midas Civil calculates Vri_Concrete and compare with Vfi. If Vri_Concrete > Vfi, the concrete can resiste against the shear force. In case that the concrete fail to resiste against the shear-friction force, midas Civil calculates the Shear-friction reinforcement, Vri_reinforcement and compare with Vfi. If Vri_reinforcement > Vfi, the reinforcement can resist against the shear force.

2.9 Check shear resistance

midas Civil checks the shear strength limit state for the Vmax and Vmin cases among the Active: Strength/Stress load combinations, which are defined in the Load Combinations dialog as in Fig.1.10.

2.10 Check Shear resistance results

2.10.1 by Result Tables

Shear resistance results can be checked as shown in the table below

Design>PSC Design>PSC Design Result Tables>Check Shear Strength…

[Fig.1. 16] Result table for shear resistance

Elem : Element number Part : Check location (I-End, J-End) of each element Max./Min. : Maximum shear, minimum shear LCom. Name : Load combination name. Type : Displays the set of member forces corresponding to moving load case

or settlement load case for which the maximum stresses are produced. CHK : Shear strength check for element Vf : Maximum shear force among Strength/Stress load combinations Vc : factored shear resistance by concrete Vs : factored shear resistance by shear reinforcement Vp : Shear force of the effective prestressing force Ft : Tension resistant force by tensile reinforcements and tendon Fc : Compression resistant force by compressive reinforcements


Flt : Tension developed due to bending moment and shear forces Flc : Compression developed due to bending moment and shear forces Vui : Interface Shear force Vri : Shear resistance force of concrete or shear-friction reinforcement Interface Shear CHK : Interface shear check

2.10.2 by Excel Report

Detailed results with basis of calculation can be found in an excel report.


[Fig.1. 17] Excel report table for shear resistance


3. Torsion resistance Check combined shear and torsional resistance.

3.1 Dimension of section for torsion The following is nomenclature used in the torsion check.

Where, Aoh : Area enclosed by the centerline of exterior

closed transverse torsion reinforcement (mm2) Ph : Perimeter of the centerline of the closed tranverse torsion reinforcement (mm) Acp : Total area enclosed by outside Perimeter of the concrete section (mm2) P : The length of the outside perimeter of concrete section (mm)

[Fig.1. 18] Dimension of section for torsion

3.2 Calculate torsional resistance

Torsional resistance can be checked according to the following steps: 1) Calculate torsional cracking moment (Tcr) 2) Determine the need of consideration of the torsional effects by comparing the factored torsional moment with 0.25 Tcr 3) In case where the torsional effects are included, Calculate torsional resistance, then compare it (Tr) with Tf

3.2.1 Torsional cracking moment (Tcr)

0.52

0.8 10.8

cp cecr c cr

c c cr

A fT f

p f (1.30)

Where,

fcr : 0.4 'cf

fce is calculated as follows. When the centroid is in the flange: calculate at the junction of the flange and the web meet.

intps e ps e p

ce jog g

A f A f ef y

A I

(1.31)

Where, yjoint: the distance from the centroid to the junction of the web and flange

CAN/CSA-S6-14 (8.9.1.1)

CAN/CSA-S6-14 (8.4.1.8.1)


When the centroid is in the web: calculate at the centroid of the cross-section.

ps ece

g

A ff

A (1.32)

3.2.2 Determination of inclusion of torsional effects

0.25f crT T : torsional effects ignored

0.25f crT T : torsional effects considered

3.2.3 Torsional resistance

Torsion resistance is calculated as follows.

2 coto s t yr

A A fT

s (1.33)

where Ao : 0.8Aoh At : Awt value within the torsional reinforcements in Section Manager > Reinforcements is applied s : Spacing (pitch) value within the torsional reinforcements in Section Manager > Reinforcements

is applied

(29 7000 ) 0.882500

zex

S(1.34)

where Sze : Refer to Clause 1.3.3.1

/ 0.52( )

f v f p f ps fpox

s s p ps

M d V V N A f

E A E A(1.35)

For details regarding εx, refer to Section 1.3.1.3 in this document

22 0.9

2h f

f f p vo

p TM V V d

A

(1.36)

CAN/CSA-S6-14 (8.9.3.17)

CAN/CSA-S6-14 (8.9.1.2)


Torsional reinforcement data can be checked as in the following figure. Properties>Section Manager>Reinforcements

[Fig.1. 19] Diagonal Reinforcement

- Pitch : spacing of transverse torsional reinforcement - Awt : area of transverse torsional reinforcement

(the area of a single stirrup among the outer closed stirrups) - Alt : area of longitudinal torsional reinforcement

(the area of all reinforcing steels which are close against the outer closed stirrups)

3.3 Check combined torsional and shear

There are two types of sections that require a check of stress due to shear and torsion;

they are a box section and a solid section.

▪ Box section It is considered safe if the following is satisfied.

'0.251.7

f p fc c

v v oh

V V Tf

b d A t

oh

h

Aif t

p (1.37)

'2 0.25

1.7f p u h

c cv v oh

V V T pf

b d A

oh

h

Aif t

p (1.38)

‘t’ in the above equations is the thickness of the box section, which can be entered as red-marked in Fig.1.20. When “Auto” is checked, it is taken as the smallest value among t1, t2, and t3. To consider the maximum combined stress, absolute values are taken in the calculation of the above equations.

▪ Solid section

It is considered safe if the following is satisfied.

2 2'

2 0.251.7

f p u hc c

v v oh

V V T pf

b d A (1.39)

PSC box data can be entered in the Section Data dialog as shown in Fig.1.20.

CAN/CSA-S6-14 (8.9.3.18)

CAN/CSA-S6-14 (8.9.3.19)

Torsional reinforcement


Property > Section Property > Section >PSC

[Fig.1. 20] PSC section data dialog

Cell type sections are defined as a box section in the PSC section data dialog.

3.4 Check torsional moment resistance midas Civil checks the combined shear and torsional strength limit state for the Vmax, Vmin and Tmax cases among the Active: Strength/Stress load combinations, which are defined in Fig.1.10 Load Combinations dialog.

3.5 Check torsional resistance results


Torsional resistance results can be checked as shown in the table below.

Design>PSC Design>PSC Design Result Tables>Check Combined Shear and Torsion Strength…

[Fig.1. 21] Result Table for torsional resistance

Elem : Element number Part : Check location (I-End, J-End) of each element Max./Min.: Maximum torsion/shear, minimum torsion/shear LCom Name: Load combination name. Type: Displays the set of member forces corresponding to moving load case

or settlement load case for which the maximum stresses are produced. CHK: Shear and torsion strength check for element Tf : torsional moment for the corresponding Lcom 0.25Tcr : a value to check where to include the torsional effects Tr : factored torsional resistance Sig_comb : stress due to combination of bending moment and shear forces 0.25phiF : limit value (= 0.25Φsfc’) compared with the combined stress


3.5.2 by Excel Report Detailed torsional resistance results can be checked with the basis of calculation in an excel report.


[Fig.1. 22] Excel report for torsional resistance

Chapter 1. Prestressed Concrete Girder Design : CSA-S6-14

Serviceability Limit State

26Chapter 1. Prestressed Concrete Girder Design

1. Stress for cross section at a construction stage The allowable stress at a construction stage differs depending on the generated stress because the pre-compressed tensile zone is defined differently depending on the generated stress. Therefore, the generated stress at every stage and step is compared to the corresponding allowable stress, and the most unfavorable ratio of the generated stress to the allowable stress is searched and checked against the criteria. That is to say, calculate the ratio of generated stress to allowable stress for every stage and see if the highest ratio meets the criteria.

1.1 Allowable stress of concrete

(1) Allowable compressive stress of concrete

σca = 0.60 f’ci (1.40)

Refer to 2.1.3 for the definition of f’ci.

(2) Allowable tensile stress of concrete Allowable tensile stress in midas Civil is applied as shown in Table 2.1.

[Table1.4] Allowable tensile stress at construction stage Construction Type Case Allowable Stress To be checked

Segment & Joint No Reinforcement бta = 0 Concrete Stress

Reinforcement TS 0.5fcri бta = 0.5fcri Steel Stress TS > 0.5fcri бta = 0.5fcri Concrete Stress

All else No Reinforcement бta = 0.5fcri Concrete Stress

Reinforcement TS > 0.5fcri Steel Stress TS 0.5fcri бta = 0.5fcri Concrete Stress

Tensile Stress : TS

CAN/CSA-S6-14 (8.8.4.6)

CAN/CSA-S6-14 (8.8.4.6)


The following is an explanation of classification of allowable stress 1) Segmental construction Assign the construction type as shown in the figure in red. (select Segmental for the Construction Type)


[Fig.2.1] PSC Design parameter Dialog - Construction Type

Segmental : this applies to post-tensioned girders made of match-cast or cast-in-place concrete segments. Non-Segmental : this applies to those that do not belong to the segmental case.

2) Joint/non-Joint In midas Civil, joints can be defined in the dialog below:

PSC> PSC Segment Assignment

[Fig.2.2] PSC Segment Assignment

As shown in Fig.2.2, if elements 1, 2 and 3 are assigned as one segment, i-end of element 1 and j-end of element 3 become the joints and the rest become the non-joints.


3) Effectiveness of reinforcement If reinforcements exist in a tension region with respect to the centroid, the reinforcements are considered effective. In the case of a negative moment (tension in top and compression in bottom), for example, if a concrete section contains reinforcements only in the bottom with respect to the centroid, the reinforcements are considered ineffective.

As stated in Table 2.1, one of the two cases below needs to be checked.

1) Check the stress in concrete

Tensile stress developed in the considered section is compared with an allowable stress.

It is considered safe when the tensile stress is less than the allowable stress.

2) Check the stress in reinforcement

Compute the concrete triangular stress block on the tension zone, using the extreme fiber tension stress and the extreme fiber compression stress of concrete.

Compute the tension force of concrete(TTFc) by multiplying the compression stress by the area of the concrete triangular stress block.

Compute the tension force of reinforcement(TTFs) by multiplying the area of reinforcement and tendon, which are included in the triangular stress block, by the specific stress(240Mpa).

If the tension force of reinforcement is larger than that of concrete, it is concluded that the tensile stress of reinforcement satisfies the regulation.

1.2 f’ci

The Code defines f’ci as:

f’ci is compressive strength of concrete at transfer

midas Civi computes the compressive strength of concrete (f’ci) during construction stages

according to the construction days defined in Fig.2.4 and the function of concrete strength

in Fig.2.5.

The days for each construction stage can be defined in Fig2.3.

Load> Construction Stage> Compose construction Stage…

[Fig.2.3] Compose construction Stage dialog

CAN/CSA-S6-14 (8.3)

Additional Steps

Stage

Activation


Stage>Duration: Enter the duration of the construction stage. It is the basic unit where elements become active or inactive, boundary conditions become active or inactive and loads are applied or removed

Additional Step>age: Define the specific days for the analysis steps within the construction stage. Within a construction stage where the model and boundary conditions remain unchanged, changes in load application timing or additional loads may be incorporated through additional steps. Activation>Group List>age: Select relevant element groups, which are applicable to the current stage, in the Group List and activate the selected groups by moving them to Activation Group List. Specify the Age of the selected element groups. The age entered here will be used to reflect the effects of creep and shrinkage that took place prior to the current construction stage. The age of the element, which is casted at the start of the current construction stage, is zero. The age typically represents the time span from the time of concrete casting to the time of removal of formwork during which the concrete is considered as a structural element, that is to say the curing period of concrete. Based on the inputs shown in Fig.2.4, midas Civil takes the following days for the construction stage analysis:

The duration of the construction stage CS1 is 30 days, the duration of the additional step within CS1 is 15 days, and the Activation age is 5 days.

The actual duration of CS1 is 35 days (Stage Duration + Activation age).

The compressive strength of concrete is computed at 5 days, 20 days and 35 days for CS1.

If the next stage CS2 is defined with the duration of 20 days, CS2 starts at 35 days and ends at 55 days.

The development of concrete compressive strength with days is defined in the dialog below

Properties> Time Dependent Materials>Comp. Strength…

[Fig.2.4] Time Dependent Materials dialog

Development of Strength: Define a function to compute the compressive strength of concrete at construction stages. It can be defined by selecting ACI,CEF-FIP or the Structural Concrete Design Code, or by directly defining a value for the strength.


Variation of the elastic modulus of concrete with its age needs to be considered in the calculation of the compressive strength. For CS1 the compressive strengths of concrete are computed at 5 days, 20 days and 35 days, and they are compared to the corresponding stresses.

1.3 Check stress for cross section at a construction stage

cac , ( )t ta or TTFs TTFc (1.41)

1.4 Check stress results for cross section at a construction stage


Results can be checked as shown in the table below.

Design>PSC Design>PSC Design Result Tables>Check stress for cross section at a construction stage.

[Fig.2.5] Result table for stress at a construction stage Elem : Element number Part : Check location (I-End, J-End) of each element

Comp./Tens.: Compression or Tension Stress Stage: Construction stage at which stresses are maximum at the corresponding section. CHK : Combined stress check for construction stages FT : Combined Stress due to My and axial force at Top fiber FB : Combined Stress due to My and axial force at Bottom fiber FTL : Combined Stress due to My, Mz and axial force at Top Left fiber FBL : Combined Stress due to My, Mz and axial force at Bottom Left fiber FTR : Combined Stress due to My, Mz and axial force at Top Right fiber FBR : Combined Stress due to My, Mz and axial force at Bottom Right fiber FMAX : Maximum combined stress out of the above six components. ALW : Allowable stress of cross section at construction stage. TTFc : Tensile resistance of concrete corresponding to the triangular block TTFs : Tensile resistance of tensile reinforcement


1.4.2 by Excel Report Verification results can be checked in an excel report.

Design>PSC Design>PSC Design Calculation>Check stress for cross section at a construcion stage…

[Fig.2.6] Excel Report for allowable stresses in concrete construction stage

2. Stress for cross section at service loads The element stress at service loads after losses shall meet the following conditions: The maximum compressive stress at service loads after losses ≤ allowable compressive stress of concrete: σc ≤ σca The maximum tensile stress at service loads after losses ≤ allowable tensile stress of concrete: σt

≤ σta

Load combinations that are defined as “Serviceability” in the Load Combination dialog (As shown in Fig.2.7) are verified as per their serviceability limit states.

Results>Load combinations>Concrete Design tab

[Fig.2.7] Load Combinations dialog

Active: Serviceability


2.1 Allowable stress of concrete (1) Allowable compressive stress of concrete

σca = 0.60 f’c (1.36)

(2) Allowable tensile stress of concrete midas Civil calculates the allowable tensile stress of concrete using the design code, as summarized in the table below.

[Table.1.5] Allowable stress of concrete at service load Construction

Type Case Allowable Stress To be checked

Segment & Joint No Reinforcement 0 Concrete Stress

Reinforcement fcr Concrete Stress

All else - fcr Concrete Stress

Refer to Section 2.1.1 for the classification of allowable stress.

2.2 Check stress for cross section at a service loads

cac , tat (1.42)

2.3 Check stress results for cross section at service loads

2.3.1 by Result Tables Results can be checked as shown in the table below.

Design>PSC Design>PSC Design Result Tables>Check stress for cross section at service loads…

[Fig.2.8] Result table for stress at a service loads

Elem: Element number Part: Check location (I-End, J-End) of each element

Comp./Tens.: Compression or Tension Stress LCom Name: Load Combination Name Type: Displays the set of member forces corresponding to moving load case

or settlement load case for which the maximum stresses are produced

CAN/CSA-S6-14 (8.8.4.6)

CAN/CSA-S6-14 (8.8.4.6)


CHK: Combined stress check for Service loads FT: Combined Stress due to My and axial force at Top fiber FB: Combined Stress due to My and axial force at Bottom fiber FTL: Combined Stress due to My, Mz and axial force at Top Left fiber FBL: Combined Stress due to My, Mz and axial force at Bottom Left fiber FTR: Combined Stress due to My, Mz and axial force at Top Right fiber FBR: Combined Stress due to My, Mz and axial force at Bottom Right fiber FMAX: Maximum combined stress out of the above six components. ALW: Allowable stress in concrete at service limit state.

2.3.2 by Excel Report Verification results can be checked in an excel report as shown in the table below.


[Fig.2.9] Excel Report for stress at service loads


3. Tensile stress for Prestressing tendons Compare the stress in tendon with the allowable stress for each tendon group. After immediate losses at anchorages, the maximum stress in tendon ≤ allowable stress. Elsewhere away from anchorages, the maximum stress in tendon ≤ allowable stress. After all losses, the maximum stress in tendon ≥ 0.45fpu

3.1 Allowable stress of tendon The Code presents the following stress limits for tendons depending on the tendon types:

[Fig.2.10] Allowable stress of tendon

Tendon Type can be specified in Fig1.8 Design parameter dialog. Pre/Post tensioning can be specified in Fig1.7 Tendon Property dialog. Midas Civil checks the following: Stress in tendon reflecting the initial losses at anchorages (FDL1) Stress in tendon immediately after anchor set elsewhere (FDL2) Stress in tendon at service limit state after all losses (FLL1) Allowable stresses corresponding to the described stresses above are set based on Fig.2.11 as follows.

(1) Allowable stress in tendon immediately after anchor set at anchorages (AFDL1) It is the maximum allowable stress in tendon at anchorages after immediate losses. The values for “At transfer > Pretensioning and Post-tensioning > At anchorages and couplers” in Fig.2.11. It is considered safe when FDL1 ≤ AFDL1.

(2) Allowable Stress in Tendon immediately after anchor set elsewhere (AFDL2) This is the maximum allowable stress immediately after anchor set elsewhere. The values for “At transfer > Post-tensioning > Elsewhere” in Fig.2.11. It is considered safe when FDL2 ≤ AFDL2.

(3) Allowable stress in tendon at service limit state after losses (AFLL1) This is the maximum allowable stress at service limit state after all losses. It is stated in the code that it should be at least 0.45fpu. It is considered safe when FLL1 ≥ AFLL1.

CAN/CSA-S6-14 (8.7.1)

CAN/CSA-S6-14 (8.7.1)


3.2 Check the stress in Prestressing tendons

3.2.1 Tendon Time-dependent Loss Graph Result>Bridge>Tendon Loss Graph

[Fig.2.11] Tendon Time-dependent Loss Graph

Stress in tendon can be checked with the Tendon Time-dependent Loss Graph.


Verification results can be checked in an excel format as shown in the table below. Design>PSC Design>PSC Design Result Tables>Check tensile stress for Prestressing

tendons

[Fig.2.12] Result table for tensile stress for prestressing tendons

Tendon: Tendon profile name. For Post-tensioned: FDL1: Stress in tendon at anchorages.

The maximum stress in tendon at anchorages after immediate losses AFDL1: Allowable stress in tendon immediately after anchor set at anchorages. The allowable stress for FDL1 FDL2: Maximum stress in tendon along the length of the member away from anchorages, immediately

after anchor set. The maximum stress in tendon elsewhere along length of member away from anchorages

immediately after anchor set AFDL2: Allowable stress in tendon immediately after anchor set elsewhere.

The allowable stress for FDL2 FLL1: Maximum stress in tendon after all losses at the last stage.

The maximum stress in tendon at service limit state after all losses AFLL1: Allowable stress in tendon at service limit state after losses.

The allowable stress for FLL1(=0.45fpu) Elem : Element number for the Tendon

Part : Element location for the Tendon (I, 1/4, 1/2, 3/4, J) For Pre-tensioned: FDL1: Stress in tendon. FDL2: - FLL1: Maximum stress in tendon after all losses at the last stage. AFDL1: Allowable stress in tendon prior to transfer. AFDL2: - AFLL1: Allowable stress in tendon at service limit state after losses.

Elem : Element number for the Tendon Part : Element location for the Tendon (I, 1/4, 1/2, 3/4, J)


3.2.3 by Excel Report Verification results can be checked in an Excel report as shown in the table below.

Design>PSC Design>PSC Design Calculation> Check tensile stress for Prestressing

tendons…

[Fig.2.13] Excel Report for tensile stress for prestressing tendons


4. Principal stress at a construction stageFind the maximum principal tensile stress among the stress check points 1~10 of the cross-section at a construction stage and compare it to the allowable stress. In other words, maximum principal tensile stress ≤ allowable stress.

4.1 Allowable tensile stress

'0.110ta cif

(1.43)

Where f’ci is identical to that in Section 2.1.2.

4.2 Maximum principal stress The maximum principal tensile stress for each point at a constructions stage is computed as follows:

22 421

ptszxzxps

(1.44)

where

σx : Sum of axial stresses in ECS x-direction

σz : Sum of axial stresses in ECS z-direction

τs : Shear stress due to shear.

τt : Shear stress due to torsion.

τp : Shear stress due to shear reinforcement.

4.2.1 Beam stresses of PSC

The stress components to compute the maximum principal tensile stress can be checked in a result table as shown below:

Results>Result Tables>Beam>Stress(PSC)…

[Fig.2.14] Beam stresses of PSC

Sig-xx (Axial): Axial stress due to the axial force (Fx) in the ECS x-direction

Sig-xx (Moment-y): Stress due to My (moment about the ECS y-axis) in ECS x-direction

Sig-xx (Moment-z): Stress due to Mz (moment about the ECS z-axis) in ECS x-direction

Sig-xx (Bar): Axial stress due to shear steel bars in the ECS x-direction

Sig-xx (Summation): Sum of the axial stress in the ECS x-direction and the axial stress

due to shear steel bars in the ECS x-direction

Sig-zz: Stress in the ECS z-direction

Sig-xz (shear): Sum of shear stresses due to shear force and shear steel bars

Sig-xz (torsion): Shear stress due to torsion

Sig-xz (bar): Shear stress due to shear steel bars

AASHTO LRFD12 (5.9.4.1.2)


Sig-Is (shear): Diagonal stress due to shear force

Sig-Is (shear+torsion): Diagonal stress due to torsion and shear force

Sig-Ps1: Maximum principal stress

Sig-Ps2: Minimum principal stress

4.3 Check principal stress at a construction stage

ps ta (1.45)

4.4 Check the principal stress results at a construction stage


Design>PSC Design>PSC Design Result Tables>Principal stress at a construction stage …

[Fig.2.16] Result table for principal stress at a construction stage

Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange. Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web. When the user select Result Table, in case of composite section, all Principal Stress will be deactivated, and if the composite and noncomposite sections are modelled together, all principal stress will be activated. In case of noncomposite section, CHK and allowable stress(Sig_AP) will not be presented.

4.4.2 by Excel Report Verification results can be checked in an Excel report as shown in the figure below.


[Fig.2.17] Excel Report for principal stress at a construction stage


5. Principal stress at service loads(Excluding torsional shear stress)

Find the maximum principal tensile stress among the stress check points 1~10 of the cross-section at service loads and compare it to the allowable stress. In other words, maximum principal tensile stress ≤ allowable stress. Note that in this calculation, the shear effects due to torsion are excluded.

5.1 Allowable tensile stress The code does not present allowable stress values regarding the maximum principal tensile stress during construction stage. The program refers to AASHTO-LRFD12 for this particular case.

'0.110ta cf

(1.46)

5.2 Maximum principal stress The maximum principal tensile stress for each point at a construction stage is computed as follows:

22 4

21

ptszxzxps

(1.47)

where,






5.2.1 Beam stresses of PSC The stress components to compute the maximum principal tensile stress can be checked from a result table shown below: Refer to 2.4.2.1 Beam stresses of PSC.

5.3 Check principal stress at service loads

ps ta (1.48)

5.4 Check the principal stress results at service loads


Design>PSC Design>PSC Design Result Tables> Result table for principal stress at service

loads(excluding torsional shear stress)…

[Fig.2.18] Result table for principal stress at service loads (excluding torsional shear stress)


Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange. Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web.


Verification results can be checked in an excel report as shown in the table below.


[Fig.2.19] Excel Report for principal stress at service loads (excluding torsional shear stress)

6. Principal stress at service loads Find the maximum principal tensile stress among the stress check points 1~10 of the cross-section at service loads and compare it to the allowable stress. Here both shear and torsion will be reflected in the stress calculation. In other words, maximum principal tensile stress ≤ allowable stress.

6.1 Allowable tensile stress

'0.110ta cf (1.49)

6.2 Maximum principal stress The maximum principal tensile stress for each point at a construction stage is computed as follows:

22 4

21

ptszxzxps

(1.50)

where,







6.2.1 Beam stresses of PSC The stress components to compute the maximum principal tensile stress can be checked from a result table shown below: Refer to 2.4.2.1 Beam stresses of PSC.

6.3 Check principal stress at service loads

ps ta (1.51)

6.4 Check the principal stress results at service loads


Design>PSC Design>PSC Design Result Tables>Principal stress at service loads…

[Fig.2.20] Result table for principal stress at service loads

Elem: Element number. Part: Check location (I-End, J-End) of each element. Comp./Tens.: Compression or Tension Stress. Stage: Construction stage. CHK: Principal stress check for construction stages. Sig_P1: Principal Stress at the left top of top flange. Sig_P2: Principal Stress at the right top of top flange. Sig_P3: Principal Stress at the right bottom of bottom flange. Sig_P4: Principal Stress at the left bottom of bottom flange. Sig_P5: Principal Stress at the top of left web.(at Z1 Level) Sig_P6: Principal Stress at the top of right web.(at Z1 Level) Sig_P7: Principal Stress at the neutral axis in left web.(at Z2 Level) Sig_P8: Principal Stress at the neutral axis in right web.(at Z2 Level) Sig_P9: Principal Stress at the bottom of left web.(at Z3 Level) Sig_P10: Principal Stress at the bottom of right web.(at Z3 Level) Sig_MAX: The maximum Principal stress among P1-P10. Sig_AP: Allowable principal stress at neutral axis in the web.


Verification results can be checked in an excel report as shown in the table below.


[Fig.2.21] Excel Report for principal stress at service loads


7. Check crack Maximum crack width is compared with a calculated (expected) crack width for the crack limit state check. In other words, calculated crack width ≤ maximum crack width

7.1 Calculate crack widths

(1) Determine srm

50 0.25 brm c

c

ds k

(1.52)

where kc : 0.5 for bending db : Diameter of outer reinforcement(tendon) (bottom row)

sc

ct

AA for bending

As : the area of reinforcement contained within Act Act : the effective tension area of concrete cross-section in hc,ef.

, min 2.5 ,3c ef

h xh h d

(1.53)

[Fig.2.22] effective tension area of concrete cross-section

(2) Determine εsm

2

1s wsm

s s

f fE f

(1.54)

where fs : stress in reinforcement at the serviceability limit state on the basis of crack section

midas Civil uses the stress, at service loads, of reinforcement(or tendon) located at a greatest distance from the extreme compression fiber.

fw : stress in reinforcement under the conditions causing initial cracking on the basis of crack section

Stress of reinforcement at initial crack is calculated with the following steps. Strain of concrete is first calulcated based on the crack strength(fcr).

εc = Ec/fcr (1.55) εc is the strain of concrete at crack strengthas well as the strain of concrete at the extreme tension fiber.

CAN/CSA-S6-14 (8.12.3.2)


1) Using εc, the strain (εs) of the outer reinforcement is computed.

2) Stress of reinforcement is calculated based on its strain(εs).

fw = Es εs (1.56) 3) Determine w

b c rm smw k s (1.57)

Where

Kb : 1.2 for epoxy-coated reinforcing steel

1.0 for all other component

Coating condition of reinforcement can be entered in the PSC Design parameter dialog.


[Fig.2.23] PSC Design parameter Dialog – Reinforcing Rebar

βc : 1.7 when cracking is caused by load

7.2 Maximum crack width, wmax

Wmax is determined depending on the type of exposure as shown in the table below.

[Fig.1.45] Maximum crack width, wmax

CAN/CSA-S6-14 (8.12.3.1)


Environmental Exposure (type of exposure) can be entered in the Design parameter dialog.


[Fig.2.24] PSC Design parameter Dialog – Environmental Exposure

Wmax is determined depending on the type of exposure as shown in the table below.

[Table1.6 ]Coefficient k2

Type of Exposure wmax

(a) De-icing Chemical 0.15

(b) No deicing chemical 0.2

(c) Exposed to earth or fresh water 0.2 (d) Exposed to swamps maash, salt

water, or aggressive back fill

0.15

(e) Cast against and Permanently 0.2

(f) various 0.2

7.3 Check crack width results at service loads


Design>PSC Design>PSC Design Result Tables>Check crack width at service loads…

[Fig.2.25]Result table for crack width at service loads

Elem: Element number Part: Check location (I-End, J-End) of each element Top/Bottom: At top of element, at bottom of element


LCom. Name: Load combination name. Type: produce maximum and minimum member force components for the load

combinations including moving load cases or settlement load cases. Check:OK/NG FT : Stress at the top (+ compression, - tension) FB : Stress at the bottom (+ compression, - tension) Wk : calculated crack width Wmax : Maximum crack width

7.3.2 by Excel Report Verification results can be checked in an excel report as shown in the table below.


[Fig.2.26]Excel Report for crack width at service loads

CAN/CSA S6 -14

Chapter 2.

Steel CompositeI - Girder Design

Steel Composite I-Girder DesignChapter 2.

Steel Composite I-Girder Bridge

Check Constructability

Check Shear Connector

Chapter 2. Steel Composite I-Girder Design : CAN/CSA S6-14

Introduction

Chapter2. Steel Composite I-Girder Design – CAN/CSA S6-14 49

1. CAN/CSA S6-14 Steel Composite I-Girder 1.1 Check List of CAN/CSA S6-14 Steel Composite I-Girder For CAN/CSA S6-14 Steel Composite Design, Limit State Design is applied. The criteria that Steel Composite I-Girder must follow for Limit State Design is as follows.

(1) Ultimate Limit State Review on bending strength, lateral torsional buckling and shear strength (2) Serviceability Limit State Review on permanent deformation (3) Constructibility Review on bending and shear occurring from load combinations during construction stages (4) Fatigue Limit State Review on fatigue in steel and concrete materials in Steel Composite girder

1.2 Classification of Steel Composite Steel Composite section can be categorized by the following classification groups.

(1) Section Shape Type There are three main section shape types in midas Civil; I, Box and Tub shapes. In the case ofbox and tub sections, there are two more cases, single or multiple box section.

I Box Tub

Figure 1.1 Section Shape Type (2) Moment Type : Positive / Negative For continuous beams, negative moments may occur around interior supports. Design codemay apply different formulas for these cases. (3) Bridge Type : Straight / Curved Based on the horizontal alignment of a bridge, it can be classified as either straight or curved. The program recognizes curved bridges based on the input of the girder radius for each element.


(4) Classification of Cross-sections: Class 1 / Class 2 / Class 3 / Class 4 Structural sections shall be designated as Class 1, 2, 3, or 4 depending on the width-to-thickness ratio of the elements that make up the cross-section and on the conditions ofloading.

Table 1.1 Steel Section Classification

Type Description

Class 1 A Class 1 section is one that will attain the plastic moment capacity, adjusted for the presence of axial force if necessary, and permit subsequent redistribution of bending moment.

Class 2 A Class 2 section is one that will attain the plastic moment capacity, adjusted for the presence of axial force if necessary, but not necessarily permit subsequent moment redistribution.

Class 3 A Class 3 section is one that will attain the yield moment capacity, adjusted for the presence of axial force if necessary.

Class 4 A Class 4 section is one in which the slenderness of the elements making up the cross-section exceeds the limits of Class 3.

1.3 Stiffeners of Steel Composite The program considers transverse and longitudinal stiffeners.

Table 1.2 Types of Stiffeners

Type Description

Transverse Stiffeners

Transverse stiffeners are usually provided to increase shear resistance by tension field action. These work as anchors for the tension so that post buckling shear resistance can be developed. It should be noted that elastic web shear buckling cannot be prevented by transverse stiffeners.

Longitudinal Stiffeners

Longitudinal stiffeners may be provided to increase flexural resistance by preventing local buckling. These work as restraining boundaries for compression elements so that inelastic flexural buckling stress can be developed in a web. It consists of either a plate welded longitudinally to one side of the web, or a bolted angle.

Figure 1.2 Longitudinal Stiffener and Transverse Stiffener

CAN/CSA S6-14 10.9.2.1

51Chapter 2. Steel Composite I-Girder Design - CAN/CSA S6-14

2. Considerations of Steel Composite Design 2.1 Construction Stage for steel composite During the construction of a steel composite bridge, the steel girder is constructed before theconstruction of the concrete deck of the upper part of the structure. The steel composite sectionis divided into three major steps.

Table 1.3 Construction Stage for Steel Composite Section

Construction stage for steel composite section

Description

Only Steel Girder (non-composite)

Only the steel girder has been constructed.

Steel girder and concrete deck

as load (non-composite)

Although the concrete deck has been constructed, it has not hardened yet. Therefore, the weight of the wet concrete is applied to the steel girder as a load condition.


as member (composite)

After concrete is hardened, the strength and stiffness are formed. Hereafter, the steel girder and concrete deck work as a complete composite section.

2.2 Time Dependent Material ▪ Steel composite section is composed of steel and concrete. Concrete is a time dependentmaterial and transforms due to creep and shrinkage. Also, the restraints imposed by the shearconnectors cause additional stresses within the composite section. Therefore, time dependentcharacteristics (creep and shrinkage) must be taken into consideration. ▪ Modular ratio is the ratio of modulus of elasticity of steel to that of concrete. The short-termmodular ratio "n" is used for transient loads in the program. Long-term modular ratio "3n" is usedfor permanent loads acting after composite action.

3. Calculation of Plastic Moment and Yield Moment 3.1 Section Classification

The steel section is classified in accordance with Clause 10.9.2. The classification is carriedout separately for positive and negative bending for both composite and non-compositesections. The classification of a cross-section depends on the width to thickness ratio of theparts subject to compression. A cross-section is classified according to the highest (leastfavorable) class of its compression parts. For calculating the limiting width-to-thickness ratios of the web of monosymmetric steelsections, h is replaced by 2dc. However, for the classification of composite section, the h is

CAN/CSA S6-14 10.9.2.1 CAN/CSA S6-14 10.10.2.1


used for the web. The resistance of the top flange of the composite section under positive moment is assumedas not being limited by its local buckling resistance since it is restrained by effective attachment to a concrete flange by shear connectors. The top flange is always classified asClass 1.

3.2 Plastic Moment (Mp) of Composite Section in Positive Flexure

If the positive moment is applied on a class 1 or class 2 section, MP is calculated as shown inTable 1.4.

Figure 1.3 Case of calculation of Mp in positive moment

Table 1.4 Calculation of and Mp for section in Positive Flexure

Case PNA Condition and pM

In Web wt PP

rtrbsc PPPP

]1[2 w

rbrtsct

PPPPPPD

Y

])([2

22YtY

DP

M w

][ ttwwrbrbrtrtss dPdPdPdPdP

In Top flange

cwt PPP

rtrbs PPP

])([2

22YtY

tP

Mc

c


Concrete Deck, Below Prb

cwt PPP

rtrbss

rb PPPtc

s

s

tPY

M2

2

][ ttwwccrbrbrtrt dPdPdPdPdP

Concrete Deck, at Prb

rbcwt PPPP

rtss

rb PPtc

rbCY

s

s

tPY

M2

2

][ ttwwccrtrt dPdPdPdP


Concrete Deck, Above Prb Below Prt

rbcwt PPPP

rtss

rt PPtc

s

rbrttwcs P

PPPPPtY )(

s

s

tPY

M2

2


Concrete Deck, at Prt

rtrbcwt PPPPP

ss

rt Ptc

rtCY

s

s

tPY

M2

2

][ ttwwccrbrb dPdPdPdP

Concrete Deck, Above Prt

rtrbcwt PPPPP

ss

rt Ptc

s

rttwcrbs P

PPPPPtY )(

s

s

tPY

M2

2


Where, : Distance from the plastic neutral axis to the centerline of the top layer of longitudinal concrete

deck. : Distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal

concrete deck. : Distance from the plastic neutral axis to the midthickness of the tension flange. : Distance from the plastic neutral axis to middepth of the web. : Distance from the plastic neutral axis to midthickness of the compression flange. : Distance from the plastic neutral axis to midthickness of the concrete deck.

(by reinforcement) (by reinforcement)

(by steel girder)

(by steel girder) (by steel girder)

(by concrete slab)

3.3 Plastic Moment (Mp) of Composite Section in Negative Flexure Under negative moment, Mp is calculated by either of the two following methods. Please refer to Table 1.5 for the equations.

Figure 1.4 Case of calculation of Mp in Negative Moment


Table 1.5 Calculation of and Mp for section in Negative Flexure


In Web rtrbtwc PPPPP

In Top flange rtrbtwc PPPPP

Where,



(by steel girder)


Modeling and Design Variables

Chapter2. Steel Composite I-Girder Design – CAN/CSA S6-14 55

1. Modeling Design Variables In this chapter, the design variable values, the meaning behind the design requirements, and the design process for Steel Composite Design in midas Civil are explained.

1.1. Composite Section Data The steel composite section is mainly composed of steel girder and concrete slab. Stiffeners can be added to steel girder section while longitudinal reinforcement can be added to reinforce concrete slab. In this section, the input methods for these sections and the meaning and application of design variables are explained.

1.1.1 Composite Section (1) Composite Section Data

Properties > Section > Section Properties> Add > Composite Tab

Figure 1.5 Section Data Dialog Box


1) The value of Bc for the slab is used as the effective width of the concrete deck. 2) Multiple Modulus of Elasticity Option To design the steel composite section, the modulus of elasticity for short-term and long-term effect in creep and shrinkage can be input. The modulus of elasticity input here is applied for construction stage analysis of Steel Composite section as shown in Figure 1.6.

Figure 1.6 Elastic Modulus ratio for Construction Stage


(2) Section Stiffener

Properties > Section > Section Properties> Add > Composite Tab > Stiffeners Button...

Figure 1.7 Section Stiffener Dialog Box

1.1.2 Longitudinal Reinforcement

Design > Composite Design > Longitudinal

Reinforcement ...

Figure 1.8 Longitudinal Reinforcement Dialog Box

(2) Section Stiffener (Longitudinal)

1) Types of longitudinal stiffeners that are useable are Flat, Tee, and U-Rib. 2) For I sections, stiffeners can be added on either side of the web. For Box/Tub sections, upper and lower flanges can be installed as well as the web panel. 3) When the check box under c column is checked on, the stiffness value of the stiffener is considered in analysis. Otherwise, the value is not considered for analysis. Regardless of whether or not the check box is checked on or off, longitudinal stiffeners are considered in design. It is also required for classifying the interior panels in shear check as stiffened/unstiffened.


In a steel composite section, the longitudinal reinforcements are arranged within the concrete deck. The moment resistance is calculated as shown in Table 1.6.

Table 1.6 Applicability of concrete and reinforcement for the calculation of moment resistance

Case Positive Bending

Negative Bending

Figure

Concrete Slab Applied None

Rebar Applied Applied


1.1.3 Transverse Stiffener (1) Transverse Stiffener

Design > Composite Design > Transverse Stiffener ...

Figure 1.9 Transverse Stiffener Dialog Box

Figure 1.10 Stiffener Type Dialog Box

1.1.3 Transverse Stiffener

Figure 1.9 shows the window in which users can arrange transverse stiffeners in steel composite section. When the transverse stiffeners are installed, the existence and spacing between stiffeners determine whether the web is stiffened or unstiffened under ultimate limit state.

Figure 1.11 Transverse Stiffener Parameters

Stiffener Type 1) One / Two Stiffener Option Button Choose between one or two stiffeners. Transverse stiffeners can be provided on one or both sides of the web.

2) Pitch Pitch refers to transverse stiffener spacing. At the ultimate limit state, this can be used to distinguish between stiffened and unstiffened webs or calculate shear strength of the web.


1.2. Design Material Data For the design of steel composite section, construction stage and time dependent material properties of concrete can be applied. In this section, the input method for the time dependent properties of concrete and material data for steel composite section is explained.

Contents Explanation

1.2.1 Time Dependent Material (1) Creep/Shrinkage

Properties > Time Dependent Material > Creep/Shrinkage ...

Figure 1.12 Add/Modify Time Dependent Material Dialog Box

(Creep/Shrinkage)

(2) Comp. Strength

Properties > Time Dependent Material > Comp. Strength ...


(Compression Strength)

1.2.1 Time Dependent Material (1) Creep/Shrinkage The time dependent properties of concrete, such as creep and shrinkage, are defined. During construction stage analysis of bridges, these properties are utilized for concrete material.

(2) Comp. Strength

In order to reflect the change in the modulus of elasticity of concrete, the change in compressive strength or modulus of elasticity is defined. Aging effects may vary for each construction stage since concrete is poured at different locations.



1.2.2 Modify Composite Material (1) Modify Composite Material

Design > Composite Design > Design Material ...

Figure 1.14 Modify Composite Material Dialog Box

1.2.2 Modify Composite Material The materials utilized for steel composite sections are provided in the SRC material properties. The materials should be defined as SRC Type.

(1) Modify Composite Material Figure 1.14 shows the dialog box where users can type in material characteristics for the steel composite section design. The material property values entered will have a priority over the values entered in the Material Data dialog box.

1) Steel Material Selection Define modulus of elasticity, yield strength and tensile strength of steel for design purpose. In the current version, different yield strengths for different thicknesses of steel are not supported.

2) Concrete Material Selection Define compressive strength of concrete slab for design purpose.

3) Reinforcement Selection Define yield strength of reinforcement in the slab.


1.3. Design Parameters for Composite Section


1.3.1 Design Parameter

Design > Composite Design > Design Parameters ...

Figure 1.15 Composite Steel Girder Design Parameter Dialog Box

1.3.2 Unbraced Length

Design > Composite Design > Unbraced Length ...

Figure 1.16 Unbraced Length Dialog Box


(1) Strength Resistance Factor Strength Resistance Factor is defined.

By clicking , the resistance factors are automatically set to the default values defined in CAN/CSA S6-14. The values can also be modified or entered manually.

(2) Girder Type for Box/Tub Section If Single Box Section is selected, the following clauses are applied for the box/ tub girder design. 10.12.8.4 Moment resistances 10.12.8.5 Combined shear and torsion

(3) Options For Construction Stage

If this option is checked, ULS check for steel section only during construction is performed.

(4) Design Parameters Design and result outputs are generated for the limit states checked in the Design Parameters.

1.3.2 Unbraced Length Unbraced length for steel composite section is considered. The value input here has higher priority than the value calculated from Span Group.

(1) Lb Laterally Unbraced Length is used to calculate lateral torsional buckling resistance in compression flange of I Girder or top flange of Tub Girder. Laterally Unbraced Length is automatically determined using ‘Span Information’ and by assigning member type of cross-frames as ‘Brace’ using the Common Parameter > Modify Member Type function. The user can define/modify the laterally unbraced lengths.



1.3.3 Shear Connectors

Design > Composite Design > Shear Connectors ...

Figure 1.17 Shear Connector Dialog Box

1.3.3 Shear Connectors In this program, studs are used for shear connectors. The parameters used for calculation are shown below.

(1) Category Category for fatigue check, it is fixed as D. (2) Fu Minimum tensile strength of the stud steel (3) Shear Connector Parameters

Figure 1.18 Shear Connector Parameters

(4) Length Between Maximum Moment and Zero Moment The Length between Maximum Moment and Zero Moment needs to be inputted by users to verify pitch as per ultimate limit state.



1.3.4 Fatigue Parameter

Design > Composite Design > Fatigue Parameter ...

Figure 1.19 Fatigue Parameters Dialog Box

1.3.5 Span Information

Structure > Wizard > Composite Bridge > Span Information ...

Figure 1.20 Span Information Dialog Box

1.3.4 Fatigue Parameter (1) Weight of Truck(W)

Load level in CL-W, kN (2) Design Life(y)

Design life, years (3) Number of Stress Cycles(Nd) Number of design stress cycles experienced for each passage of the design truck (4) Reduction Factor(ρ) (5) Average Daily Truck Traffic

1.3.5 Span Information The elements of composite sections are defined as one Span Group. The Span Group will serve the following functions.

- Calculation of Unbraced Length When assigning a span group, support properties are considered for calculating the unbraced length. The unbraced length can also be manually inputted once the corresponding support conditions under the support column are selected. Using the span parameters inputted, the unbraced length can be calculated automatically. However, if the unbraced length is inputted in Section 1.3.2, this value will be applied as the unbraced length first.



1.3.6 Curved Bridge Information

Design > Composite Design > Curved Bridge Info ...

Figure 1.21 Curved Bridge Information Dialog Box

1.3.7 Design Force/Moment

Design > Composite Design > Design Tables > Design Force/Moment...

Figure 1.22 Design Force/Moment Dialog Box

1.3.6 Curved Bridge Information Once the girder radius value of the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges.

(1) Radius is used to determine the factored bending moment in the flange due to torsional warping. (2) In the current version, the curve type of convex or concave is not used.

1.3.7 Design Force/Moment This feature displays design member forces (strong axis moment, My), weak-axis moment (Mz) and shear stress (VU) for the local axis of elements under selected load combination of steel composite section.


1.4 Load Combination for steel composite section 1.4.1 Application of load combination in midas Civil for CAN/CSA S6-14

(1) Application of load combinations and factors in midas Civil for CAN/CSA S6-14 The load combinations used for the review of each limit state are shown below.

Figure 1.23 Load factors and load combinations

Using the Auto Generation feature of the program, the load combinations regulated by the design code can be automatically generated. Load factors are considered for each load combinations in this program.

Figure 1.24 Live load factors ultimate limit states

Figure 1.25 Permanent loads — Maximum and minimum values of load factors for ULS


(1) Auto Generation of Load Combinations

Result > Combination > Load Combination > Composite Steel Girder Design > Auto Generation ...

Figure 1.26 Automatic Generation of Load Combinations

Dialog Box

(1) Auto Generation of Load Combinations This feature automatically generates load combinations under provision of CAN/CSA S6-14.

1) Design Code When load combinations are generated, they strictly follow the design code selected by the user. 2) Load Factors for Permanent Loads (αD, αE, αP) The user can generate load combinations using maximum value or minimum value or both. When associated load type does not exist, these factors are not activated.


1.4.2 Load combination type for steel composite design Load combination type must be assigned before performing design. When load combinations are generated by auto-generation, the load combination type is automatically assigned, but when load combinations are defined manually or modified, the load combination type should be assigned by the user. Load combinations used in the steel composite section design are categorized under Load Combination Type.


(1) Load Combination Type

Design > Composite Design > Load Combination Type...

Figure 1.27 Load Combination Type Dialog Box

(1) Load Combination Type 1) Ultimate Limit State Choose load combinations for use under review of ultimate limit state. 2) Service Limit State Choose load combinations for review of serviceability limit state. 3) Fatigue Limit State Choose load combinations for review in fatigue limit state.

1.5 Modeling Steel Composite Sections for Construction Stage Analysis In this section, methods of construction stage modeling, implementation of time-dependent material properties of concrete in steel composite section and 3 types of design member forces applied to steel composite section design are explained. Construction stages of steel composite section can be implemented differently for case 1 to 3 as in Table 1.7.

Table 1.7 Modeling Construction Stage Cases for Steel Composite Design

Case Construction Stage Time Dependent Material(Creep / Shrinkage)

Case 1 Defined

Defined

Case 2 Not Defined (Apply modular ratio of 3n)

Case 3 Not Defined Not Defined (Apply modular ratio of 3n)

1.5.1 Member forces and stresses used in steel composite section design

(1) Member forces For design of steel composite section, member forces per construction stage of steel composite section must be calculated. The program considers two main factors for design and review of construction stage of steel composite section. ▪Construction stages of steel composite section ▪Time dependent material properties of Concrete (Creep, Shrinkage and Compressive Strength)


Design member forces used for design of steel composite section are divided into three main categories. Table 1.8 Design Force and Moment for Steel Composite Design

Design Force/Moment Description

Dead (Before) Member forces due to permanent loads occurring before the concrete deck is activated. Only steel section properties are used to calculate stresses. ex) Self weight of steel and concrete deck

Dead (After) Member forces due to permanent loads occurring after concrete deck is activated Long term section properties of composite section are used. ex) Self weight of wearing surface and barrier

Short Term Member forces from the post-construction state and load cases not included in the above categories. Short term section properties of composite section are used. ex) Traffic loads, wind loads

When construction stages are included in the model in midas Civil, the design moments for Dead (Before) are taken as the moments of steel section due to Dead Load (CS) and Erection Load (CS) whose load type is Dead Load (D) and the design moments for Dead (After) are taken as the moments of composite section due to Erection Load (CS) whose load type is Dead Load of Component and Attachments (DC) or Dead Load of Wearing Surfaces and Utilities (DW). Example:

Permanent Loads Load Type Analysis results

Load Factor

Design forces Stage 1

Steel only Stage 2

Composite Dead

(Before) Dead

(After) Self Weight of Steel Dead Load (CS) 100 100 1.1 110

Self Weight of Concrete Erection (D) 100 100 1.2 120 Self Weight of Barrier Erection (DC) 0 100 1.2 120

Self Weight of Wearing Surface

Erection (DW) 0 100 1.5 150

Sum 230 270

Above rule has changed in Civil 2018 (v1.2) in order to account for various erection sequence of slab. The design moments for Dead (Before) and Dead (After) are determined as shown in the table below.

Dead Load (CS) Erection Load (CS) Moments applied to steel section Dead (Before) Dead (Before) Moments applied to composite section Ignored Dead (After)

(2) Stress Bending stress used for design of steel composite section is calculated as follows:

Where,

Md : bending moment at SLS due to dead load, steel section only

Msd : bending moment at SLS due to superimposed dead load, composite section

ML : bending moment at SLS due to live load, composite section

S : elastic section modulus of steel section

S3n : elastic modulus of section comprising the steel beam and the concrete slab, calculated using a modular ratio of 3n, long-term load, positive moment


Sn : elastic modulus of section comprising the steel beam and the concrete slab, calculated using a modular ratio of n, short-term load, positive moment

S’ : elastic modulus of composite section comprising the steel section and reinforcement, negative moment 1.5.2 Case 1 In Case 1, construction stages and time dependent material properties of concrete (Creep/Shrinkage) are defined and Multiple Modulus of Elasticity is not checked on in the Section Data dialog. The effects of creep and shrinkage of concrete are directly calculated and checked by Creep Secondary (CS) or Shrinkage Secondary (CS) load cases. The Composite sections for Construction Stage function must be defined. Otherwise, the sections shall be excluded from design. Note that if time dependent material property information is inputted as well as long-term modulus of elasticity, long-term modulus of elasticity has higher priority in consideration of calculation.

Define Composite Section for Construction Stage


Composite Section for Construction Stage

Load >Load Type> Construction Stage > Composite Section for C.S...

Figure 1.28 Add/Modify Composite Section for Construction Stage Dialog

Composite Section for Construction Stage For definition of composite section for construction stage, information in this window must be defined. (1) Active Stage Construction stage where steel composite section should be activated is inserted. (2) Construction sequence

1) "Material Type" column □ By choosing Element, material property of the element is used. □ By selecting Material, material information chosen under "Material" Column is applied with higher priority. 2) Composite Stage column Construction stages where steel girder and concrete slab should be activated are chosen separately. 3) Age column Age information when each part is activated is input. Information in this column has higher priority over the age input during definition of construction stage.


Define Erection Load

(1) Define Erection Load

Analysis > Analysis Control > Construction Stage > Load Cases to be Distinguished from Dead Load for C.S Output >Add (Modify/delete)...

Figure 1.29 Define Erection Load Dialog

1) Define Erection Load Erection Load is defined.

1) Load Type for C.S Determine the Load Type for the construction stages of the composite section. Load types are considered by the software for auto generation of load combinations. 2) Assignment Load Cases Define Erection Load by selecting and moving the Load Cases desired from the List of Load Case panel to the Selected Load Case panel.

1.5.3 Case 2 In Case 2, construction stages are defined without the time dependent material property (Creep/Shrinkage) information. Long term effects are considered using the long term modular ratio entered in the Section Data dialog box. Sections for different construction stages must be defined and differentiated using the Composite Section for Construction Stage definition. Otherwise, they will not be considered for the design check.

(1) Member forces under Dead (Before) Dead (Before) is applied before the concrete deck is activated. (Refer to Table 1.8 in the "Introduction") Self weight of steel and concrete belongs to Dead (Before).

(2) Member forces under Dead (After) The effects of Creep/Shrinkage are reflected by applying the ratio of elastic modulus that is inputted in the Section Data (Refer to Section 1.1.1 (1)) for the long-term stage. In other words, the Creep/Shrinkage effects are reflected by using the section information with the ratio of elastic modulus that considers the time dependent material property for the analysis and design. These long term modular ratios defined for considering creep and shrinkage, automatically generate Section Stiffness Scale Factors for the sections in which these are inputted. Section Stiffness Scale Factors need to be activated in the construction stages in accordance with the Composite Section for Construction Stage definition, i.e. the Section Stiffness Scale Factors are activated when the corresponding section becomes composite as per the definition of composite section for CS. Super-imposed dead loads, i.e. wearing surface, barrier belong to Dead (After).

(3) Short term member forces The ratio of elastic modulus of the composite section is calculated using the DB value inputted. All the load cases which are not activated in the Construction Stage are considered as the short-term loads.


1.5.4 Case 3 In case the construction stages are not defined, users can model and define steel composite sections by using the Load Case for Pre-Composite Section function.

Load > Load Type > Settlement/Misc. > Misc. > Pre-composite Section. For this case, short- and long-term ratios of elastic modulus defined in the section data (Refer to Section 1.1.1 (1)) are used. In this case, instead of member forces per construction stages, member forces under Dead (Before) is used to check the constructibility of the model.

(1) Member force under Dead (Before) In the Load Cases for Pre-Composite Section dialog box, users can define which load cases to account for the member forces and apply as Dead (Before) in design. Since this is for pre-composite state, the steel only section properties are used (Refer to Section 1.1.1 (1)).

Figure 1.30 Load Cases for Pre-Composite Section

(2) Member forces under Dead (After) Member forces under Dead (After) use the long term section properties. These loads should be separated from the short term member forces by the use of Analysis > Analysis Control > Boundary Change Assignment.

1) Data Selection Check the box corresponding to Section Stiffness Scale Factor. As explained earlier, Section Stiffness Scale Factors are used for considering the long term section properties.

2) Boundary Group Combination Create a boundary group combination considering the appropriate boundary groups from the boundary group list. The created boundary group combinations need to be selected for the post composite long term load cases. For the static load cases assigned with the section stiffness scale factor boundary groups, long term section property will be used.

Dead Load (Before)


Figure 1.31 Load Cases for Post-Composite Section

(3) Short-term member forces The ratio of elastic modulus from the database is used for the short-term loads of the composite section. All load cases are considered for the short-term loads except the ones considered for the Dead (Before) and Dead (After).

Dead Load (After)


Application of CAN/CSA S6-14

72Chapter 2. Steel Composite I-Girder Design – CAN/CSA S6-14

1. Composite I Girder 1.1. ULS

1.1.1 Bending (1) Positive Moment - Class 1 & 2 sections Width-to-thickness ratio of elements in compression

Top Flange The flange is assumed to be restrained by concrete slab. Thus, it is considered as Class 1.

Web

Stress distribution Fully plastic stress distribution as shown in Figure 1.32.

CAN/CSA S6-14 10.11.5.1 10.9.2

CAN/CSA S6-14 10.11.5.2.1

73 Chapter 2. Steel Composite I-Girder Design – CAN/CSA S6-14

Figure 1.32 Class 1 and 2 sections in positive moment regions

Factored moment resistance, Mr Mr is calculated as shown in Table 1.9.




In Web wt PP

rtrbsc PPPP

]1[2 w

rbrtsct

PPPPPPD

Y

])([2

22YtY

DP

M w


In Top flange

cwt PPP

rtrbs PPP

])([2

22YtY

tP

Mc

c



cwt PPP

rtrbss

rb PPPtc

s

s

tPY

M2

2




rbcwt PPPP

rtss

rb PPtc

rbCY

s

s

tPY

M2

2



rbcwt PPPP

rtss

rt PPtc

s

rbrttwcs P

PPPPPtY )(

s

s

tPY

M2

2



rtrbcwt PPPPP

ss

rt Ptc

rtCY

s

s

tPY

M2

2



rtrbcwt PPPPP

ss

rt Ptc

s

rttwcrbs P

PPPPPtY )(

s

s

tPY

M2

2



deck. : Distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal concrete

deck. : Distance from the plastic neutral axis to the midthickness of the tension flange. : Distance from the plastic neutral axis to middepth of the web. : Distance from the plastic neutral axis to midthickness of the compression flange. : Distance from the plastic neutral axis to midthickness of the concrete deck.


(by steel girder)


(by concrete slab)

- Class 3 sections Width-to-thickness ratio of elements in compression


Web

CAN/CSA S6-14 10.11.6.1

10.9.2


Factored moment resistance, Mr For composite sections in which the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, equals or is less than

, the factored moment resistance is determined in the same way as Class 1 & 2 under positive moment. When the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, exceeds , the factored moment resistance, Mr, of the composite section is calculated on the basis of fully plastic stress blocks, as shown in Figure 1.34, as follows:

The area of the steel section in compression, A‘sc , includes the top flange and a web area of

, and the area of the steel section in tension, A‘st , is calculated as follows:

Figure 1.34 Class 3 Sections in positive moment regions

- Class 4 sections This section is not valid. Therefore, the moment resistance check is skipped. -Stiffened plate girders Width-to-thickness ratio of elements in compression


Web The width-to-thickness ratio of a transversely stiffened web, h/w without longitudinal stiffeners, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. The following provision of CAN/CSA S6-14 is not supported in the program. “In determining a width-to-thickness ratio, Fy may be replaced by the maximum compressive stress due to the factored ULS loads if the maximum shear at the FLS does not exceed Vr calculated in accordance with Clause 10.10.5.1, taking Ft = 0 and φs = 1.0.” When a longitudinal stiffener is provided, the width-to-thickness ratio, h/w, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped.

CAN/CSA S6-14 10.11.6.2.1

10.11.5.2

CAN/CSA S6-14 10.11.6.2.2

CAN/CSA S6-14 10.11.7.1

10.10.4.1 10.10.4.2


Factored moment resistance, Mr For composite sections in which the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, does not exceed

, the factored moment resistance is determined in the same way as Class 1 & 2 under positive moment. When the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, exceeds , whether or not longitudinal stiffeners are provided, the factored moment resistance, Mr, of the composite section is calculated in the same way as Class 3 under positive moment. (2) Negative Moment - Class 1 & 2 sections Width-to-thickness ratio of elements in compression

Bottom Flange

Web

Factored moment resistance, Mr When it is braced against lateral torsional buckling, Mr is calculated on the basis of a fully plastic stress distribution in the structural steel and reinforcement, as shown in Table 1.10.






CAN/CSA S6-14 10.11.7.2.1

10.11.5.2

CAN/CSA S6-14 10.11.7.2.2

10.11.6.2.2

CAN/CSA S6-14 10.11.5.1

10.9.2


Where,

(by reinforcement)

(by reinforcement) (by steel girder) (by steel girder)

(by steel girder)

For laterally unbraced members, Mr is based on its lateral torsional buckling resistance. The unbraced bending resistance of the structural steel section alone is used. For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr, is calculated as

The critical elastic moment, Mu, of a monosymmetric section is taken as

where

where

Mmax = maximum absolute value of factored bending moment in unbraced segment, Nmm

Ma = factored bending moment at one-quarter point of unbraced segment, N mm

Mb = factored bending moment at midpoint of unbraced segment, N mm

Mc = factored bending moment at three-quarter point of unbraced segment, N mm L = length of unbraced segment of beam, mm

where βx= coefficient of monosymmetry

For doubly symmetric sections,

βx= 0.0 B1 = 0.0

so that

The general expression for the critical elastic moment and formulas for β x, J, and Cw for I-girder as specified in Clause C10.10.2.3 of CSA S6.1 are used.

CAN/CSA S6-14 10.11.5.3.1 10.10.2.3

CAN/CSA S6.1-14 10.10.2.3


where Iyc : minor axis moment of inertia of the compression flange only Iy : minor axis moment of inertia of the cross-section Ix : major axis moment of inertia of the cross-section


Bottom Flange

Web

Stress distribution Linear stress distribution at first yielding or buckling, as shown in Figure 1.36

Figure 1.36 Class 3 Sections in negative moment regions

CAN/CSA S6-14 10.11.6.1 10.9.2

CAN/CSA S6-14 10.11.6.3.1.1


Factored moment resistance, Mr The following requirements are checked:

where S and S are the elastic section moduli with respect to the bottom fibre,

, and Mr is determined as follows, based on the steel section. Mr is provided in the design result table.


where

where







βx= 0.0 B1 = 0.0

so that



CAN/CSA S6-14 10.11.6.3.1.2

CAN/CSA S6.1-14 10.10.2.3


where S and S are the elastic section moduli with respect to the top fibre of the steel section.

where S is the elastic section modulus with respect to the centroid of the top layer of longitudinal slab reinforcement. Fatigue limit check for longitudinal reinforcement is not supported. The requirement of 10.11.5.3.2 of CAN/CSA S6-14 is not supported.


Bottom Flange

Web

The width-to-thickness ratio of a transversely stiffened web, h/w without longitudinal stiffeners, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. The following provision of CAN/CSA S6-14 is not supported in the program.

“In determining a width-to-thickness ratio, Fy may be replaced by the maximum compressive stress due to the factored ULS loads if the maximum shear at the FLS does not exceed Vr calculated in accordance with Clause 10.10.5.1, taking Ft = 0 and φs = 1.0.”

When a longitudinal stiffener is provided, the width-to-thickness ratio, h/w, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped.

CAN/CSA S6-14 10.11.7.1 10.10.4.1 10.10.4.2


Factored moment resistance, Mr The factored moment resistance, Mr is calculated in the same way as Class 3 under negative moment. If longitudinal stiffeners are not provided and , the factored moment resistance, calculated for the compression flange, is reduced by the following factor.

1.1.2 Shear (1) Factored shear resistance The factored shear resistance of the web of a flexural member, Vr , is taken as

where Aw, the shear area, is calculated using d for rolled shapes and h for fabricated or manufactured girders, and Fs , the ultimate shear stress, is equal to Fcr + Ft , where Fcr and Ft are taken as follows:

For unstiffened webs, a/h is considered infinite, so that kv = 5.34. At girder end panels and adjacent to large openings in the web, the resistance shall be calculated using Ft = 0. However, there is no consideration about the end panels and openings in the web in the program. (2) Combined shear and moment When subject to the simultaneous action of shear and moment, transversely stiffened webs that depend on tension field action to carry shear, i.e., with , are proportioned so that

CAN/CSA S6-14 10.11.7.3.1 10.11.6.3.1 10.10.4.3

CAN/CSA S6-14 10.11.2 CAN/CSA S6-14 10.10.5.1

CAN/CSA S6-14 10.10.5.2


(3) Intermediate transverse stiffeners The distance between stiffeners, a, shall not exceed when h/w is greater than 150 and shall not exceed 3h when h/w is less than or equal to 150. Intermediate transverse stiffeners provided on one or both sides of the web are proportioned so that

I is taken about an axis at the mid-plane of the web for stiffener pairs or at the near face of the web for single stiffeners.

Vf / Vr = the ratio at the end of element

D = 1.0 for stiffeners provided in pairs = 2.4 for single-plate stiffeners Single-angle stiffeners are not supported.

The width of a plate used as a stiffener shall not be less than 50 mm plus h/30 and shall not be less than one-quarter of the full width of the flange. The width-to-thickness ratio of intermediate transverse stiffeners shall not exceed . The projecting stiffener width shall not exceed 30t. (4) Longitudinal web stiffeners The spacing, a, of transverse stiffeners of longitudinally stiffened webs shall not exceed 1.5hp , where hp is the maximum subpanel depth. The total web depth, h, is used in determining the shear capacity, Vr, of longitudinally stiffened girders. Longitudinal stiffeners shall be proportioned so that (a) the stiffener width-to-thickness ratio does not exceed ; (b) the projecting stiffener width is less than or equal to 30t;

where I and r are calculated about a centroidal axis parallel to the web for a section comprising the stiffener or stiffeners and a strip of web 10w wide on each side. Additional requirements of transverse stiffeners for longitudinally stiffened webs are not checked by the program. (5) Bearing stiffeners Bearing stiffener check is not supported in the program.

CAN/CSA S6-14 10.10.6.1

CAN/CSA S6-14 10.10.6.2

CAN/CSA S6-14 10.10.7.1

CAN/CSA S6-14 10.10.7.2


1.2 Serviceability Limit State 1.2.1 Control of permanent deflections For composite beams and girders, the normal stress in either flange of the steel section due to serviceability dead and live loads shall not exceed 0.90 Fy. The following requirements shall be satisfied: (a) in positive moment regions:

(b) in negative moment regions:

1.3 Fatigue Limit State 1.3.1 General The FLS considered includes direct live load effects, i.e., live load-induced fatigue. The effects of local distortion within the structure, i.e., distortion-induced fatigue are not taken into account in the program. (1) Fatigue check location Fatigue of the base metal at the connection plate welds to the flanges at the intermediate cross-frame

o Bottom surface of top flange o Top surface of bottom flange

Fatigue of the base metal at the stud shear-connector weld to the top flange

o Top surface of top flange Fatigue resistance of high-strength bolts loaded in tension is not supported. Fatigue resistance of stud shear connectors is supported and explained in the separate clause in this document. 1.3.2 Calculation of stress range The stress range for load-induced fatigue is calculated as the difference between the maximum stress and minimum stress at a given location due to live load. At locations where the stresses resulting from the permanent loads are compressive, load-induced fatigue is disregarded when the compressive stress is at least twice the maximum tensile live load stress. 1.3.3 Design criteria For load-induced fatigue, each detail shall satisfy the requirement that

where CL = 1.0 when W ≤ 625 kN CL = 0.20 + 500/W when W > 625 kN fsr = calculated fatigue stress range at the detail due to passage of the CL-W Truck The load-indueced fatigue check in bridge decks is not supported. 1.3.4 Fatigue stress range resistance (1) Fatigue stress range resistance of a member or detail The fatigue stress range resistance of a member or a detail, Fsr , other than for shear studs, is calculated as follows: Fsr = fatigue resistance

CAN/CSA S6-14 10.11.4

CAN/CSA S6-14 10.17.2.1

CAN/CSA S6-14 10.17.2.2

CAN/CSA S6-14 10.17.2.3.1


where γ , γ ‘ = fatigue life constants pertaining to the detail category and specified in Table 1.11 Fsrt = constant amplitude threshold stress range, MPa

where y = design life (equal to 75 years) Nd = number of design stress cycles experienced for each passage of the design truck, as specified in Table 1.12 ADTTf = single-lane average daily truck traffic, which is estimated as p (ADTT), where p is 1.0, 0.85, or 0.80 for the cases of one, two, or three or more lanes available to trucks, respectively, and ADTT shall be as specified in Table 1.13

Table 1.11 Fatigue life constants and constant amplitude threshold stress ranges

Table 1.12 Values of Nd

The values of Nd can be defined either by the program or user input. For the auto-calculation, the span length should be defined from the ‘Span Information’ function. Table 1.13 Average daily truck traffic


1.3.5 Detail categories The detail categories used in the design are as follows: -Bottom surface of top flange & Top surface of bottom flange

Detail category C1, Example 6 -Top surface of top flange

Detail category C, Example 13 Table 1.14 Detail categories for load-induced fatigue

CAN/CSA S6-14 10.17.2.4


2. Shear Connector 2.1. ULS

2.1.1 Shear connector resistance (1) General The ULS check of shear connectors is performed by checking if the number of shear connectors applied in each shear span exceeds the minimum number of shear connectors. The number of shear connectors applied in the shear span, Nuse, is calculated as follows:

where a shear span, L, is a segment between points of maximum and zero moment at the ULS and it should be entered by the user. p = pitch of shear connectors floor function rounds a number down to the nearest integer. Nsc = number of shear connectors in a row The minimum number of shear connectors in each shear span is calculated as follows:

P is determined as follows: (a) for positive moment:

(i) when the plastic neutral axis is in the concrete slab: ; and (ii) when the plastic neutral axis is in the steel section: ; and

(b) for negative moment: . (2) Stud connectors in cast-in-place deck slab The factored shear resistance, qr , of a headed stud shear connector with h/d ≥ 4 is taken as

where Fu = minimum tensile strength of the stud steel Asc = cross-sectional area of one stud shear connector The program checks if the spacing of shear connectors is not less than 4d, nor greater than 600 mm. (3) Stud connectors in full-depth precast panels This is not supported in the program. (4) Channel connectors in cast-in-place deck slab Channel connectors are not supported in the program. 2.1.2 Longitudinal shear The longitudinal shear check along potential shear planes is not supported.

2.2. FLS 2.2.1 Fatigue resistance of stud shear connectors Stud shear connectors are designed for the following stress range, τ rs :

where CL = 1.0 when W ≤ 625 kN = 0.20 + 500/W when W > 625 kN Vsc = range of design shear force at the section along the length of the beam where the fatigue resistance of the shear connectors is being evaluated, N

CAN/CSA S6-14 10.11.8.3.1

CAN/CSA S6-14 10.11.8.3.2

CAN/CSA S6-14 10.11.8.4

CAN/CSA S6-14 10.17.2.7


Q = first moment of area of the transformed section at the interface between the concrete slab and the steel section, mm3 s = shear stud group spacing, mm Asc = cross-sectional area of a shear stud, mm2 n = number of shear studs in the group at the cross-section being evaluated It = moment of inertia of the transformed composite section about the axis of bending, mm4

= fatigue stress range resistance for Category D, as determined as follows:

Fatigue life constant, γ =

Fatigue life constant, γ’ = Fsrt = constant amplitude threshold stress range, MPa



The values of Nd can be defined either by the program or user input. For the auto-calculation, the span length should be defined from the ‘Span Information’ function. When stud shear connectors are not provided in negative moment regions, additional connectors, Na in number, shall be provided at each location of contraflexure, where

This requirement is not considered in the program.


3. Constructibility of a composite I Girder 3.1. ULS

3.1.1 Bending (1) Class 1 & 2 sections - Width-to-thickness ratios of elements in compression

Flange

Web

dc = depth of compression portion of web in flexure, mm

- Laterally supported members

- Laterally unbraced members For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr, is calculated as


where

where Mmax = maximum absolute value of factored bending moment in unbraced segment Ma = factored bending moment at one-quarter point of unbraced segment Mb = factored bending moment at midpoint of unbraced segment Mc = factored bending moment at three-quarter point of unbraced segment

L = length of unbraced segment of beam, mm



βx= 0.0 B1 = 0.0

so that

CAN/CSA S6-14 10.10.2.1 10.9.2

CAN/CSA S6-14 10.10.2.2

CAN/CSA S6-14 10.10.2.3




- Bending about the minor axis For a section subjected to bending about its minor axis, whether laterally braced or unbraced, the factored moment resistance, Mr, is calculated as

(2) Class 3 sections - Width-to-thickness ratio of elements in compression

Flange

Web


- Laterally supported members When continuous lateral support is provided to the compression flange of a member subject to bending about its major axis, the factored moment resistance, Mr, is calculated as

CAN/CSA S6.1-14 10.10.2.3

CAN/CSA S6-14 10.10.2.4

CAN/CSA S6-14 10.10.3.1 10.9.2

CAN/CSA S6-14 10.10.3.2


- Laterally unbraced members For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr , is calculated as

where The critical elastic moment, Mu, of doubly symmetric and monosymmetric sections is taken as

where


L = length of unbraced segment of beam



βx= 0.0 B1 = 0.0

so that



CAN/CSA S6-14 10.10.3.3

CAN/CSA S6.1-14 10.10.2.3


(3) Class 4 sections For beams and girders with continuous lateral support provided to the compression flange, with webs that meet the requirements of Class 3, and whose flanges exceed the slenderness limits of Class 3, the factored moment resistances is computed as for a Class 3 section, except that the elastic section modulus, S, is replaced by an effective section modulus, Se, determined using an effective projecting flange width of , for flanges supported along one edge. However, the projecting flange width shall not exceed 30t. - Bending about the minor axis For a section subjected to bending about its minor axis, whether laterally braced or unbraced, the factored resistance, Mr, shall be calculated as

(4) Stiffened plate girders - Width-to-thickness ratio of flanges The program checks if stiffened plate girders have Class 1, 2, or 3 flanges. - Width-to-thickness ratios of webs The width-to-thickness ratio of a transversely stiffened web, h/w, without longitudinal stiffeners, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. The following provision of CAN/CSA S6-14 is not supported in the program. “In determining a width-to-thickness ratio, Fy may be replaced by the maximum compressive stress due to the factored ULS loads if the maximum shear at the FLS does not exceed Vr calculated in accordance with Clause 10.10.5.1, taking Ft = 0 and φs = 1.0.” When a longitudinal stiffener is provided, the width-to-thickness ratio, h/w, shall not exceed

. If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped.

CAN/CSA S6-14 10.10.3.4

CAN/CSA S6-14 10.10.3.5

CAN/CSA S6-14 10.10.4.1

CAN/CSA S6-14 10.10.4.1 10.17.2.5


- Moment resistance The moment resistance, Mr is calculated in the same way as Class 3 sections. If longitudinal stiffeners are not provided and , the moment resistance, calculated for the compression flange, is reduced by the following factor.




CAN/CSA S6-14 10.10.4.3

CAN/CSA S6-14 10.10.5.1

CAN/CSA S6-14 10.10.5.2








CAN/CSA S6-14 10.10.6.1

CAN/CSA S6-14 10.10.6.2

CAN/CSA S6-14 10.10.7.1

CAN/CSA S6-14 10.10.7.2


4. Horizontally curved I-girders 4.1 Non-composite girder design

4.1.1 Limits of applicability The following requirements shall apply: (a) The absolute value of the ratio of the torsional warping normal stress to the normal flexural stress shall, as far as possible, not exceed 0.5 at any point in the girder. This should be checked separately by the user. (b) The unbraced length between cross-frames shall not exceed 25 times the width of the flange or 0.1 times the mean radius of the girder. This should be checked separately by the user. (c) Flanges shall be Class 3 or better. This is checked by the program. 4.1.2 Flanges Flanges are proportioned to satisfy the following requirements:(a) Strength of either flange:

where Mfx = factored bending moment due to flexure Mrx = φsFy Sx

where Sx = elastic section modulus of the girder about its major axis

Mfw = factored bending moment in the flange due to torsional warping. Mfw is taken as regardless of the intermediate lateral restraint.

Where L = the distance between lateral restraintswr = the lateral load on the flange is a distributed lateral load, wr = Mfx/hR. Mfx = the moment in the vertical plane on the girder h = the clear depth of web between flanges R = the radius of curvature of the girder web (user input)

Mry = φsFy Sy where Sy = elastic section modulus of the flanges only about an axis in the plane tangent to the web of the girder

(b) Stability of compression flange:

where

where

wc = 0.5 where the lateral bending moment in the flange has major reversals, but 1.0 where the lateral bending moment does not have major reversals

CAN/CSA S6-14 10.13.6.1.1

CAN/CSA S6-14 10.13.6.1.2


4.1.3 Webs The factored shear resistance is calculated in accordance with the provision for straight girders. The following requirements are also applied: (a) Webs without stiffeners: Tension-field action is neglected in webs without transverse

stiffeners. (b) Webs with transverse stiffeners only:

(i) Tension-field action is included in the calculated resistance when the geometry satisfies all of the following: (1) web slenderness h/w ≤ 160; (2) ratio of braced length to radius of horizontal curvature of the girder, Lb/R ≤ 0.1; and (3) transverse stiffener spacing a/h ≤ 3.

(ii) When subject to the simultaneous action of shear and moment, transversely stiffened webs that depend on tension-field action to carry shear is proportioned so that

(c) Webs with transverse and longitudinal stiffeners: When the longitudinal stiffeners are provided at a distance 0.2h from the compression flange, the program checks the web slenderness ratio satisfies the following condition.

When longitudinal stiffeners are located 0.2h from both the compression flange and the tension flange, the program checks if the web slenderness ratio does not exceed . Tension-field action is neglected. (d) Proportioning of transverse web stiffeners: the program checks if stiffeners are proportioned so that

I is taken about an axis at the mid-plane of the web for stiffener pairs, or at the near face of the web for single stiffeners. Where transversely stiffened webs depend on tension-field action to carry the applied shear, the program also checks if the transverse stiffeners are proportioned so that.

CAN/CSA S6-14 10.13.6.1.3




The width of a plate used as a stiffener shall not be less than 50 mm plus h/30 and shall not be less than one-quarter of the full width of the flange. The width-to-thickness ratio of intermediate transverse stiffeners shall not exceed . The projecting stiffener width shall not exceed 30t. (e) The program checks if longitudinal stiffeners are proportioned so that

(a) the stiffener width-to-thickness ratio does not exceed ; (b) the projecting stiffener width is less than or equal to 30t;

where I and r are calculated about a centroidal axis parallel to the web for a section comprising the stiffener or stiffeners and a strip of web 10w wide on each side.

(f) Monosymmetric sections: the program does not check if the slenderness ratio of the compression portion of webs of monosymmetric sections with an axis of symmetry in the plane of loading does not exceed one-half of the applicable value specified in Item (a), (b), or (c). This should be separately checked by the user.

4.2 Composite I-girders 4.2.1 Webs The web of the steel girder is designed to carry the entire vertical shear in accordance with Clause 4.1.3 of this document. 4.2.2 Flanges The program checks if flanges are Class 3 or better and meet the strength and stability requirements of Clause 4.1.2 of this document. 4.2.3 Shear connectors The program checks if shear connectors meet the requirements of Clauses 2.1 and 2.2 of this document.

CAN/CSA S6-14 10.13.6.2.2 10.13.6.1.3

CAN/CSA S6-14 10.13.6.2.3 10.13.6.1.2

CAN/CSA S6-14 10.13.6.2.4 10.11.8 10.17.2.7


Steel Composite Design Result

97Chapter 2. Steel Composite I-Girder Design – CAN/CSA S6-14

1. Ultimate Limit State Result 1.1 Flexure

(1) Result Table As shown in the table below, the results can be checked in the result table.

Design > Composite Design > Design Result Tables > Ultimate Limit State (flexure)…

Figure 1.37 Result Table for Ultimate Limit State of Flexure

Where,

Type: Load combination type (Fx-max, Fx-min, ... Mz-min). When a moving load case is included, there are 12 sets of concurrent forces. Load combination type shows which sets of concurrent forces give critical forces.

Top Class: Class of top flange Bot Class: Class of bottom flange Web Class: Class of web

My : yield moment

Mp : plastic moment. This is provided for Class 1 and 2 sections only.

Mf : factored bending moment

Mr : factored moment resistance of member


(2) Excel Report The results can be viewed in an Excel Report as shown below.

Figure 1.38 Excel Report for Ultimate Limit State of Negative Moment


1.2 Shear (1) Result Table As shown in the table below, the results can be checked in the result table.

Design > Composite Design > Design Result Tables > Ultimate Limit State (shear)…

Figure 1.39 Result Table for Ultimate Limit State of Shear

Where,

Vf : factored shear force

Vr : factored shear resistance



Vf/Vr : shear check ratio

Comb. : combined shear and moment check ratio


Figure 1.40 Excel Report for Ultimate Limit State of Shear


2. Service Limit State Result (1) Result Table

The results can be viewed in an Excel Report as shown below.

Design > Composite Design > Design Result Tables > Service Limit State…

Figure 1.41 Result Table for Service Limit State Where,

Stress 0.90Fy : limit stress in the flange of the steel section to control permanent deflections Md : bending moment at SLS due to dead load, steel section only S : elastic section modulus of steel section Msd : bending moment at SLS due to superimposed dead load, composite section S3n : elastic modulus of section comprising the steel beam and the concrete slab, calculated using amodular ratio of 3n, long-term load, positive moment ML : bending moment at SLS due to live load, composite section Sn : elastic modulus of section comprising the steel beam and the concrete slab, calculated using amodular ratio of n, short-term load, positive moment S’ : elastic modulus of composite section comprising the steel section and reinforcement, negative moment

(2) Excel Report


Figure 1.42 Excel Report for Serviceability Limit State


3. Constructibility Result 3.1 Flexure

(1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Construction Stage (flexure)...

Figure 1.43 Result Table for Constructibility Limit State of flexure

Where,

Mfy : factored bending moment about the y-axis of the cross-section Mry : factored moment resistance about the y-axis of the cross-section Mfz : factored bending moment about the z-axis of the cross-section Mrz : factored moment resistance about the z-axis of the cross-section Comb.1 : strength check ratio of flange for the combined moments Comb.2 : stability check ratio of compression flange for the combined moments (2) Excel Report The results can be viewed in an Excel Report as shown below.

Figure 1.44 Excel Report for Constructibility of Negative Moment


3.2 Shear (1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Construction Stage (shear)...

Figure 1.45 Result Table for Constructibility of Shear

Where,






Mf/Mr : moment check ratio



Figure 1.46 Excel Report for Constructibility of Shear


4. Fatigue Limit State Result (1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Fatigue Limit State...

Figure 1.47 Result Table for Fatigue Limit State

Where,

Lcom : Load combinations used in the calculation

fsr : calculated FLS stress range at the detail due to passage of the CL-W Truck

Fsr : fatigue stress range resistance

tau_rs: fatigue shear stress range for the stud shear connectors

Vsc : range of design shear force at the section along the length of the beam where the fatigue resistance of the shear connectors is being evaluated


Figure 1.48 Excel Report for Fatigue Limit State


5. Shear Connector Result (1) Result Table

The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Shear Connector...

Figure 1.49 Result Table for Shear Connector

Where,

h/d : height to diameter ratio of shear connector

qr : factored shear resistance of shear connectors

N : number of shear connectors entered in shear span

Nreq : required number of shear connectors in shear span

(2) Excel Report


Figure 1.50 Excel Report for Shear Connector


6. Stiffener Result (1) Result Table


Design > Composite Design > Design Result Tables > Transverse Stiffener...

Figure 1.51 Result Table for Stiffener

Where, h/w : ratio of clear depth of web to web thickness h/w_lim : 150, Web stiffeners are not required when the unstiffened shear resistance exceeds the factored shear and h/w ≤ 150. a : stiffener spacing a_lim : limit of stiffener spacing as per clause 10.10.6.1 As : area of stiffener or pair of stiffeners It : moment of inertia of transverse stiffener It_lim : limit of moment of inertia of transverse stiffener as per clause 10.10.6.2 w/t : width-to-thickness ratio of intermediate transverse stiffeners 200/sqrt(Fy) : limit of width-to-thickness ratio of intermediate transverse stiffeners as per clause10.10.6.2 wp : projecting stiffener width 30t : limit of projecting stiffener width as per clause 10.10.6.2

(2) Excel Report


Figure 1.52 Excel Report for Stiffener


7. Total Checking

(1) Result Table

Design > Composite Design > Design Result Table...

Summary results for each member can be viewed in a result table as shown below.

Figure 1.53 Result Table for Toal Checking

CAN/CSA S6 -14

Chapter 3.

Steel CompositeBox Girder Design

Steel Composite Box-Girder Bridge

Check Constructability

Check Shear Connector

Steel Composite Box Girder DesignChapter 3.

Chapter 3.Steel Composite Box Girder Design : CAN/CSA S6-14

Introduction

Chapter 3.Steel Composite Box Girder Design – CAN/CSA S6-14 109

1. CAN/CSA S6-14 Steel Composite Box Girder 1.1 Check List of CAN/CSA S6-14 Steel Composite Box Girder For CAN/CSA S6-14 Steel Composite Design, Limit State Design is applied. The criteria that Steel Composite Box-Girder must follow for Limit State Design is as follows.

(1) Ultimate Limit State Review on bending strength, lateral torsional buckling and shear strength (2) Serviceability Limit State Review on permanent deformation (3) Constructibility Review on bending and shear occurring from load combinations during construction stages (4) Fatigue Limit State Review on fatigue in steel and concrete materials in Steel Composite girder

1.2 Classification of Steel Composite Steel Composite section can be categorized by the following classification groups.

(1) Section Shape Type There are three main section shape types in midas Civil; I, Box and Tub shapes. In the case ofbox and tub sections, there are two more cases, single or multiple box section.

I Box Tub

Figure 1.1 Section Shape Type (2) Moment Type : Positive / Negative For continuous beams, negative moments may occur around interior supports. Design codemay apply different formulas for these cases. (3) Bridge Type : Straight / Curved Based on the horizontal alignment of a bridge, it can be classified as either straight or curved. The program recognizes curved bridges based on the input of the girder radius for each element.


(4) Classification of Cross-sections: Class 1 / Class 2 / Class 3 / Class 4 Structural sections shall be designated as Class 1, 2, 3, or 4 depending on the width-to-thickness ratio of the elements that make up the cross-section and on the conditions ofloading.

Table 1.1 Steel Section Classification

Type Description

Class 1 A Class 1 section is one that will attain the plastic moment capacity, adjusted for the presence of axial force if necessary, and permit subsequent redistribution of bending moment.

Class 2 A Class 2 section is one that will attain the plastic moment capacity, adjusted for the presence of axial force if necessary, but not necessarily permit subsequent moment redistribution.

Class 3 A Class 3 section is one that will attain the yield moment capacity, adjusted for the presence of axial force if necessary.

Class 4 A Class 4 section is one in which the slenderness of the elements making up the cross-section exceeds the limits of Class 3.

1.3 Stiffeners of Steel Composite The program considers transverse and longitudinal stiffeners.

Table 1.2 Types of Stiffeners

Type Description

Transverse Stiffeners

Transverse stiffeners are usually provided to increase shear resistance by tension field action. These work as anchors for the tension so that post buckling shear resistance can be developed. It should be noted that elastic web shear buckling cannot be prevented by transverse stiffeners.

Longitudinal Stiffeners

Longitudinal stiffeners may be provided to increase flexural resistance by preventing local buckling. These work as restraining boundaries for compression elements so that inelastic flexural buckling stress can be developed in a web. It consists of either a plate welded longitudinally to one side of the web, or a bolted angle.

Figure 1.2 Longitudinal Stiffener and Transverse Stiffener

CAN/CSA S6-14 10.9.2.1

111Chapter 3.Steel Composite Box Girder Design – CAN/CSA S6-14

2. Considerations of Steel Composite Design 2.1 Construction Stage for steel composite During the construction of a steel composite bridge, the steel girder is constructed before theconstruction of the concrete deck of the upper part of the structure. The steel composite sectionis divided into three major steps.

Table 1.3 Construction Stage for Steel Composite Section

Construction stage for steel composite section

Description

Only Steel Girder (non-composite)

Only the steel girder has been constructed.


as load (non-composite)

Although the concrete deck has been constructed, it has not hardened yet. Therefore, the weight of the wet concrete is applied to the steel girder as a load condition.


as member (composite)

After concrete is hardened, the strength and stiffness are formed. Hereafter, the steel girder and concrete deck work as a complete composite section.

2.2 Time Dependent Material ▪ Steel composite section is composed of steel and concrete. Concrete is a time dependentmaterial and transforms due to creep and shrinkage. Also, the restraints imposed by the shearconnectors cause additional stresses within the composite section. Therefore, time dependentcharacteristics (creep and shrinkage) must be taken into consideration. ▪ Modular ratio is the ratio of modulus of elasticity of steel to that of concrete. The short-termmodular ratio "n" is used for transient loads in the program. Long-term modular ratio "3n" is usedfor permanent loads acting after composite action.

3. Calculation of Plastic Moment and Yield Moment 3.1 Section Classification

The steel section is classified in accordance with Clause 10.9.2 of CAN/CSA S6-14. Theclassification is carried out separately for positive and negative bending for both compositeand non-composite sections. The classification of a cross-section depends on the width tothickness ratio of the parts subject to compression. A cross-section is classified according tothe highest (least favorable) class of its compression parts. For calculating the limiting width-to-thickness ratios of the web of monosymmetric steelsections, h is replaced by 2dc. However, for the classification of composite section, the h is

CAN/CSA S6-14 10.9.2.1 CAN/CSA S6-14 10.10.2.1


used for the web. The resistance of the top flange of the composite section under positive moment is assumedas not being limited by its local buckling resistance since it is restrained by effective attachment to a concrete flange by shear connectors. The top flange is always classified as Class 1.

3.2 Plastic Moment (Mp) of Composite Section in Positive Flexure

If the positive moment is applied on a class 1 or class 2 section, MP is calculated as shown inTable 1.4.




In Web wt PP

rtrbsc PPPP

]1[2 w

rbrtsct

PPPPPPD

Y

])([2

22YtY

DP

M w


In Top flange

cwt PPP

rtrbs PPP

])([2

22YtY

tP

Mc

c



cwt PPP

rtrbss

rb PPPtc

s

s

tPY

M2

2



rbcwt PPPP

rtss

rb PPtc

rbCY

s

s

tPY

M2

2




rbcwt PPPP

rtss

rt PPtc

s

rbrttwcs P

PPPPPtY )(

s

s

tPY

M2

2



rtrbcwt PPPPP

ss

rt Ptc

rtCY

s

s

tPY

M2

2



rtrbcwt PPPPP

ss

rt Ptc

s

rttwcrbs P

PPPPPtY )(

s

s

tPY

M2

2



deck. : Distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal

concrete deck. : Distance from the plastic neutral axis to the midthickness of the tension flange. : Distance from the plastic neutral axis to middepth of the web. : Distance from the plastic neutral axis to midthickness of the compression flange. : Distance from the plastic neutral axis to midthickness of the concrete deck.


(by steel girder)


(by concrete slab)

3.3 Plastic Moment (Mp) of Composite Section in Negative Flexure Under negative moment, Mp is calculated by either of the two following methods. Please refer to Table 1.5 for the equations.







Where,



(by steel girder)

Chapter 3. Steel Composite Box Girder Design : CAN/CSA S6-14

Modeling and Design Variables

Chapter 3.Steel Composite Box Girder Design – CAN/CSA S6-14 115

1. Modeling Design Variables In this chapter, the design variable values, the meaning behind the design requirements, and the design process for Steel Composite Design in midas Civil are explained.

1.1. Composite Section Data The steel composite section is mainly composed of steel girder and concrete slab. Stiffeners can be added to steel girder section while longitudinal reinforcement can be added to reinforce concrete slab. In this section, the input methods for these sections and the meaning and application of design variables are explained.


Properties > Section > Section Properties> Add > Composite Tab

Figure 1.5 Section Data Dialog Box


1) The value of Bc for the slab is used as the effective width of the concrete deck. 2) Multiple Modulus of Elasticity Option To design the steel composite section, the modulus of elasticity for short-term and long-term effect in creep and shrinkage can be input. The modulus of elasticity input here is applied for construction stage analysis of Steel Composite section as shown in Figure 1.6.

Figure 1.6 Elastic Modulus ratio for Construction Stage


(2) Section Stiffener

Properties > Section > Section Properties> Add > Composite Tab > Stiffeners Button...

Figure 1.7 Section Stiffener Dialog Box


Design > Composite Design > Longitudinal

Reinforcement ...

Figure 1.8 Longitudinal Reinforcement Dialog Box

(2) Section Stiffener (Longitudinal)

1) Types of longitudinal stiffeners that are useable are Flat, Tee, and U-Rib. 2) For I sections, stiffeners can be added on either side of the web. For Box/Tub sections, upper and lower flanges can be installed as well as the web panel. 3) When the check box under ‘c’ column is checked on, the stiffness value of the stiffener is considered in analysis. Otherwise, the value is not considered for analysis. Regardless of whether or not the check box is checked on or off, longitudinal stiffeners are considered in design. It is also required for classifying the interior panels in shear check as stiffened/unstiffened.


In a steel composite section, the longitudinal reinforcements are arranged within the concrete deck. The moment resistance is calculated as shown in Table 1.6.

Table 1.6 Applicability of concrete and reinforcement for the calculation of moment resistance

Case Positive Bending

Negative Bending

Figure

Concrete Slab Applied None

Rebar Applied Applied


1.1.3 Transverse Stiffener (1) Transverse Stiffener

Design > Composite Design > Transverse Stiffener ...

Figure 1.9 Transverse Stiffener Dialog Box

Figure 1.10 Stiffener Type Dialog Box

1.1.3 Transverse Stiffener

Figure 1.9 shows the window in which users can arrange transverse stiffeners in steel composite section. When the transverse stiffeners are installed, the existence and spacing between stiffeners determine whether the web is stiffened or unstiffened under ultimate limit state.

Figure 1.11 Transverse Stiffener Parameters

Stiffener Type 1) One / Two Stiffener Option Button Choose between one or two stiffeners. Transverse stiffeners can be provided on one or both sides of the web.

2) Pitch Pitch refers to transverse stiffener spacing. At the ultimate limit state, this can be used to distinguish between stiffened and unstiffened webs or calculate shear strength of the web.


1.2. Design Material Data For the design of steel composite section, construction stage and time dependent material properties of concrete can be applied. In this section, the input method for the time dependent properties of concrete and material data for steel composite section is explained.


1.2.1 Time Dependent Material (1) Creep/Shrinkage

Properties > Time Dependent Material > Creep/Shrinkage ...


(Creep/Shrinkage)

(2) Comp. Strength

Properties > Time Dependent Material > Comp. Strength ...


(Compression Strength)

1.2.1 Time Dependent Material (1) Creep/Shrinkage The time dependent properties of concrete, such as creep and shrinkage, are defined. During construction stage analysis of bridges, these properties are utilized for concrete material.

(2) Comp. Strength

In order to reflect the change in the modulus of elasticity of concrete, the change in compressive strength or modulus of elasticity is defined. Aging effects may vary for each construction stage since concrete is poured at different locations.



1.2.2 Modify Composite Material (1) Modify Composite Material

Design > Composite Design > Design Material ...

Figure 1.14 Modify Composite Material Dialog Box

1.2.2 Modify Composite Material The materials utilized for steel composite sections are provided in the SRC material properties. The materials should be defined as SRC Type.

(1) Modify Composite Material Figure 1.14 shows the dialog box where users can type in material characteristics for the steel composite section design. The material property values entered will have a priority over the values entered in the Material Data dialog box.

1) Steel Material Selection Define modulus of elasticity, yield strength and tensile strength of steel for design purpose. In the current version, different yield strengths for different thicknesses of steel are not supported.

2) Concrete Material Selection Define compressive strength of concrete slab for design purpose.

3) Reinforcement Selection Define yield strength of reinforcement in the slab.


1.3. Design Parameters for Composite Section



Design > Composite Design > Design Parameters ...

Figure 1.15 Composite Steel Girder Design Parameter Dialog Box

1.3.2 Unbraced Length

Design > Composite Design > Unbraced Length ...

Figure 1.16 Unbraced Length Dialog Box


(1) Strength Resistance Factor Strength Resistance Factor is defined.

By clicking , the resistance factors are automatically set to the default values defined in CAN/CSA S6-14. The values can also be modified or entered manually.

(2) Girder Type for Box/Tub Section If Single Box Section is selected, the following clauses are applied for the box/ tub girder design. 10.12.8.4 Moment resistances 10.12.8.5 Combined shear and torsion

(3) Options For Construction Stage

If this option is checked, ULS check for steel section only during construction is performed.

(4) Design Parameters Design and result outputs are generated for the limit states checked in the Design Parameters.

1.3.2 Unbraced Length Unbraced length for steel composite section is considered. The value input here has higher priority than the value calculated from Span Group.

(1) Lb Laterally Unbraced Length is used to calculate lateral torsional buckling resistance in compression flange of I Girder or top flange of Tub Girder. Laterally Unbraced Length is automatically determined using ‘Span Information’ and by assigning member type of cross-frames as ‘Brace’ using the Common Parameter > Modify Member Type function. The user can define/modify the laterally unbraced lengths.



1.3.3 Shear Connectors

Design > Composite Design > Shear Connectors ...

Figure 1.17 Shear Connector Dialog Box

1.3.3 Shear Connectors In this program, studs are used for shear connectors. The parameters used for calculation are shown below.

(1) Category Category for fatigue check, it is fixed as D. (2) Fu Minimum tensile strength of the stud steel (3) Shear Connector Parameters

Figure 1.18 Shear Connector Parameters

(4) Length Between Maximum Moment and Zero Moment The Length between Maximum Moment and Zero Moment needs to be inputted by users to verify pitch as per ultimate limit state.



1.3.4 Fatigue Parameter

Design > Composite Design > Fatigue Parameter ...

Figure 1.19 Fatigue Parameters Dialog Box

1.3.5 Span Information

Structure > Wizard > Composite Bridge > Span Information ...

Figure 1.20 Span Information Dialog Box

1.3.4 Fatigue Parameter (1) Weight of Truck(W)

Load level in CL-W, kN (2) Design Life(y)

Design life, years (3) Number of Stress Cycles(Nd) Number of design stress cycles experienced for each passage of the design truck (4) Reduction Factor(ρ) (5) Average Daily Truck Traffic

1.3.5 Span Information The elements of composite sections are defined as one Span Group. The Span Group will serve the following functions.

- Calculation of Unbraced Length When assigning a span group, support properties are considered for calculating the unbraced length. The unbraced length can also be manually inputted once the corresponding support conditions under the support column are selected. Using the span parameters inputted, the unbraced length can be calculated automatically. However, if the unbraced length is inputted in Section 1.3.2, this value will be applied as the unbraced length first.



1.3.6 Curved Bridge Information

Design > Composite Design > Curved Bridge Info ...

Figure 1.21 Curved Bridge Information Dialog Box

1.3.7 Design Force/Moment

Design > Composite Design > Design Tables > Design Force/Moment...

Figure 1.22 Design Force/Moment Dialog Box

1.3.6 Curved Bridge Information Once the girder radius value of the element units in the steel composite section is entered, the corresponding elements are categorized as curved bridges.

(1) Radius is used to determine the factored bending moment in the flange due to torsional warping. (2) In the current version, the curve type of convex or concave is not used.

1.3.7 Design Force/Moment This feature displays design member forces (strong axis moment, My), weak-axis moment (Mz) and shear stress (VU) for the local axis of elements under selected load combination of steel composite section.


1.4 Load Combination for steel composite section 1.4.1 Application of load combination in midas Civil for CAN/CSA S6-14

(1) Application of load combinations and factors in midas Civil for CAN/CSA S6-14 The load combinations used for the review of each limit state are shown below.

Figure 1.23 Load factors and load combinations

Using the Auto Generation feature of the program, the load combinations regulated by the design code can be automatically generated. Load factors are considered for each load combinations in this program.

Figure 1.24 Live load factors ultimate limit states

Figure 1.25 Permanent loads — Maximum and minimum values of load factors for ULS


(1) Auto Generation of Load Combinations

Result > Combination > Load Combination > Composite Steel Girder Design > Auto Generation ...

Figure 1.26 Automatic Generation of Load Combinations

Dialog Box

(1) Auto Generation of Load Combinations This feature automatically generates load combinations under provision of CAN/CSA S6-14.

1) Design Code When load combinations are generated, they strictly follow the design code selected by the user. 2) Load Factors for Permanent Loads (αD, αE, αP) The user can generate load combinations using maximum value or minimum value or both. When associated load type does not exist, these factors are not activated.


1.4.2 Load combination type for steel composite design Load combination type must be assigned before performing design. When load combinations are generated by auto-generation, the load combination type is automatically assigned, but when load combinations are defined manually or modified, the load combination type should be assigned by the user. Load combinations used in the steel composite section design are categorized under Load Combination Type.


(1) Load Combination Type

Design > Composite Design > Load Combination Type...

Figure 1.27 Load Combination Type Dialog Box

(1) Load Combination Type 1) Ultimate Limit State Choose load combinations for use under review of ultimate limit state. 2) Service Limit State Choose load combinations for review of serviceability limit state. 3) Fatigue Limit State Choose load combinations for review in fatigue limit state.

1.5 Modeling Steel Composite Sections for Construction Stage Analysis In this section, methods of construction stage modeling, implementation of time-dependent material properties of concrete in steel composite section and 3 types of design member forces applied to steel composite section design are explained. Construction stages of steel composite section can be implemented differently for case 1 to 3 as in Table 1.7.

Table 1.7 Modeling Construction Stage Cases for Steel Composite Design

Case Construction Stage Time Dependent Material(Creep / Shrinkage)

Case 1 Defined

Defined

Case 2 Not Defined (Apply modular ratio of 3n)

Case 3 Not Defined Not Defined (Apply modular ratio of 3n)

1.5.1 Member forces and stresses used in steel composite section design

(1) Member forces For design of steel composite section, member forces per construction stage of steel composite section must be calculated. The program considers two main factors for design and review of construction stage of steel composite section. ▪Construction stages of steel composite section ▪Time dependent material properties of Concrete (Creep, Shrinkage and Compressive Strength)


Design member forces used for design of steel composite section are divided into three main categories. Table 1.8 Design Force and Moment for Steel Composite Design

Design Force/Moment Description

Dead (Before) Member forces due to permanent loads occurring before the concrete deck is activated. Only steel section properties are used to calculate stresses. ex) Self weight of steel and concrete deck

Dead (After) Member forces due to permanent loads occurring after concrete deck is activated Long term section properties of composite section are used. ex) Self weight of wearing surface and barrier

Short Term Member forces from the post-construction state and load cases not included in the above categories. Short term section properties of composite section are used. ex) Traffic loads, wind loads

When construction stages are included in the model in midas Civil, the design moments for Dead (Before) are taken as the moments of steel section due to Dead Load (CS) and Erection Load (CS) whose load type is Dead Load (D) and the design moments for Dead (After) are taken as the moments of composite section due to Erection Load (CS) whose load type is Dead Load of Component and Attachements (DC) or Dead Load of Wearing Surfaces and Utilities (DW). Example:

Permanent loads Load Type Analysis results

Load Factor

Design forces Stage 1

Steel only Stage 2

Composite Dead (Before)

Dead (After)

Self Weight of Steel Dead Load (CS) 100 100 1.1 110 Self Weight of Concrete Erection (D) 100 100 1.2 120

Self Weight of Barrier Erection (DC) 0 100 1.2 120 Self Weight of Wearing

Surface Erection (DW) 0 100 1.5 150

Sum 230 270

Above rule has changed in Civil 2018 (v1.2) in order to account for various erection sequence of slab. The design moments for Dead (Before) and Dead (After) are determined as shown in the table below.

Dead Load (CS) Erection Load (CS) Moments applied to steel section Dead (Before) Dead (Before) Moments applied to composite section Ignored Dead (After)

(2) Stress Bending stress used for design of steel composite section is calculated as follows:

Where,

Md : bending moment at SLS due to dead load, steel section only

Msd : bending moment at SLS due to superimposed dead load, composite section

ML : bending moment at SLS due to live load, composite section

S : elastic section modulus of steel section

S3n : elastic modulus of section comprising the steel beam and the concrete slab, calculated using a modular ratio of 3n, long-term load, positive moment


Sn : elastic modulus of section comprising the steel beam and the concrete slab, calculated using a modular ratio of n, short-term load, positive moment

S’ : elastic modulus of composite section comprising the steel section and reinforcement, negative moment 1.5.2 Case 1 In Case 1, construction stages and time dependent material properties of concrete (Creep/Shrinkage) are defined and Multiple Modulus of Elasticity is not checked on in the Section Data dialog. The effects of creep and shrinkage of concrete are directly calculated and checked by Creep Secondary (CS) or Shrinkage Secondary (CS) load cases. The Composite sections for Construction Stage function must be defined. Otherwise, the sections shall be excluded from design. Note that if time dependent material property information is inputted as well as long-term modulus of elasticity, long-term modulus of elasticity has higher priority in consideration of calculation.

Define Composite Section for Construction Stage


Composite Section for Construction Stage

Load >Load Type> Construction Stage > Composite Section for C.S...

Figure 1.28 Add/Modify Composite Section for

Construction Stage Dialog

Composite Section for Construction Stage For definition of composite section for construction stage, information in this window must be defined. (1) Active Stage Construction stage where steel composite section should be activated is inserted. (2) Construction sequence

1) "Material Type" column □ By choosing Element, material property of the element is used. □ By selecting Material, material information chosen under "Material" Column is applied with higher priority. 2) Composite Stage column Construction stages where steel girder and concrete slab should be activated are chosen separately. 3) Age column Age information when each part is activated is input. Information in this column has higher priority over the age input during definition of construction stage.


Define Erection Load

(1) Define Erection Load

Analysis > Analysis Control > Construction Stage > Load Cases to be Distinguished from Dead Load for C.S Output >Add (Modify/delete)...

Figure 1.29 Define Erection Load Dialog

1) Define Erection Load Erection Load is defined.

1) Load Type for C.S Determine the Load Type for the construction stages of the composite section. Load types are considered by the software for auto generation of load combinations. 2) Assignment Load Cases Define Erection Load by selecting and moving the Load Cases desired from the List of Load Case panel to the Selected Load Case panel.

1.5.3 Case 2 In Case 2, construction stages are defined without the time dependent material property (Creep/Shrinkage) information. Long term effects are considered using the long term modular ratio entered in the Section Data dialog box. Sections for different construction stages must be defined and differentiated using the Composite Section for Construction Stage definition. Otherwise, they will not be considered for the design check.

(1) Member forces under Dead (Before) Dead (Before) is applied before the concrete deck is activated. (Refer to Table 1.8 in the "Introduction") Self weight of steel and concrete belongs to Dead (Before).

(2) Member forces under Dead (After) The effects of Creep/Shrinkage are reflected by applying the ratio of elastic modulus that is inputted in the Section Data (Refer to Section 1.1.1 (1)) for the long-term stage. In other words, the Creep/Shrinkage effects are reflected by using the section information with the ratio of elastic modulus that considers the time dependent material property for the analysis and design. These long term modular ratios defined for considering creep and shrinkage, automatically generate Section Stiffness Scale Factors for the sections in which these are inputted. Section Stiffness Scale Factors need to be activated in the construction stages in accordance with the Composite Section for Construction Stage definition, i.e. the Section Stiffness Scale Factors are activated when the corresponding section becomes composite as per the definition of composite section for CS. Super-imposed dead loads, i.e. wearing surface, barrier belong to Dead (After).

(3) Short term member forces The ratio of elastic modulus of the composite section is calculated using the DB value inputted. All the load cases which are not activated in the Construction Stage are considered as the short-term loads.


1.5.4 Case 3 In case the construction stages are not defined, users can model and define steel composite sections by using the Load Case for Pre-Composite Section function.

Load > Load Type > Settlement/Misc. > Misc. > Pre-composite Section. For this case, short- and long-term ratios of elastic modulus defined in the section data (Refer to Section 1.1.1 (1)) are used. In this case, instead of member forces per construction stages, member forces under Dead (Before) is used to check the constructibility of the model.

(1) Member force under Dead (Before) In the Load Cases for Pre-Composite Section dialog box, users can define which load cases to account for the member forces and apply as Dead (Before) in design. Since this is for pre-composite state, the steel only section properties are used (Refer to Section 1.1.1 (1)).

Figure 1.30 Load Cases for Pre-Composite Section

(2) Member forces under Dead (After) Member forces under Dead (After) use the long term section properties. These loads should be separated from the short term member forces by the use of Analysis > Analysis Control > Boundary Change Assignment.

1) Data Selection Check the box corresponding to Section Stiffness Scale Factor. As explained earlier, Section Stiffness Scale Factors are used for considering the long term section properties.

2) Boundary Group Combination Create a boundary group combination considering the appropriate boundary groups from the boundary group list. The created boundary group combinations need to be selected for the post composite long term load cases. For the static load cases assigned with the section stiffness scale factor boundary groups, long term section property will be used.

Dead Load (Before)


Figure 1.31 Load Cases for Post-Composite Section

(3) Short-term member forces The ratio of elastic modulus from the database is used for the short-term loads of the composite section. All load cases are considered for the short-term loads except the ones considered for the Dead (Before) and Dead (After).

1.5.5 Torsional constant of tub girder before composite section

The torsional constant of a tub girder before the concrete slab is activated is somewhere between open section and closed section. Top flanges of tub section are restrained by the top lateral bracing system. The behaviour of a tub girder before the concrete deck has cured may be analyzed as a quasi-closed section by replacing the lateral bracing with an equivalent plate. In this version, the quasi-closed section method is not supported. The torsional constant is calculated based on closed section using the thickness of top flange. It is recommend that the user adjust the torsional constant using Stiffness Scale Factor.

Dead Load (After)


Application of CAN/CSA S6-14

132Chapter 3. Steel Composite Box Girder Design – CAN/CSA S6-14

1. Composite Box Girder 1.1 Overview

1.1.1 General This design function applies to the design of simple and continuous composite box girder bridges of spans up to 110 m, consisting of one or more straight steel single-cell box girders, acting compositely with a concrete deck, and symmetrical about a vertical axis. The top of the box may be open with twin steel flanges or closed with a steel flange plate. (1) Proportioning The program checks if the steel section alone is proportioned to support all factored loads applied before the concrete is activated. The lateral restraint conditions existing when the different loads are applied are taken into account. The web of the steel section is designed to carry the total vertical shear and is proportioned in accordance with the requirements of Clauses 10.10.5 to 10.10.8 of CAN/CSA S6-14. The control of cracking of the slab is not taken into account. The program assumes that the whole width of slab is effective. (2) Effects of creep and shrinkage To account for the effect of creep due to that portion of dead load that is applied after the concrete slab is activated, time-dependent material properties can be applied or a modular ratio of 3n can be used in calculating the section properties. 1.1.2 Effective width of tension flanges The effective width of bottom flange plates in tension shall be taken as not more than one-fifth of the span for simply supported structures and not more than one-fifth of the distance between points of contraflexure under dead load for continuous structures. The program assumes that the whole width of tension flanges is effective. 1.1.3 Web plates Webs are proportioned in accordance with Clause 10.10 of CAN/CSA S6-14 and, for single box girders, both the web plates and the shear connectors are proportioned for the sum of the factored shears due to bending and torsion. The shear force to be considered on each web is Vf /cosθ , where Vf is one-half of the total vertical shear force at the ULS on one box girder and θ is the angle of inclination of the web plate to the vertical. The inclination of the web plates shall not exceed 1 horizontal to 4 vertical. The program does not check the inclination of the web plates.

Chapter 3. Steel Composite Box Girder Design – CAN/CSA S6-14 133

1.1. ULS 1.1.1 Bending The factored moment resistance of the composite section is determined as follows: (1) Positive Moment - Class 1 & 2 sections Width-to-thickness ratio of elements in compression


Web

Stress distribution Fully plastic stress distribution as shown in Figure 1.32.

Figure 1.32 Class 1 and 2 sections in positive moment regions

Factored moment resistance, Mr

Single box girder The factored moment resistance of single box girders, Mr is calculated as shown in Table 1.9 using a reduced normal stress, Rv Fy , for the tensile resistance of the bottom flange in place of Fy. It is assumed that the whole width of tension flange is effective.

CAN/CSA S6-14 10.11.5.1 10.9.2

CAN/CSA S6-14 10.11.5.2.1

CAN/CSA S6-14 10.12.5.1.2 10.11 10.12.2 10.12.8.4





In Web wt PP

rtrbsc PPPP

]1[2 w

rbrtsct

PPPPPPD

Y

])([2

22YtY

DP

M w


In Top flange

cwt PPP

rtrbs PPP

])([2

22YtY

tP

Mc

c



cwt PPP

rtrbss

rb PPPtc

s

s

tPY

M2

2



rbcwt PPPP

rtss

rb PPtc

rbCY

s

s

tPY

M2

2



rbcwt PPPP

rtss

rt PPtc

s

rbrttwcs P

PPPPPtY )(

s

s

tPY

M2

2



rtrbcwt PPPPP rtCY


ss

rt Ptc

s

s

tPY

M2

2



rtrbcwt PPPPP

ss

rt Ptc

s

rttwcrbs P

PPPPPtY )(

s

s

tPY

M2

2



deck. : Distance from the plastic neutral axis to the centerline of the bottom layer of longitudinal concrete

deck. : Distance from the plastic neutral axis to the midthickness of the tension flange. : Distance from the plastic neutral axis to middepth of the web. : Distance from the plastic neutral axis to midthickness of the compression flange. : Distance from the plastic neutral axis to midthickness of the concrete deck.

(by reinforcement)

(by reinforcement)

(by steel girder) (by steel girder) (by steel girder)

(by concrete slab)

Multiple box girder Same method as single box girder is applied except that the tensile resistance of the bottom flange is not reduced by Rv.



Web


Single box girder For composite sections in which the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, equals or is less than , the factored moment resistance of single box girders is determined in the same way as Class 1 & 2 under positive moment.

When the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, exceeds , the factored moment resistance, Mr, of the single box girders is calculated on the basis of fully plastic stress blocks, as shown in Figure 1.34, using a reduced normal stress, Rv Fy , for the tensile resistance of the bottom flange in place of Fy. It is assumed that the whole width of tension flange is effective.

CAN/CSA S6-14 10.11.6.1 10.9.2

CAN/CSA S6-14 10.12.5.1.2 10.12.2 10.12.8.4 10.11.6.2.1 10.11.5.2

CAN/CSA S6-14 10.12.5.1.2 10.11.6.2.2


where fs : coexisting shear stress due to warping torsion

The area of the steel section in compression, A‘sc , includes the top flange and a web area of

, and the area of the steel section in tension, A‘st , is calculated as follows:

Figure 1.34 Class 3 Sections in positive moment regions

Multiple box girder

Same method as single box girder is applied except that the tensile resistance of the bottom flange is not reduced by Rv.



Web The width-to-thickness ratio of a transversely stiffened web, h/w without longitudinal stiffeners, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. The following provision of CAN/CSA S6-14 is not supported in the program. “In determining a width-to-thickness ratio, Fy may be replaced by the maximum compressive stress due to the factored ULS loads if the maximum shear at the FLS does not exceed Vr calculated in accordance with Clause 10.10.5.1, taking Ft = 0 and φs = 1.0.” When a longitudinal stiffener is provided, the width-to-thickness ratio, h/w, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped.

CAN/CSA S6-14 10.11.7.1

10.10.4.1 10.10.4.2



Single box girder For composite sections in which the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, does not exceed

, the factored moment resistance is determined in the same way as Class 1 & 2 under positive moment.

When the depth of the compression portion of the web of the steel section, calculated on the basis of a fully plastic stress distribution, exceeds , whether or not longitudinal stiffeners are provided, the factored moment resistance, Mr, of the composite section is calculated in the same way as Class 3 under positive moment. Multiple box girder

Same method as single box girder is applied except that the tensile resistance of the bottom flange is not reduced by Rv.

(2) Negative Moment - Class 1 & 2 sections Width-to-thickness ratio of elements in compression

Bottom Flange

Web


Single box girder When it is braced against lateral torsional buckling, Mr is calculated on the basis of a fully plastic stress distribution in the structural steel and reinforcement, as shown in Table 1.10.





CAN/CSA S6-14 10.12.5.1.2 10.11.7.2.1

10.11.5.2

CAN/CSA S6-14 10.12.5.1.2 10.11.7.2.2

10.11.6.2.2

CAN/CSA S6-14 10.11.5.1

10.9.2



Where,



(by steel girder)

For laterally unbraced members, Mr is based on its lateral torsional buckling resistance. The unbraced bending resistance of the structural steel section alone is used. For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr, is calculated as


where

where







βx= 0.0 B1 = 0.0

so that

CAN/CSA S6-14 10.11.5.3.1 10.10.2.3


The general expression for the critical elastic moment and formulas for β x, J, and Cw for open-top box girder as specified in Clause C10.10.2.3 of CSA S6.1 are used.

where

, positive when S on compression side of C Iyy : minor axis moment of inertia of the cross-section

Multiple box girder Same method as single box girder is applied.


Bottom Flange

Web

Stress distribution Linear stress distribution at first yielding or buckling, as shown in Figure 1.36

CAN/CSA S6.1-14 10.10.2.3

CAN/CSA S6-14 10.11.6.1 10.9.2

CAN/CSA S6-14 10.11.6.3.1.1


Figure 1.36 Class 3 Sections in negative moment regions


Single box girder The following requirements are checked:

where S and S are the elastic section moduli with respect to the bottom fibre. Fcr is determined as follows. Unstiffened compression flanges i) when :

ii) when :

iii) when :

Compression flanges stiffened longitudinally

i) when :

ii) when :

iii) when :

The buckling coefficient, k1, is determined as follows:

For n = 1:

CAN/CSA S6-14 10.12.5.1.2 10.11.6.3.1.2

CAN/CSA S6-14 10.12.5.2

CAN/CSA S6-14 10.12.5.3


For n > 1:

where n = number of longitudinal stiffeners Is = moment of inertia of each stiffener about an axis parallel to the flange and at the base of the stiffener

Compression flanges stiffened longitudinally and transversely This is not supported in this version.

where S and S are the elastic section moduli with respect to the top fibre of the steel section.

where S is the elastic section modulus with respect to the centroid of the top layer of longitudinal slab reinforcement.

Fatigue limit check for longitudinal reinforcement is not supported. The requirement of 10.11.5.3.2 of CAN/CSA S6-14 is not supported.

Multiple box girder Same method as single box girder is applied.


Bottom Flange

Web




CAN/CSA S6-14 10.12.5.1.2 10.11.7.1 10.10.4.1 10.10.4.2


Factored moment resistance, Mr Single box girder

The factored moment resistance, Mr is calculated in the same way as Class 3 under negative moment. If longitudinal stiffeners are not provided and , the factored moment resistance, calculated for the compression flange, is reduced by the following factor.

Multiple box girder

Same method as single box girder is applied. 1.1.2 Shear (1) Factored shear resistance The factored shear resistance of the web of a flexural member, Vr , is taken as


For unstiffened webs, a/h is considered infinite, so that kv = 5.34. At girder end panels and adjacent to large openings in the web, the resistance shall be calculated using Ft = 0. However, there is no consideration about the end panels and openings in the web in the program.

CAN/CSA S6-14 10.12.5.1.2 10.11.7.3.1 10.11.6.3.1 10.10.4.3

CAN/CSA S6-14 10.11.2 CAN/CSA S6-14 10.10.5.1


(2) Combined shear and moment When subject to the simultaneous action of shear and moment, transversely stiffened webs that depend on tension field action to carry shear, i.e., with , are proportioned so that

(3) Combined shear and torsion The web plates are proportioned for the sum of the factored shears due to bending and torsion.





The width of a plate used as a stiffener shall not be less than 50 mm plus h/30 and shall not be less than one-quarter of the full width of the flange. The width-to-thickness ratio of intermediate transverse stiffeners shall not exceed . The projecting stiffener width shall not exceed 30t. (5) Longitudinal web stiffeners The spacing, a, of transverse stiffeners of longitudinally stiffened webs shall not exceed 1.5hp , where hp is the maximum subpanel depth. The total web depth, h, is used in determining the shear capacity, Vr, of longitudinally stiffened girders. Longitudinal stiffeners shall be proportioned so that

CAN/CSA S6-14 10.10.5.2

CAN/CSA S6-14 10.12.8.5

CAN/CSA S6-14 10.10.6.1

CAN/CSA S6-14 10.10.6.2

CAN/CSA S6-14 10.10.7.1

CAN/CSA S6-14 10.10.7.2




1.2 Serviceability Limit State 1.2.1 Control of permanent deflections For composite beams and girders, the normal stress in either flange of the steel section due to serviceability dead and live loads shall not exceed 0.90 Fy. The following requirements shall be satisfied: (a) in positive moment regions:

(b) in negative moment regions:

1.3 Fatigue Limit State 1.3.1 General The FLS considered includes direct live load effects, i.e., live load-induced fatigue. The effects of local distortion within the structure, i.e., distortion-induced fatigue are not taken into account in the program. (1) Fatigue check location Fatigue of the base metal at the connection plate welds to the flanges at the intermediate cross-frame

o Bottom surface of top flange o Top surface of bottom flange

Fatigue of the base metal at the stud shear-connector weld to the top flange

o Top surface of top flange Fatigue resistance of high-strength bolts loaded in tension is not supported. Fatigue resistance of stud shear connectors is supported and explained in the separate clause in this document. (2) Longitudinal warping normal stress For single box girders, longitudinal warping normal stresses shall be taken into account for fatigue. This is not taken into account in this version. 1.3.2 Calculation of stress range The stress range for load-induced fatigue is calculated as the difference between the maximum stress and minimum stress at a given location due to live load. At locations where the stresses resulting from the permanent loads are compressive, load-induced fatigue is disregarded when the compressive stress is at least twice the maximum tensile live load stress.

CAN/CSA S6-14 10.11.4

CAN/CSA S6-14 10.17.2.1


1.3.3 Design criteria For load-induced fatigue, each detail shall satisfy the requirement that

where CL = 1.0 when W ≤ 625 kN CL = 0.20 + 500/W when W > 625 kN fsr = calculated fatigue stress range at the detail due to passage of the CL-W Truck The load-indueced fatigue check in bridge decks is not supported. 1.3.4 Fatigue stress range resistance (1) Fatigue stress range resistance of a member or detail The fatigue stress range resistance of a member or a detail, Fsr , other than for shear studs, is calculated as follows: Fsr = fatigue resistance

where γ , γ ‘ = fatigue life constants pertaining to the detail category and specified in Table 1.11 Fsrt = constant amplitude threshold stress range


Table 1.11 Fatigue life constants and constant amplitude threshold stress ranges


CAN/CSA S6-14 10.17.2.2

CAN/CSA S6-14 10.17.2.3.1


The values of Nd can be defined either by the program or user input. For the auto-calculation, the span length should be defined from the ‘Span Information’ function. Table 1.13 Average daily truck traffic

1.3.5 Detail categories The detail categories used in the design are as follows: -Bottom surface of top flange & Top surface of bottom flange

Detail category C1, Example 6 -Top surface of top flange

Detail category C, Example 13 Table 1.14 Detail categories for load-induced fatigue

CAN/CSA S6-14 10.17.2.4


2. Shear Connector 2.1. ULS

2.1.1 Shear connector resistance (1) General The ULS check of shear connectors is performed by checking if the number of shear connectors applied in each shear span exceeds the minimum number of shear connectors. The number of shear connectors applied in the shear span, Nuse, is calculated as follows:

where a shear span, L, is a segment between points of maximum and zero moment at the ULS and it should be entered by the user. p = pitch of shear connectors floor function rounds a number down to the nearest integer. Nsc = number of shear connectors in a row The minimum number of shear connectors in each shear span is calculated as follows:

P is determined as follows: (a) for positive moment:

(i) when the plastic neutral axis is in the concrete slab: ; and (ii) when the plastic neutral axis is in the steel section: ; and

(b) for negative moment: . (2) Stud connectors in cast-in-place deck slab The factored shear resistance, qr , of a headed stud shear connector with h/d ≥ 4 is taken as

where Fu = minimum tensile strength of the stud steel Asc = cross-sectional area of one stud shear connector The program checks if the spacing of shear connectors is not less than 4d, nor greater than 600 mm. (3) Stud connectors in full-depth precast panels This is not supported in the program. (4) Channel connectors in cast-in-place deck slab Channel connectors are not supported in the program. 2.1.2 Longitudinal shear The longitudinal shear check along potential shear planes is not supported.

2.2. FLS 2.2.1 Fatigue resistance of stud shear connectors Stud shear connectors are designed for the following stress range, τ rs :

where CL = 1.0 when W ≤ 625 kN = 0.20 + 500/W when W > 625 kN Vsc = range of design shear force at the section along the length of the beam where the fatigue resistance of the shear connectors is being evaluated. The shear connectors are proportioned

CAN/CSA S6-14 10.11.8.3.1

CAN/CSA S6-14 10.11.8.3.2

CAN/CSA S6-14 10.11.8.4

CAN/CSA S6-14 10.17.2.7


for the sum of the factored shears due to bending and torsion. Q = first moment of area of the transformed section at the interface between the concrete slab and the steel section s = shear stud group spacing Asc = cross-sectional area of a shear stud n = number of shear studs in the group at the cross-section being evaluated It = moment of inertia of the transformed composite section about the axis of bending

= fatigue stress range resistance for Category D, as determined as follows:

Fatigue life constant, γ =

Fatigue life constant, γ’ = Fsrt = constant amplitude threshold stress range

where y = design life (equal to 75 years) Nd = number of design stress cycles experienced for each passage of the design truck, as specified in Table 1.14 ADTTf = single-lane average daily truck traffic, which is estimated as p (ADTT), where p is 1.0, 0.85, or 0.80 for the cases of one, two, or three or more lanes available to trucks, respectively, and ADTT shall be as specified in Table 1.13.


The values of Nd can be defined either by the program or user input. For the auto-calculation, the span length should be defined from the ‘Span Information’ function. When stud shear connectors are not provided in negative moment regions, additional connectors, Na in number, shall be provided at each location of contraflexure, where

This requirement is not considered in the program.


3. Constructibility of a Composite Box Girder3.1. ULS

3.1.1 Bending (1) Positive moment (Tub girder) - Class 1 & 2 sections - Width-to-thickness ratios of elements in compression

Top Flange

Web


- Factored moment resistanc, Mr

- Laterally supported members The factored moment resistance, Mr is calculated based on the equation below.

The tensile resistance of the bottom flange is reduced to Rv Fy and it is assumed that the whole width of tension flange is effective.

- Laterally unbraced members For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr, is calculated as


where


L = length of unbraced segment of beam, mm


CAN/CSA S6-14 10.10.2.1 10.9.2

CAN/CSA S6-14 12.5.1.1 10.10.2.2

CAN/CSA S6-14 10.10.2.3


For doubly symmetric sections, βx= 0.0 B1 = 0.0

so that


where

, positive when S on compression side of C Iyy : minor axis moment of inertia of the cross-section

- Bending about the minor axis For a section subjected to bending about its minor axis, whether laterally braced or unbraced, the factored moment resistance, Mr, is calculated as

CAN/CSA S6.1-14 10.10.2.3

CAN/CSA S6-14 10.10.2.4


- Class 3 sections - Width-to-thickness ratio of elements in compression

Top Flange

Web



Laterally supported members When continuous lateral support is provided to the compression flange of a member subject to bending about its major axis, the factored moment resistance, Mr, is calculated as

The tensile resistance of the bottom flange is reduced to Rv Fy and it is assumed that the whole width of tension flange is effective.

Laterally unbraced members For a section subjected to bending about its major axis and laterally unbraced over a length, L, the factored moment resistance, Mr , is calculated as

where The critical elastic moment, Mu, of doubly symmetric and monosymmetric sections is taken as

where


L = length of unbraced segment of beam



βx= 0.0 B1 = 0.0

so that

CAN/CSA S6-14 10.10.3.1 10.9.2

CAN/CSA S6-14 10.10.3.2

CAN/CSA S6-14 10.10.3.3



- Class 4 sections For beams and girders with continuous lateral support provided to the compression flange, with webs that meet the requirements of Class 3, and whose flanges exceed the slenderness limits of Class 3, the factored moment resistances is computed as for a Class 3 section, except that the elastic section modulus, S, is replaced by an effective section modulus, Se, determined using (a) an effective flange width of , for flanges supported along two edges; and (b) an effective projecting flange width of , for flanges supported along one edge. However, the projecting flange width shall not exceed 30t. - Bending about the minor axis For a section subjected to bending about its minor axis, whether laterally braced or unbraced, the factored resistance, Mr, shall be calculated as

- Stiffened plate girders - Width-to-thickness ratio of flanges The program checks if stiffened plate girders have Class 1, 2, or 3 flanges. - Width-to-thickness ratios of webs The width-to-thickness ratio of a transversely stiffened web, h/w, without longitudinal stiffeners, shall not exceed . If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. The following provision of CAN/CSA S6-14 is not supported in the program. “In determining a width-to-thickness ratio, Fy may be replaced by the maximum compressive stress due to the factored ULS loads if the maximum shear at the FLS does not exceed Vr calculated in accordance with Clause 10.10.5.1, taking Ft = 0 and φs = 1.0.” When a longitudinal stiffener is provided, the width-to-thickness ratio, h/w, shall not exceed

. If this requirement is not satisfied, the section is not valid. Therefore, the moment resistance check is skipped. - Moment resistance The moment resistance, Mr is calculated in the same way as Class 3 sections. If longitudinal stiffeners are not provided and , the moment resistance, calculated for the compression flange, is reduced by the following factor.

(2) Negative moment (Tub girder) - Class 1, 2 & 3 sections - Width-to-thickness ratios of elements in compression

Bottom Flange

CAN/CSA S6.1-14 10.10.2.3

CAN/CSA S6-14 10.10.3.4

CAN/CSA S6-14 10.10.3.5

CAN/CSA S6-14 10.10.4.1

CAN/CSA S6-14 10.10.4.1 10.17.2.5

CAN/CSA S6-14 10.10.4.3


Web

h = dc = depth of compression portion of web in flexure, mm


The factored moment resistance of the steel section acting alone before the attainment of composite action, whether laterally braced or unbraced, is determined as follows: Top flange in tension The factored moment resistance, Mr is calculated using the elastic section modulus of the steel section alone. Unstiffened compression flanges The factored moment resistance with respect to the compression flange is calculated as follows: i) when :

ii) when :

iii) when :

Compression flanges stiffened longitudinally The factored moment resistance with respect to the compression flange is calculated as follows: i) when :

ii) when :

iii) when :

CAN/CSA S6-14 10.12.5.1.1

CAN/CSA S6-14 10.12.5.2

CAN/CSA S6-14 10.12.5.3


The buckling coefficient, k1, is determined as follows:

For n = 1:

For n > 1:

where n = number of longitudinal stiffeners Is = moment of inertia of each stiffener about an axis parallel to the flange and at the base of the stiffener

Compression flanges stiffened longitudinally and transversely This is not supported in this version.

- Class 4 sections For beams and girders with continuous lateral support provided to the compression flange, with webs that meet the requirements of Class 3, and whose flanges exceed the slenderness limits of Class 3, the factored moment resistances is computed as for a Class 3 section, except that the elastic section modulus, S, is replaced by an effective section modulus, Se, determined using an effective flange width of , for flanges supported along two edges. - Bending about the minor axis For a section subjected to bending about its minor axis, whether laterally braced or unbraced, the factored resistance, Mr, shall be calculated as

-Stiffened plate girders Width-to-thickness ratio of elements in compression

Bottom Flange

Web




Factored moment resistance, Mr The factored moment resistance, Mr is calculated in the same way as Class 1, 2 & 3 under negative moment. If longitudinal stiffeners are not provided and ,

CAN/CSA S6-14 10.10.3.4

CAN/CSA S6-14 10.10.3.5

CAN/CSA S6-14 10.10.4.1

CAN/CSA S6-14 10.10.4.1 10.17.2.5

CAN/CSA S6-14 10.10.4.3


the factored moment resistance, calculated for the compression flange, is reduced by the following factor.




CAN/CSA S6-14 10.10.5.1

CAN/CSA S6-14 10.10.5.2








CAN/CSA S6-14 10.10.6.1

CAN/CSA S6-14 10.10.6.2

CAN/CSA S6-14 10.10.7.1

CAN/CSA S6-14 10.10.7.2


4. Horizontally curved box girders 4.1 Composite box girder

4.1.1 Torsional constant of tub girder before composite section The torsional constant of a tub girder before the concrete slab is activated is somewhere between open section and closed section. Top flanges of tub section are restrained by the top lateral bracing system. The behaviour of a tub girder before the concrete deck has cured may be analyzed as a quasi-closed section by replacing the lateral bracing with an equivalent plate. In this version, the quasi-closed section method is not supported. The torsional constant is calculated based on closed section using the thickness of top flange. It is recommended that the user adjust the torsional constant using Stiffness Scale Factor. 4.1.2 Top flanges Top flanges shall be Class 3 or better. Flanges are proportioned to satisfy the following requirements: (a) Strength of either flange:

where Mfx = factored bending moment due to flexure Mrx = φsFy Sx

where Sx = elastic section modulus of the girder about its major axis

Mfw = factored bending moment in the flange due to torsional warping. Mfw is taken as regardless of the intermediate lateral restraint.

Where L = the distance between lateral restraintswr = the lateral load on the flange is a distributed lateral load, wr = Mfx/hR. Mfx = the moment in the vertical plane on the girder h = the clear depth of web between flanges R = the radius of curvature of the girder web (user input)

Mry = φsFy Sy where Sy = elastic section modulus of the flanges only about an axis in the plane tangent to the web of the girder

(b) Stability of compression flange:

where

where

wc = 0.5 where the lateral bending moment in the flange has major reversals, but 1.0 where the lateral bending moment does not have major reversals

CAN/CSA S6-14 10.13.7.1

CAN/CSA S6-14 10.13.7.3 10.13.6.1.2

CAN/CSA S6-14


4.1.3 Bottom flanges (a) Tension flanges The factored moment resistance with respect to the tension flange is determined using a reduced normal stress, Rv Fy , in place of Fy , with Rv as follows:

It is assumed that total width is effective. (b) Stiffened compression flanges The following requirements shall apply to stiffened compression flanges:

When the torsional shear stress When , the factored moment resistance, Mr, is taken as

When and , the factored moment resistance,

Mr, is taken as

where k1 = the buckling coefficient, which shall not exceed 4.0 and, when at least one longitudinal stiffener is provided,

where

10.13.7.4.1

CAN/CSA S6-14 10.13.7.4.2.1


Is = moment of inertia of stiffener (c) Unstiffened compression flanges The requirements of stiffened compression flange apply to unstiffened compression flanges, except that the following values apply:

k1 = 4; ks = 5.34; and bs = b = width of flange between webs.

4.1.4 Webs The factored shear resistance is calculated in accordance with the provision for straight girders. The following requirements are also applied: (a) Webs without stiffeners: Tension-field action is neglected in webs without transverse

stiffeners. (b) Webs with transverse stiffeners only:

(i) Tension-field action is included in the calculated resistance when the geometry satisfies all of the following: (1) web slenderness h/w ≤ 160; (2) ratio of braced length to radius of horizontal curvature of the girder, Lb/R ≤ 0.1; and (3) transverse stiffener spacing a/h ≤ 3.

(ii) When subject to the simultaneous action of shear and moment, transversely stiffened webs that depend on tension-field action to carry shear is proportioned so that

(c) Webs with transverse and longitudinal stiffeners: When the longitudinal stiffeners are provided at a distance 0.2h from the compression flange, the program checks the web slenderness ratio satisfies the following condition.

When longitudinal stiffeners are located 0.2h from both the compression flange and the tension flange, the program checks if the web slenderness ratio does not exceed . Tension-field action is neglected. (d) Proportioning of transverse web stiffeners: the program checks if stiffeners are proportioned so that

CAN/CSA S6-14 10.13.7.4.2.2

CAN/CSA S6-14 10.13.6.1.3


I is taken about an axis at the mid-plane of the web for stiffener pairs, or at the near face of the web for single stiffeners. Where transversely stiffened webs depend on tension-field action to carry the applied shear, the program also checks if the transverse stiffeners are proportioned so that.



The width of a plate used as a stiffener shall not be less than 50 mm plus h/30 and shall not be less than one-quarter of the full width of the flange. The width-to-thickness ratio of intermediate transverse stiffeners shall not exceed . The projecting stiffener width shall not exceed 30t. (e) The program checks if longitudinal stiffeners are proportioned so that


where I and r are calculated about a centroidal axis parallel to the web for a section comprising the stiffener or stiffeners and a strip of web 10w wide on each side.

(f) Monosymmetric sections: the program does not check if the slenderness ratio of the compression portion of webs of monosymmetric sections with an axis of symmetry in the plane of loading does not exceed one-half of the applicable value specified in Item (a), (b), or (c). This should be separately checked by the user.


Steel Composite Design Result

163Chapter 3. Steel Composite Box Girder Design – CAN/CSA S6-14

1. Ultimate Limit State Result 1.1 Flexure

(1) Result Table As shown in the table below, the results can be checked in the result table.

Design > Composite Design > Design Result Tables > Ultimate Limit State (flexure)…

Figure 1.37 Result Table for Ultimate Limit State of Flexure

Where,

Type: Load combination type (Fx-max, Fx-min, ... Mz-min). When a moving load case is included, there are 12 sets of concurrent forces. Load combination type shows which sets of concurrent forces givecritical forces.

Top Class: Class of top flange Bot Class: Class of bottom flange Web Class: Class of web

My : yield moment

Mp : plastic moment. This is provided for Class 1 and 2 sections only.





Figure 1.38 Excel Report for Ultimate Limit State of Negative Moment


1.2 Shear (1) Result Table As shown in the table below, the results can be checked in the result table.

Design > Composite Design > Design Result Tables > Ultimate Limit State (shear)…

Figure 1.39 Result Table for Ultimate Limit State of Shear

Where,








Figure 1.40 Excel Report for Ultimate Limit State of Shear


2. Service Limit State Result (1) Result Table


Design > Composite Design > Design Result Tables > Service Limit State…

Figure 1.41 Result Table for Service Limit State Where,

Stress 0.90Fy : limit stress in the flange of the steel section to control permanent deflections Md : bending moment at SLS due to dead load, steel section only S : elastic section modulus of steel section Msd : bending moment at SLS due to superimposed dead load, composite section S3n : elastic modulus of section comprising the steel beam and the concrete slab, calculated using amodular ratio of 3n, long-term load, positive moment ML : bending moment at SLS due to live load, composite section Sn : elastic modulus of section comprising the steel beam and the concrete slab, calculated using amodular ratio of n, short-term load, positive moment S’ : elastic modulus of composite section comprising the steel section and reinforcement, negative moment

(2) Excel Report


Figure 1.42 Excel Report for Serviceability Limit State


3. Constructibility Result 3.1 Flexure

(1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Construction Stage (flexure)...

Figure 1.43 Result Table for Constructibility Limit State of flexure

Where,

Mfy : factored bending moment about the y-axis of the cross-section Mry : factored moment resistance about the y-axis of the cross-section Mfz : factored bending moment about the z-axis of the cross-section Mrz : factored moment resistance about the z-axis of the cross-section Comb.1 : strength check ratio of flange for the combined moments Comb.2 : stability check ratio of compression flange for the combined moments (2) Excel Report The results can be viewed in an Excel Report as shown below.

Figure 1.44 Excel Report for Constructibility of Negative Moment


3.2 Shear (1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Construction Stage (shear)...

Figure 1.45 Result Table for Constructibility of Shear

Where,






Mf/Mr : moment check ratio



Figure 1.46 Excel Report for Constructibility of Shear


4. Fatigue Limit State Result (1) Result Table The results can be viewed in a result table as shown below.

Design > Composite Design > Design Result Tables > Fatigue Limit State...

Figure 1.47 Result Table for Fatigue Limit State

Where,

Lcom : Load combinations used in the calculation

fsr : calculated FLS stress range at the detail due to passage of the CL-W Truck

Fsr : fatigue stress range resistance

tau_rs: fatigue shear stress range for the stud shear connectors

Vsc : range of design shear force at the section along the length of the beam where the fatigueresistance of the shear connectors is being evaluated


Figure 1.48 Excel Report for Fatigue Limit State


5. Shear Connector Result (1) Result Table


Design > Composite Design > Design Result Tables > Shear Connector...

Figure 1.49 Result Table for Shear Connector

Where,

h/d : height to diameter ratio of shear connector

qr : factored shear resistance of shear connectors

N : number of shear connectors entered in shear span

Nreq : required number of shear connectors in shear span

(2) Excel Report


Figure 1.50 Excel Report for Shear Connector


6. Stiffener Result (1) Result Table


Design > Composite Design > Design Result Tables > Transverse Stiffener...

Figure 1.51 Result Table for Stiffener

Where, h/w : ratio of clear depth of web to web thickness h/w_lim : 150, Web stiffeners are not required when the unstiffened shear resistance exceeds the factored shear and h/w ≤ 150. a : stiffener spacing a_lim : limit of stiffener spacing as per clause 10.10.6.1 As : area of stiffener or pair of stiffeners It : moment of inertia of transverse stiffener It_lim : limit of moment of inertia of transverse stiffener as per clause 10.10.6.2 w/t : width-to-thickness ratio of intermediate transverse stiffeners 200/sqrt(Fy) : limit of width-to-thickness ratio of intermediate transverse stiffeners as per clause10.10.6.2 wp : projecting stiffener width 30t : limit of projecting stiffener width as per clause 10.10.6.2

(2) Excel Report


Figure 1.52 Excel Report for Stiffener


7. Total Checking

(1) Result Table

Design > Composite Design > Design Result Table...

Summary results for each member can be viewed in a result table as shown below.

Figure 1.53 Result Table for Toal Checking

CAN/CSA S6-14for midas CivilDESIGN GUIDE

design guide for midas civil can/csa s6-14 - bridge/tutorials... · 4 design guide for midas civil...

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