DESIGN GUIDE

for midas Civil

AASHTO LRFD

Prestressed Concrete Girder Design

Steel Composite Girder Design

Steel Composite Bridge Load Rating

dŚĞŽďũĞĐƟǀĞŽĨƚŚŝƐĚĞƐŝŐŶŐƵŝĚĞŝƐƚŽŽƵƚůŝŶĞƚŚĞĚĞƐŝŐŶ

ĂůŐŽƌŝƚŚŵƐǁŚŝĐŚĂƌĞĂƉƉůŝĞĚŝŶŵŝĚĂƐŝǀŝůĮŶŝƚĞĞůĞŵĞŶƚ

analysis and design system. The guide aims to provide

ƐƵĸĐŝĞŶƚŝŶĨŽƌŵĂƟŽŶĨŽƌƚŚĞƵƐĞƌƚŽƵŶĚĞƌƐƚĂŶĚƚŚĞ

ƐĐŽƉĞ͕ůŝŵŝƚĂƟŽŶƐĂŶĚĨŽƌŵƵůĂƐĂƉƉůŝĞĚŝŶƚŚĞĚĞƐŝŐŶ

features and to provide relevant references to the clauses

in the Design standards.

The design guide covers prestressed concrete girder

design, steel composite girder design and steel composite

ŐŝƌĚĞƌďƌŝĚŐĞƌĂƟŶŐĂƐƉĞƌ^,dK>Z&͘

It is recommended that you read this guide and review

corresponding tutorials, which are found on our web site,

ŚƩƉ͗ͬͬǁǁǁ͘DŝĚĂƐhƐĞƌ͘ĐŽŵ͕ďĞĨŽƌĞĚĞƐŝŐŶŝŶŐ͘ĚĚŝƟŽŶĂů

ŝŶĨŽƌŵĂƟŽŶĐĂŶďĞĨŽƵŶĚŝŶƚŚĞŽŶůŝŶĞŚĞůƉĂǀĂŝůĂďůĞŝŶ

the program’s main menu.

DISCLAIMER

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

'd^͕^ŽŝůtŽƌŬƐ͕ŵŝĚĂƐE&y͖ŚĞƌĞŝŶĂŌĞƌƌĞĨĞƌƌĞĚƚŽĂƐ

“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

ƉƌŽĮƚ͕ůŽƐƐŽĨďƵƐŝŶĞƐƐ͕ŽƌĮŶĂŶĐŝĂůůŽƐƐǁŚŝĐŚŵĂǇďĞ

caused directly or indirectly by the MIDAS package, when

used for any purpose or use, due to any defect or

ĚĞĮĐŝĞŶĐǇƚŚĞƌĞŝŶ͘ĐĐŽƌĚŝŶŐůǇ͕ƚŚĞƵƐĞƌŝƐĞŶĐŽƵƌĂŐĞĚƚŽ

fully understand the bases of the program and become

familiar with the users manuals. The user shall also independently verify the results produced by the program.

Foreword

dŚĞŽďũĞĐƟǀĞŽĨƚŚŝƐĚĞƐŝŐŶŐƵŝĚĞŝƐƚŽŽƵƚůŝŶĞƚŚĞĚĞƐŝŐŶĂůŐŽƌŝƚŚŵƐ

ǁŚŝĐŚĂƌĞĂƉƉůŝĞĚŝŶŵŝĚĂƐŝǀŝůĮŶŝƚĞĞůĞŵĞŶƚĂŶĂůǇƐŝƐĂŶĚĚĞƐŝŐŶ

ƐǇƐƚĞŵ͘dŚĞŐƵŝĚĞĂŝŵƐƚŽƉƌŽǀŝĚĞƐƵĸĐŝĞŶƚŝŶĨŽƌŵĂƟŽŶĨŽƌƚŚĞƵƐĞƌƚŽ

ƵŶĚĞƌƐƚĂŶĚƚŚĞƐĐŽƉĞ͕ůŝŵŝƚĂƟŽŶƐĂŶĚĨŽƌŵƵůĂƐĂƉƉůŝĞĚŝŶƚŚĞĚĞƐŝŐŶ

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

standards.

The design guide covers prestressed concrete girder design, steel

ĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌĚĞƐŝŐŶĂŶĚƐƚĞĞůĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌďƌŝĚŐĞƌĂƟŶŐĂƐƉĞƌ

^,dK>Z&͘

It is recommended that you read this guide and review corresponding

ƚƵƚŽƌŝĂůƐ͕ǁŚŝĐŚĂƌĞĨŽƵŶĚŽŶŽƵƌǁĞďƐŝƚĞ͕ŚƩƉ͗ͬͬǁǁǁ͘DŝĚĂƐhƐĞƌ͘ĐŽŵ͕

ďĞĨŽƌĞĚĞƐŝŐŶŝŶŐ͘ĚĚŝƟŽŶĂůŝŶĨŽƌŵĂƟŽŶĐĂŶďĞĨŽƵŶĚŝŶƚŚĞŽŶůŝŶĞ

help available in the program’s main menu.

Organization

dŚŝƐŐƵŝĚĞŝƐĚĞƐŝŐŶĞĚƚŽŚĞůƉǇŽƵƋƵŝĐŬůǇďĞĐŽŵĞƉƌŽĚƵĐƟǀĞǁŝƚŚ

ƚŚĞĚĞƐŝŐŶŽƉƟŽŶƐŽĨ^,dK>Z&͘

ŚĂƉƚĞƌϭƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƉƌĞƐƚƌĞƐƐĞĚĐŽŶĐƌĞƚĞ

ŐŝƌĚĞƌĚĞƐŝŐŶƚŽ^,dK>Z&͘

ŚĂƉƚĞƌϮƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƐƚĞĞůĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌ

ĚĞƐŝŐŶƚŽ^,dK>Z&͘

ŚĂƉƚĞƌϯƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƐƚĞĞůĐŽŵƉŽƐŝƚĞďƌŝĚŐĞ

ůŽĂĚƌĂƟŶŐƚŽ^,dK>Z&Z͘

Contents

Chapter 1.

Prestressed Concrete Girder Design ;^,dK>Z&Ϳ

01

Strength Limit States

1. Flexural resistance

03

2. Shear resistance

16

3. Torsion resistance

28

Serviceability Limit States

ϭ͘^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

34

Ϯ͘^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚƐĞƌǀŝĐĞůŽĂĚƐ

40

3. Tensile stress for Prestressing tendons

44

ϰ͘WƌŝŶĐŝƉĂůƐƚƌĞƐƐĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

47

5. Principal stress at service loads

49

6. Principal stress at service loads

51

7. Check crack

52

ŚĂƉƚĞƌϮ͘

Steel Composite Girder Design

;^,dK>Z&Ϳ

55

/ŶƚƌŽĚƵĐƟŽŶ

ϭ͘^,dK>Z&ϬϳĂŶĚϭϮ^ƚĞĞůŽŵƉŽƐŝƚĞ

57

Ϯ͘ŽŶƐŝĚĞƌĂƟŽŶƐ^ƚĞĞůŽŵƉŽƐŝƚĞĞƐŝŐŶ

59

ϯ͘ĂůĐƵůĂƟŽŶŽĨWůĂƐƟĐDŽŵĞŶƚĂŶĚzŝĞůĚDŽŵĞŶƚ

59

Modeling and Design Variables

1. Modeling Design Variables

67

ƉƉůŝĐĂƟŽŶŽĨ^,dK>Z&ϭϮ

ϭ͘/'ŝƌĚĞƌ^ĞĐƟŽŶ

87

Ϯ͘ŽǆͬdƵď'ŝƌĚĞƌ^ĞĐƟŽŶ

111

3. Shear Connector

127

ϰ͘^ƟīĞŶĞƌ

131

ϱ͘ŝīĞƌĞŶĐĞĞƚǁĞĞŶ^,dKͲ>Z&ϰƚŚ(2007) and 6th(2012)

135

^ƚĞĞůŽŵƉŽƐŝƚĞĞƐŝŐŶZĞƐƵůƚ

ϭ͘^ƚƌĞŶŐƚŚ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

138

Ϯ͘^ĞƌǀŝĐĞ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

141

ϯ͘ŽŶƐƚƌƵĐƟďŝůŝƚǇZĞƐƵůƚ

142

ϰ͘&ĂƟŐƵĞ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

145

ϱ͘^ŚĞĂƌŽŶŶĞĐƚŽƌZĞƐƵůƚ

146

ϲ͘^ƟīĞŶĞƌZĞƐƵůƚ

147

7. Span Checking

148

8. Total Checking

149

Chapter 3.

^ƚĞĞůŽŵƉŽƐŝƚĞƌŝĚŐĞ>ŽĂĚZĂƟŶŐ ;^,dK>Z&Ϳ

151

/ŶƚƌŽĚƵĐƟŽŶ

ϭ͘^,dK>Z&ZϮϬϭϭƌŝĚŐĞ>ŽĂĚZĂƟŶŐ

153

Ϯ͘>ŽĂĚZĂƟŶŐ>ĞǀĞůƐ

155

ϯ͘WƌŽĐĞƐƐŽĨ>ŽĂĚZĂƟŶŐ

157

Modeling and Design Variables

1. Modeling Design Variables

158

ƉƉůŝĐĂƟŽŶŽĨ^,dK>Z&Zϭϭ

ϭ͘ZĂƟŶŐ&ĂĐƚŽƌĂůĐƵůĂƟŽŶ

171

Ϯ͘^ƚƌĞŶŐƚŚ>ŝŵŝƚ^ƚĂƚĞ

178

ϯ͘^ĞƌǀŝĐĞ>ŝŵŝƚ^ƚĂƚĞ

180

ϰ͘&ĂƟŐƵĞ>ŝŵŝƚ^ƚĂƚĞ

181

ƌŝĚŐĞ>ŽĂĚZĂƟŶŐZĞƐƵůƚ

ϭ͘ZĞƐƵůƚdĂďůĞƐ

186

Ϯ͘ZĂƟŶŐĞƚĂŝůdĂďůĞ

191

ϯ͘>ŽĂĚZĂƟŶŐZĞƉŽƌƚ

194

Chapter 1.

Prestressed Concrete

Girder Design

AASHTO LRFD 7th (2014)

Chapter 1.

Prestressed Concrete Girder Design ;^,dK>Z&ϭϰͿ

Prestressed concrete box girders and composite girders need to be designed to

ƐĂƟƐĨǇƚŚĞĨŽůůŽǁŝŶŐůŝŵŝƚƐƚĂƚĞƐ͘

hůƟŵĂƚĞ>ŝŵŝƚ^ƚĂƚĞƐ

&ůĞǆƵƌĂůZĞƐŝƐƚĂŶĐĞ

^ŚĞĂƌZĞƐŝƐƚĂŶĐĞ

dŽƌƐŝŽŶZĞƐŝƐƚĂŶĐĞ

Serviceability Limit States

^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚƐĞƌǀŝĐĞůŽĂĚƐ

Tensile stress for Prestressing tendons

WƌŝŶĐŝƉĂůƐƚƌĞƐƐĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

Principal stress at service loads

Check crack

Chapter 1. Prestressed Concrete Girder Design:AASHTO-LRFD 7th (2014)

Strength Limit States

1. Flexural resistance

The factored flexural resistance shall satisfy the following condition, Mu ≤ΦMn.

Where, Mu : Factored moment at the section due to strength load combination

ΦMn : Factored flexural resistance

1.1. Resistance Factor

AASHTO LRFD14

(5.5.4.2.1)

Resistance factor Φ shall be taken as follow.

[Fig.1. 1] Resistance Factor

I

0.75

I

0.583 0.25

I 1.0

if H t d 0.002

dt

c

if 0.002 H t 0.005

(1.1)

if H t t 0.005

Where,

dt : Distance from extreme compression fiber to the centroid of the extreme tension steel element

c : Distance from the extreme compression fiber to the neutral axis

εt : Net tensile Strain

In midas Civil, εt is applied as strain of a reinforcement which is entered at the extreme tensile

fiber.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

4

3

Input reinforcements to be used in the calculation of resistance in the dialog box below.

Model>Properties>Section Manager>Reinforcements

Rebar coordinate

at the section

Entered rebar data

[Fig.1. 2] Input Longitudinal reinforcement

Once reinforcement is entered at the PSC section, the rebar which is placed at the closest

position to 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. And the rebar at the top most is used

under the hogging moment.

Input tendon profile to be used in PSC design in the dialog box below.

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

Tendon position which is placed at the closest

position to the extreme tensile fiber will be used

to calculate the strain.

[Fig.1.3] Tendon Profile

4

Design Guide for midas Civil

1.2 Calculate neutral axis depth

Neutral axis is determined by the iteration approach as shown in the figure below.

Assume neutral axis depth, c

Initial c = H/2

(H=Section Height)

Calculate Cc (Concrete)

(1)

Calculate Ts, Cs (Reinforcement)

(2)

Calculate Tps (Tendon)

(3)

(4)

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

NO

YES

Get neutral axis depth, c

[Fig.1. 4] Flow chart to calculate neutral axis depth, c

(1) Calculate force of concrete, Cc.

In midas Civil, the natural relationship between concrete stress and strain is considered as

the equivalent rectangular concrete compressive stress block.(Compressive strain limit of

concrete, εcu = 0.003)

[Fig.1. 5] Calculate force of concrete, Cc

Cc 0.85 f 'c Ac

(1.2)

Where,

f 'c : Specified compressive strength of concrete for design

Compressive strength to be used in PSC design is defined in PSC Design Material dialog box.

E

Ac

0.85

if f 'c d 4.0ksi

0.85 0.05( f 'c 4.0) t 0.65

if f 'c ! 4.0ksi

: Concrete area of compressive zone

(E1c) u width

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

5

PSC>PSC Design Data> PSC Design Material…

Concrete

[Fig.1. 6] PSC Design Material

Enter the concrete and reinforcement grade to be used in PSC design. The strength can be

checked for the selected material grade according to the selected material code. When

“None” is selected in Code field, the strength of concrete and reinforcement can be directly

entered.

AASHTO LRFD14

(5.7.2.2)

Fig.1. 3 PSC Design Material (Composite)

For the composite type PSC sections, the Design Material window changes to allow users to

define the material properties of the slab. The concrete and rebar material properties

entered for slab are used for every calculation such as the neutral axis calculation.

6

Design Guide for midas Civil

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

Tensile resistance due to longitudinal reinforcement (Ts)and compression resistance due to

concrete (Cs) is calculated as shown in the following equation.

Ts

As f s , Cs

As ' f s '

(1.3)

Where,

As, As’ : the cross sectional area of tensile and compressive reinforcement

It is entered in Section Manager>Reinforcements as shown in the Fig1. 2.

fs , fs’: the stress of tensile and compressive reinforcement

In order to calculate the tensile stress of reinforcement, midas Civil calculate the

corresponding strains as per the strain compatibility condition. And then the related tensile

stresses are calculated by the stress-strain relationship. The equation is shown as follows.

▪ Strain

Hs

dt c

H cu , H s '

c

c dc

H cu

c

(1.4)

Where,

εs : the strain of tensile reinforcement.

εs’ : the strain of compressive reinforcement.

εcu : the ultimate compressive strain in the concrete. (εcu = 0.003)

c : the neutral axis depth.

dt : Distance from the compression fiber of concrete to the extreme tensile fiber of reinforcement

dc : Distance from the compression fiber of concrete to the extreme compressive fiber of reinforcement

▪ Stress

If the tensile stress of reinforcement reaches its yield stress limit, tensile stress will be

applied as yield stress. If not, the tensile stress will be calculated as “εs x Es”.

fs

H s Es

®

¯ fy

( fs d f y )

( fs ! f y )

,

H s ' Es

fs ' ®

¯ fy

( fs ' d f y )

( fs ' ! f y )

(1.5)

Where,

Es : Modulus of elasticity in reinforcement

Fy : Yield tensile stress in reinforcement

(3) Calculate force of tendon, Tps.

Tensile resistance of prestressing steel, Tps, is calculated as shown in the following equation.

Tps

¦A

p

f ps

(1.6)

Where,

Ap : the cross sectional area of tendon.

fps : the stress of tendon.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

7

PSC> Design Parameter> Parameters…

[Fig.1. 7] PSC Design parameter Dialog - Flexural Strength

Tensile stress of prestressing steel fps can be calculated by code or strain compatibility as

specified in PSC design Parameter dialog box. When code is selected in flexural strength option,

the tensile stress fps is calculated by the equation as per AASHTO-LRFD for bonded and

unbounded tendon respectively. When strain compatibility is used, the tensile stress fps is

calculated by the stress-strain relationship.

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

Tendon Type

Total Tendon Area

fpu

fpy

Bond Type

[Fig.1. 8] Tendon Property Dialog

▪ Tendon Type

Internal(Pre-Tension)

Internal(Post-Tension)

External

▪ Bond Type

Bonded: Section properties reflect the duct area after grouting.

When tendon type is specified as Internal (Pre-Tension), bond type will be taken as Bonded

Type.

Unbonded: Section properties exclude the duct area.

8

Design Guide for midas Civil

When tendon type is specified as external, bond type will be taken as Unbonded Type.

[Table1. 1] Applicable Bond Type by Tendon Types

Tendon Type

Internal (Pre-tension)

Bond Type

Bonded

Bonded

Unbonded

Unbonded

Internal (Post-tension)

External

▪ Total Tendon Area

Enter the tendon area (Ap). Click

to select the number of strands and diameter in order

to calculate the tendon area automatically.

▪ fpu, fpy

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

Tensile stress of prestressing steel fps will be calculated as shown in the following table.

[Table1. 2] Calculation of tensile stress of prestressing steel

Flexure Strength option

Code

Strain compatibility

Bond Type

Bonded

Unbonded

Bonded

Unbonded*

Tensile Stress

fps for Bonded Type

fps for Unbonded Type

Strain compatibility

fps for Unbonded Type

* When flexure strength option is entered as strain compatibility and bond type is entered as

unbonded type, tensile stress will be calculated using the code equation of unbonded tendon

instead of strain compatibility method. It is because strain compatibility method is valid for fully

bonded tendons.

Tensile stress of prestressing steel fps is calculated as follows.

▪Code equation for bonded type tendon

AASHTO LRFD14

(5.7.3.1.1)

(Eq. 5.7.3.1.1-1)

§

c ·

f pu ¨1 k ¸

¨

d p ¸¹

©

f ps

(1.7)

§

f py ·

2 ¨1.04

¸

¨

f pu ¸¹

©

k

(1.8)

AASHTO LRFD14

(5.7.3.1.1)

(Eq. 5.7.3.1.1-2)

Where,

fpy: Yield strength of prestressing steel

fpu: Specified tensile strength of prestressing steel

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

c: Distance between the neutral axis and the compressive face

▪ Code equation for unbonded type tendon

f ps

le

§ dp c ·

f pe 900 ¨

¸ d f py

© le ¹

2li

2 Ns

(1.9)

(1.10)

AASHTO LRFD14

(5.7.3.1.2)

(Eq. 5.7.3.1.2-1)

AASHTO LRFD14

(5.7.3.1.2)

(Eq. 5.7.3.1.2-2)

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

9

Where,

li : length of tendon between anchorages

Ni : number of support hinges crossed by the tendon between anchorages or discretely bonded point. It

is always applied as “0” in midas Civil.

▪ fps by Strain compatibility

When flexure resistance is calculated by strain compatibility method, tensile stress of

prestressing tendon is calculated by the stress-strain relationship.

[Fig.1. 9] Stress-strain model of prestressing tendon

(4) Determination of neutral axis position

In order to find the neutral axis, the iteration analysis will be performed until compressive

strength (C=Cc+Cs) becomes equal to the tensile strength (T=Ts+Tps).

The convergence criterion is applied as shown in the following equation.

• Convergence condition:

C

1.0 0.001 (Tolerance)

T

(1.11)

1.3 Calculate moment resistance Mn

Once the neutral axis is determined, flexural resistance is calculated by multiplying the

distance from the neutral axis.

Mn

Cc ac Cs as ' Ts as ¦ Tps a pi

where,

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

10

Design Guide for midas Civil

(1.12)

0.85f˅c

a

ac

c

as

ap

Cc

as'

Cs

As˅

Ap

Tps

As

Ts

[Fig.1. 10] Forces and distances from neutral axis depth for Mn

If a tendon in tension is located at the upper part from the neutral axis under the sagging

moment, the flexural resistance will have (-) sign and it will reduce the total moment

resistance.

Mn

Cc ac Cs as ' Ts as ¦ Tps a pi Tps' a 'pi

(1.13)

1.4 Factored Flexural Resistance

Mr

IMn

(1.14)

AASHTO LRFD14

(5.7.3.2.1)

(Eq. 5.7.3.2.1-1)

where,

Mn : nominal resistance

Φ : resistance factor

1.5 Minimum Reinforcement

The moment resistance with considering entered reinforcements or tendons shall satisfy the

following condition.

M r t max(1.33M u , M cr )

AASHTO LRFD14

(5.7.3.3.2)

(1.15)

▪ Cracked Moment ( Mcr)

For composite sections, the equation 1.16 is used to calculate the cracked moment (Mcr).

M cr

ª

§ Sc

·º

1¸ »

© Snc

¹¼

J 3 «(J 1 f r J 2 f cpe )Sc M dnc ¨

¬

(1.16)

AASHTO LRFD14

(5.7.3.3.2)

(Eq. 5.7.3.3.2-1)

The Mdnc is taken from the Muy caused by the dead load of girder section during the

construction stage analysis.

The Snc value is obtained from the section modulus of the pre-composite section under the

tensile stress. The Sc value is taken from the section modulus of the post-composite section

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

11

under the tensile stress.

In midas Civil, cracked moment shall be calculated as per the following equation.

(For the composite type sections, the equation 1.16 is used; for the non-composite type

sections, the equation 1.17 is used.

M cr

J 3 ª¬(J 1 f r J 2 fcpe )Sc º¼

(1.17)

Where,

γ1 :

flexural cracking variability factor

1.2 for precast segmental structures

1.6 for all other concrete structures

γ2 :

prestress variability factor

1.1 for bonded tendons

1.0 for unbounded tendons

If both bonded and unbonded type tendons are assigned in a section,

which is more conservative value.

γ3 :

J 2 will be applied as 1.0

ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement

0.67 for A615 ,Grade 60 reinforcement

0.75 for A706, Grade 60 reinforcement

1.00 for prestressed concrete structures

In midas Civil,

J 3 wil be applied as 1.0.

fr : modulus of rupture of concrete specified in Article 5.4.2.6

AASHTO LRFD14

(5.4.2.6)

(C5.4.2.6)

In midas Civil, fr will be always applied as 0.37 f 'c .

Sc : section modulus for the extreme fiber of the composite section where tensile stress is caused by

3

externally applied loads (in )

In midas Civil, section modulus under tension is applied.

fcpe : compressive stress in concrete due to effective prestress forces only (after allowance for all

prestress losses) at extreme fiber of section where tensile stress is caused by externally applied

loads (ksi)

It is obtained in elastic state (uncracked section) and the following equation has been

applied in midas Civil.

f cpe

¦A

f

ps e

Ag

¦A

fe

ps e p

S

(1.18)

Where,

f e : Effective prestress forces of prestressing tendons

e p : Distance from the neutral axis to the centroid of the prestressing tendons

Aps : Area of prestressing tendon

Ag : Gross area of cross-section

S : Sectional modulus in compression

In midas Civil, construction type of PSC section is determined in PSC design parameter dialog

box.

12

Design Guide for midas Civil

PSC> Design Parameter> Parameters…

[Fig.1. 4] PSC Design parameter Dialog - Construction Type

Construction type: Segmental, Non-Segmental

The selected construction type will affect the calculation of cracked moment, shear and

torsional resistance, and tensile stress limit of concrete.

1.6 Check moment resistance

In midas Civil, factored moment is obtained from load combinations specified in Load

Combinations dialog box. In AASHTO LRFD specification, load combinations need to be

generated as shown in the fig 1.12.

AASHTO LRFD14

(3.4.1)

[Fig.1. 5] Load Combinations and Load factors for strength limit state

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

13

Results>Load combinations>Concrete Design tab

Active:

Strength/Stress

Active:

Serviceability

[Fig.1. 6] Load Combinations dialog

In midas Civil, load combinations can be automatically generated by clicking [Auto

Generation…] button. The load combinations need to be generated in concrete design tab.

The most critical load combination among Strength/Stress type load combinations will be

used to obtain factored moment, factored shear force, and factored torsional moment. The

Service type load combinations will be used to verify the serviceability limit state.

The verification of flexural moment obtained from Strength/Stress type load combination

can be divided into two following cases.

1) No need to satisfy minimum reinforcement

M r t Mu

(1.19)

2) Need to satisfy minimum reinforcement

M r t M u and M r t M cr

1.7 Moment resistance verification

1.7.1 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. 7] Result table for moment resistance

14

Design Guide for midas Civil

(1.20)

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

Muy : Design moment

Mcr : Crack Moment

Mny : Nominal moment resistance.

PhiMny : Design moment resistance.

Ratio : Muy/ PhiMny : Flexural resistance ratio, The verification is satisfied when it is less than 1.0.

PhiMny /min(1.33Muy, Mcr) : Verification of minimum reinforcement. The verification is satisfied when

it is less than 1.0. If the verification of minimum reinforcement is not required, it will be displayed as

1.0.

1.7.2 by Excel Report

Detail verification results can be checked in MS Excel report as shown in the figure below.

Design>PSC Design>PSC Design Calculation…

[Fig.1. 8] Excel report for moment resistance

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

15

2. Shear resistance

Shear resistance without consideration of effects of torsion shall be verified to satisfy the

following condition.

M u d IVn

AASHTO LRFD14

(5.5.4.2.1)

(1.21)

Where, strength reduction factor, Φ=0.9.

Refer to the clause 2.3 Torsion Resistance for the verification of shear resistance where the

effects of torsion are required to be considered. In AASHTO-LRFD (2012), the design for

shear and torsion will be performed for segmental and non-segmental box girders.

2.1 Classification of Segmental Box Girder

The program will consider a section is segmental box girder when the following 2 conditions

are satisfied.

1. In PSC Design Parameter dialog box, Construction Type is specified as Segment.

2. When a section is defined with PSC box section (ex. PSC-1CELL, 2CELL, 3CELL, nCELL,

cCELL2, PLAT, and Value type)

Property > Section Property > Section >PSC

[Fig.1.16] PSC section data dialog

2.2 Parameters for shear

2.2.1 Effective web width (bv)

bv : effective web width taken as the minimum web width within the depth d v as determined in Article

5.8.2.9 (in.)

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.

16

Design Guide for midas Civil

AASHTO LRFD14

(5.8.3.3.3)

Property > Section Property > Section >PSC

[Fig 1.17] Consideration of 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.

2.2.2 Effective shear depth (dv)

▪ Non-Segmental Box Girder

dv

: effective shear depth takem as the distance , measured perpendicular to the neutral axis,

between the resultants of the tensile and compressive forces due to flexure; it need not be

taken less than the greater of 0.9de or 0.72h(in.)

In midas Civil, the value of effective shear depth, dv, is calculated as shown in the equation

below.

dv

de

§

·

Mn

min ¨

, 0.9de , 0.72h ¸

¨ As f s Aps f ps

¸

©

¹

AASHTO LRFD14

(5.8.2.9)

(1.22)

Aps f ps d p As f s d s

(1.23)

Aps f ps As f s

Where,

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

ds : Distance from extreme fiber to the centroid of nonprestressed tensile reinforcement

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

17

for midas Civil

AASHTO LRFD

Prestressed Concrete Girder Design

Steel Composite Girder Design

Steel Composite Bridge Load Rating

dŚĞŽďũĞĐƟǀĞŽĨƚŚŝƐĚĞƐŝŐŶŐƵŝĚĞŝƐƚŽŽƵƚůŝŶĞƚŚĞĚĞƐŝŐŶ

ĂůŐŽƌŝƚŚŵƐǁŚŝĐŚĂƌĞĂƉƉůŝĞĚŝŶŵŝĚĂƐŝǀŝůĮŶŝƚĞĞůĞŵĞŶƚ

analysis and design system. The guide aims to provide

ƐƵĸĐŝĞŶƚŝŶĨŽƌŵĂƟŽŶĨŽƌƚŚĞƵƐĞƌƚŽƵŶĚĞƌƐƚĂŶĚƚŚĞ

ƐĐŽƉĞ͕ůŝŵŝƚĂƟŽŶƐĂŶĚĨŽƌŵƵůĂƐĂƉƉůŝĞĚŝŶƚŚĞĚĞƐŝŐŶ

features and to provide relevant references to the clauses

in the Design standards.

The design guide covers prestressed concrete girder

design, steel composite girder design and steel composite

ŐŝƌĚĞƌďƌŝĚŐĞƌĂƟŶŐĂƐƉĞƌ^,dK>Z&͘

It is recommended that you read this guide and review

corresponding tutorials, which are found on our web site,

ŚƩƉ͗ͬͬǁǁǁ͘DŝĚĂƐhƐĞƌ͘ĐŽŵ͕ďĞĨŽƌĞĚĞƐŝŐŶŝŶŐ͘ĚĚŝƟŽŶĂů

ŝŶĨŽƌŵĂƟŽŶĐĂŶďĞĨŽƵŶĚŝŶƚŚĞŽŶůŝŶĞŚĞůƉĂǀĂŝůĂďůĞŝŶ

the program’s main menu.

DISCLAIMER

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

'd^͕^ŽŝůtŽƌŬƐ͕ŵŝĚĂƐE&y͖ŚĞƌĞŝŶĂŌĞƌƌĞĨĞƌƌĞĚƚŽĂƐ

“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

ƉƌŽĮƚ͕ůŽƐƐŽĨďƵƐŝŶĞƐƐ͕ŽƌĮŶĂŶĐŝĂůůŽƐƐǁŚŝĐŚŵĂǇďĞ

caused directly or indirectly by the MIDAS package, when

used for any purpose or use, due to any defect or

ĚĞĮĐŝĞŶĐǇƚŚĞƌĞŝŶ͘ĐĐŽƌĚŝŶŐůǇ͕ƚŚĞƵƐĞƌŝƐĞŶĐŽƵƌĂŐĞĚƚŽ

fully understand the bases of the program and become

familiar with the users manuals. The user shall also independently verify the results produced by the program.

Foreword

dŚĞŽďũĞĐƟǀĞŽĨƚŚŝƐĚĞƐŝŐŶŐƵŝĚĞŝƐƚŽŽƵƚůŝŶĞƚŚĞĚĞƐŝŐŶĂůŐŽƌŝƚŚŵƐ

ǁŚŝĐŚĂƌĞĂƉƉůŝĞĚŝŶŵŝĚĂƐŝǀŝůĮŶŝƚĞĞůĞŵĞŶƚĂŶĂůǇƐŝƐĂŶĚĚĞƐŝŐŶ

ƐǇƐƚĞŵ͘dŚĞŐƵŝĚĞĂŝŵƐƚŽƉƌŽǀŝĚĞƐƵĸĐŝĞŶƚŝŶĨŽƌŵĂƟŽŶĨŽƌƚŚĞƵƐĞƌƚŽ

ƵŶĚĞƌƐƚĂŶĚƚŚĞƐĐŽƉĞ͕ůŝŵŝƚĂƟŽŶƐĂŶĚĨŽƌŵƵůĂƐĂƉƉůŝĞĚŝŶƚŚĞĚĞƐŝŐŶ

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

standards.

The design guide covers prestressed concrete girder design, steel

ĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌĚĞƐŝŐŶĂŶĚƐƚĞĞůĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌďƌŝĚŐĞƌĂƟŶŐĂƐƉĞƌ

^,dK>Z&͘

It is recommended that you read this guide and review corresponding

ƚƵƚŽƌŝĂůƐ͕ǁŚŝĐŚĂƌĞĨŽƵŶĚŽŶŽƵƌǁĞďƐŝƚĞ͕ŚƩƉ͗ͬͬǁǁǁ͘DŝĚĂƐhƐĞƌ͘ĐŽŵ͕

ďĞĨŽƌĞĚĞƐŝŐŶŝŶŐ͘ĚĚŝƟŽŶĂůŝŶĨŽƌŵĂƟŽŶĐĂŶďĞĨŽƵŶĚŝŶƚŚĞŽŶůŝŶĞ

help available in the program’s main menu.

Organization

dŚŝƐŐƵŝĚĞŝƐĚĞƐŝŐŶĞĚƚŽŚĞůƉǇŽƵƋƵŝĐŬůǇďĞĐŽŵĞƉƌŽĚƵĐƟǀĞǁŝƚŚ

ƚŚĞĚĞƐŝŐŶŽƉƟŽŶƐŽĨ^,dK>Z&͘

ŚĂƉƚĞƌϭƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƉƌĞƐƚƌĞƐƐĞĚĐŽŶĐƌĞƚĞ

ŐŝƌĚĞƌĚĞƐŝŐŶƚŽ^,dK>Z&͘

ŚĂƉƚĞƌϮƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƐƚĞĞůĐŽŵƉŽƐŝƚĞŐŝƌĚĞƌ

ĚĞƐŝŐŶƚŽ^,dK>Z&͘

ŚĂƉƚĞƌϯƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕

h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƐƚĞĞůĐŽŵƉŽƐŝƚĞďƌŝĚŐĞ

ůŽĂĚƌĂƟŶŐƚŽ^,dK>Z&Z͘

Contents

Chapter 1.

Prestressed Concrete Girder Design ;^,dK>Z&Ϳ

01

Strength Limit States

1. Flexural resistance

03

2. Shear resistance

16

3. Torsion resistance

28

Serviceability Limit States

ϭ͘^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

34

Ϯ͘^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚƐĞƌǀŝĐĞůŽĂĚƐ

40

3. Tensile stress for Prestressing tendons

44

ϰ͘WƌŝŶĐŝƉĂůƐƚƌĞƐƐĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

47

5. Principal stress at service loads

49

6. Principal stress at service loads

51

7. Check crack

52

ŚĂƉƚĞƌϮ͘

Steel Composite Girder Design

;^,dK>Z&Ϳ

55

/ŶƚƌŽĚƵĐƟŽŶ

ϭ͘^,dK>Z&ϬϳĂŶĚϭϮ^ƚĞĞůŽŵƉŽƐŝƚĞ

57

Ϯ͘ŽŶƐŝĚĞƌĂƟŽŶƐ^ƚĞĞůŽŵƉŽƐŝƚĞĞƐŝŐŶ

59

ϯ͘ĂůĐƵůĂƟŽŶŽĨWůĂƐƟĐDŽŵĞŶƚĂŶĚzŝĞůĚDŽŵĞŶƚ

59

Modeling and Design Variables

1. Modeling Design Variables

67

ƉƉůŝĐĂƟŽŶŽĨ^,dK>Z&ϭϮ

ϭ͘/'ŝƌĚĞƌ^ĞĐƟŽŶ

87

Ϯ͘ŽǆͬdƵď'ŝƌĚĞƌ^ĞĐƟŽŶ

111

3. Shear Connector

127

ϰ͘^ƟīĞŶĞƌ

131

ϱ͘ŝīĞƌĞŶĐĞĞƚǁĞĞŶ^,dKͲ>Z&ϰƚŚ(2007) and 6th(2012)

135

^ƚĞĞůŽŵƉŽƐŝƚĞĞƐŝŐŶZĞƐƵůƚ

ϭ͘^ƚƌĞŶŐƚŚ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

138

Ϯ͘^ĞƌǀŝĐĞ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

141

ϯ͘ŽŶƐƚƌƵĐƟďŝůŝƚǇZĞƐƵůƚ

142

ϰ͘&ĂƟŐƵĞ>ŝŵŝƚ^ƚĂƚĞZĞƐƵůƚ

145

ϱ͘^ŚĞĂƌŽŶŶĞĐƚŽƌZĞƐƵůƚ

146

ϲ͘^ƟīĞŶĞƌZĞƐƵůƚ

147

7. Span Checking

148

8. Total Checking

149

Chapter 3.

^ƚĞĞůŽŵƉŽƐŝƚĞƌŝĚŐĞ>ŽĂĚZĂƟŶŐ ;^,dK>Z&Ϳ

151

/ŶƚƌŽĚƵĐƟŽŶ

ϭ͘^,dK>Z&ZϮϬϭϭƌŝĚŐĞ>ŽĂĚZĂƟŶŐ

153

Ϯ͘>ŽĂĚZĂƟŶŐ>ĞǀĞůƐ

155

ϯ͘WƌŽĐĞƐƐŽĨ>ŽĂĚZĂƟŶŐ

157

Modeling and Design Variables

1. Modeling Design Variables

158

ƉƉůŝĐĂƟŽŶŽĨ^,dK>Z&Zϭϭ

ϭ͘ZĂƟŶŐ&ĂĐƚŽƌĂůĐƵůĂƟŽŶ

171

Ϯ͘^ƚƌĞŶŐƚŚ>ŝŵŝƚ^ƚĂƚĞ

178

ϯ͘^ĞƌǀŝĐĞ>ŝŵŝƚ^ƚĂƚĞ

180

ϰ͘&ĂƟŐƵĞ>ŝŵŝƚ^ƚĂƚĞ

181

ƌŝĚŐĞ>ŽĂĚZĂƟŶŐZĞƐƵůƚ

ϭ͘ZĞƐƵůƚdĂďůĞƐ

186

Ϯ͘ZĂƟŶŐĞƚĂŝůdĂďůĞ

191

ϯ͘>ŽĂĚZĂƟŶŐZĞƉŽƌƚ

194

Chapter 1.

Prestressed Concrete

Girder Design

AASHTO LRFD 7th (2014)

Chapter 1.

Prestressed Concrete Girder Design ;^,dK>Z&ϭϰͿ

Prestressed concrete box girders and composite girders need to be designed to

ƐĂƟƐĨǇƚŚĞĨŽůůŽǁŝŶŐůŝŵŝƚƐƚĂƚĞƐ͘

hůƟŵĂƚĞ>ŝŵŝƚ^ƚĂƚĞƐ

&ůĞǆƵƌĂůZĞƐŝƐƚĂŶĐĞ

^ŚĞĂƌZĞƐŝƐƚĂŶĐĞ

dŽƌƐŝŽŶZĞƐŝƐƚĂŶĐĞ

Serviceability Limit States

^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

^ƚƌĞƐƐĨŽƌĐƌŽƐƐƐĞĐƟŽŶĂƚƐĞƌǀŝĐĞůŽĂĚƐ

Tensile stress for Prestressing tendons

WƌŝŶĐŝƉĂůƐƚƌĞƐƐĂƚĂĐŽŶƐƚƌƵĐƟŽŶƐƚĂŐĞ

Principal stress at service loads

Check crack

Chapter 1. Prestressed Concrete Girder Design:AASHTO-LRFD 7th (2014)

Strength Limit States

1. Flexural resistance

The factored flexural resistance shall satisfy the following condition, Mu ≤ΦMn.

Where, Mu : Factored moment at the section due to strength load combination

ΦMn : Factored flexural resistance

1.1. Resistance Factor

AASHTO LRFD14

(5.5.4.2.1)

Resistance factor Φ shall be taken as follow.

[Fig.1. 1] Resistance Factor

I

0.75

I

0.583 0.25

I 1.0

if H t d 0.002

dt

c

if 0.002 H t 0.005

(1.1)

if H t t 0.005

Where,

dt : Distance from extreme compression fiber to the centroid of the extreme tension steel element

c : Distance from the extreme compression fiber to the neutral axis

εt : Net tensile Strain

In midas Civil, εt is applied as strain of a reinforcement which is entered at the extreme tensile

fiber.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

4

3

Input reinforcements to be used in the calculation of resistance in the dialog box below.

Model>Properties>Section Manager>Reinforcements

Rebar coordinate

at the section

Entered rebar data

[Fig.1. 2] Input Longitudinal reinforcement

Once reinforcement is entered at the PSC section, the rebar which is placed at the closest

position to 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. And the rebar at the top most is used

under the hogging moment.

Input tendon profile to be used in PSC design in the dialog box below.

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

Tendon position which is placed at the closest

position to the extreme tensile fiber will be used

to calculate the strain.

[Fig.1.3] Tendon Profile

4

Design Guide for midas Civil

1.2 Calculate neutral axis depth

Neutral axis is determined by the iteration approach as shown in the figure below.

Assume neutral axis depth, c

Initial c = H/2

(H=Section Height)

Calculate Cc (Concrete)

(1)

Calculate Ts, Cs (Reinforcement)

(2)

Calculate Tps (Tendon)

(3)

(4)

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

NO

YES

Get neutral axis depth, c

[Fig.1. 4] Flow chart to calculate neutral axis depth, c

(1) Calculate force of concrete, Cc.

In midas Civil, the natural relationship between concrete stress and strain is considered as

the equivalent rectangular concrete compressive stress block.(Compressive strain limit of

concrete, εcu = 0.003)

[Fig.1. 5] Calculate force of concrete, Cc

Cc 0.85 f 'c Ac

(1.2)

Where,

f 'c : Specified compressive strength of concrete for design

Compressive strength to be used in PSC design is defined in PSC Design Material dialog box.

E

Ac

0.85

if f 'c d 4.0ksi

0.85 0.05( f 'c 4.0) t 0.65

if f 'c ! 4.0ksi

: Concrete area of compressive zone

(E1c) u width

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

5

PSC>PSC Design Data> PSC Design Material…

Concrete

[Fig.1. 6] PSC Design Material

Enter the concrete and reinforcement grade to be used in PSC design. The strength can be

checked for the selected material grade according to the selected material code. When

“None” is selected in Code field, the strength of concrete and reinforcement can be directly

entered.

AASHTO LRFD14

(5.7.2.2)

Fig.1. 3 PSC Design Material (Composite)

For the composite type PSC sections, the Design Material window changes to allow users to

define the material properties of the slab. The concrete and rebar material properties

entered for slab are used for every calculation such as the neutral axis calculation.

6

Design Guide for midas Civil

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

Tensile resistance due to longitudinal reinforcement (Ts)and compression resistance due to

concrete (Cs) is calculated as shown in the following equation.

Ts

As f s , Cs

As ' f s '

(1.3)

Where,

As, As’ : the cross sectional area of tensile and compressive reinforcement

It is entered in Section Manager>Reinforcements as shown in the Fig1. 2.

fs , fs’: the stress of tensile and compressive reinforcement

In order to calculate the tensile stress of reinforcement, midas Civil calculate the

corresponding strains as per the strain compatibility condition. And then the related tensile

stresses are calculated by the stress-strain relationship. The equation is shown as follows.

▪ Strain

Hs

dt c

H cu , H s '

c

c dc

H cu

c

(1.4)

Where,

εs : the strain of tensile reinforcement.

εs’ : the strain of compressive reinforcement.

εcu : the ultimate compressive strain in the concrete. (εcu = 0.003)

c : the neutral axis depth.

dt : Distance from the compression fiber of concrete to the extreme tensile fiber of reinforcement

dc : Distance from the compression fiber of concrete to the extreme compressive fiber of reinforcement

▪ Stress

If the tensile stress of reinforcement reaches its yield stress limit, tensile stress will be

applied as yield stress. If not, the tensile stress will be calculated as “εs x Es”.

fs

H s Es

®

¯ fy

( fs d f y )

( fs ! f y )

,

H s ' Es

fs ' ®

¯ fy

( fs ' d f y )

( fs ' ! f y )

(1.5)

Where,

Es : Modulus of elasticity in reinforcement

Fy : Yield tensile stress in reinforcement

(3) Calculate force of tendon, Tps.

Tensile resistance of prestressing steel, Tps, is calculated as shown in the following equation.

Tps

¦A

p

f ps

(1.6)

Where,

Ap : the cross sectional area of tendon.

fps : the stress of tendon.

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

7

PSC> Design Parameter> Parameters…

[Fig.1. 7] PSC Design parameter Dialog - Flexural Strength

Tensile stress of prestressing steel fps can be calculated by code or strain compatibility as

specified in PSC design Parameter dialog box. When code is selected in flexural strength option,

the tensile stress fps is calculated by the equation as per AASHTO-LRFD for bonded and

unbounded tendon respectively. When strain compatibility is used, the tensile stress fps is

calculated by the stress-strain relationship.

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

Tendon Type

Total Tendon Area

fpu

fpy

Bond Type

[Fig.1. 8] Tendon Property Dialog

▪ Tendon Type

Internal(Pre-Tension)

Internal(Post-Tension)

External

▪ Bond Type

Bonded: Section properties reflect the duct area after grouting.

When tendon type is specified as Internal (Pre-Tension), bond type will be taken as Bonded

Type.

Unbonded: Section properties exclude the duct area.

8

Design Guide for midas Civil

When tendon type is specified as external, bond type will be taken as Unbonded Type.

[Table1. 1] Applicable Bond Type by Tendon Types

Tendon Type

Internal (Pre-tension)

Bond Type

Bonded

Bonded

Unbonded

Unbonded

Internal (Post-tension)

External

▪ Total Tendon Area

Enter the tendon area (Ap). Click

to select the number of strands and diameter in order

to calculate the tendon area automatically.

▪ fpu, fpy

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

Tensile stress of prestressing steel fps will be calculated as shown in the following table.

[Table1. 2] Calculation of tensile stress of prestressing steel

Flexure Strength option

Code

Strain compatibility

Bond Type

Bonded

Unbonded

Bonded

Unbonded*

Tensile Stress

fps for Bonded Type

fps for Unbonded Type

Strain compatibility

fps for Unbonded Type

* When flexure strength option is entered as strain compatibility and bond type is entered as

unbonded type, tensile stress will be calculated using the code equation of unbonded tendon

instead of strain compatibility method. It is because strain compatibility method is valid for fully

bonded tendons.

Tensile stress of prestressing steel fps is calculated as follows.

▪Code equation for bonded type tendon

AASHTO LRFD14

(5.7.3.1.1)

(Eq. 5.7.3.1.1-1)

§

c ·

f pu ¨1 k ¸

¨

d p ¸¹

©

f ps

(1.7)

§

f py ·

2 ¨1.04

¸

¨

f pu ¸¹

©

k

(1.8)

AASHTO LRFD14

(5.7.3.1.1)

(Eq. 5.7.3.1.1-2)

Where,

fpy: Yield strength of prestressing steel

fpu: Specified tensile strength of prestressing steel

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

c: Distance between the neutral axis and the compressive face

▪ Code equation for unbonded type tendon

f ps

le

§ dp c ·

f pe 900 ¨

¸ d f py

© le ¹

2li

2 Ns

(1.9)

(1.10)

AASHTO LRFD14

(5.7.3.1.2)

(Eq. 5.7.3.1.2-1)

AASHTO LRFD14

(5.7.3.1.2)

(Eq. 5.7.3.1.2-2)

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

9

Where,

li : length of tendon between anchorages

Ni : number of support hinges crossed by the tendon between anchorages or discretely bonded point. It

is always applied as “0” in midas Civil.

▪ fps by Strain compatibility

When flexure resistance is calculated by strain compatibility method, tensile stress of

prestressing tendon is calculated by the stress-strain relationship.

[Fig.1. 9] Stress-strain model of prestressing tendon

(4) Determination of neutral axis position

In order to find the neutral axis, the iteration analysis will be performed until compressive

strength (C=Cc+Cs) becomes equal to the tensile strength (T=Ts+Tps).

The convergence criterion is applied as shown in the following equation.

• Convergence condition:

C

1.0 0.001 (Tolerance)

T

(1.11)

1.3 Calculate moment resistance Mn

Once the neutral axis is determined, flexural resistance is calculated by multiplying the

distance from the neutral axis.

Mn

Cc ac Cs as ' Ts as ¦ Tps a pi

where,

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

10

Design Guide for midas Civil

(1.12)

0.85f˅c

a

ac

c

as

ap

Cc

as'

Cs

As˅

Ap

Tps

As

Ts

[Fig.1. 10] Forces and distances from neutral axis depth for Mn

If a tendon in tension is located at the upper part from the neutral axis under the sagging

moment, the flexural resistance will have (-) sign and it will reduce the total moment

resistance.

Mn

Cc ac Cs as ' Ts as ¦ Tps a pi Tps' a 'pi

(1.13)

1.4 Factored Flexural Resistance

Mr

IMn

(1.14)

AASHTO LRFD14

(5.7.3.2.1)

(Eq. 5.7.3.2.1-1)

where,

Mn : nominal resistance

Φ : resistance factor

1.5 Minimum Reinforcement

The moment resistance with considering entered reinforcements or tendons shall satisfy the

following condition.

M r t max(1.33M u , M cr )

AASHTO LRFD14

(5.7.3.3.2)

(1.15)

▪ Cracked Moment ( Mcr)

For composite sections, the equation 1.16 is used to calculate the cracked moment (Mcr).

M cr

ª

§ Sc

·º

1¸ »

© Snc

¹¼

J 3 «(J 1 f r J 2 f cpe )Sc M dnc ¨

¬

(1.16)

AASHTO LRFD14

(5.7.3.3.2)

(Eq. 5.7.3.3.2-1)

The Mdnc is taken from the Muy caused by the dead load of girder section during the

construction stage analysis.

The Snc value is obtained from the section modulus of the pre-composite section under the

tensile stress. The Sc value is taken from the section modulus of the post-composite section

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

11

under the tensile stress.

In midas Civil, cracked moment shall be calculated as per the following equation.

(For the composite type sections, the equation 1.16 is used; for the non-composite type

sections, the equation 1.17 is used.

M cr

J 3 ª¬(J 1 f r J 2 fcpe )Sc º¼

(1.17)

Where,

γ1 :

flexural cracking variability factor

1.2 for precast segmental structures

1.6 for all other concrete structures

γ2 :

prestress variability factor

1.1 for bonded tendons

1.0 for unbounded tendons

If both bonded and unbonded type tendons are assigned in a section,

which is more conservative value.

γ3 :

J 2 will be applied as 1.0

ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement

0.67 for A615 ,Grade 60 reinforcement

0.75 for A706, Grade 60 reinforcement

1.00 for prestressed concrete structures

In midas Civil,

J 3 wil be applied as 1.0.

fr : modulus of rupture of concrete specified in Article 5.4.2.6

AASHTO LRFD14

(5.4.2.6)

(C5.4.2.6)

In midas Civil, fr will be always applied as 0.37 f 'c .

Sc : section modulus for the extreme fiber of the composite section where tensile stress is caused by

3

externally applied loads (in )

In midas Civil, section modulus under tension is applied.

fcpe : compressive stress in concrete due to effective prestress forces only (after allowance for all

prestress losses) at extreme fiber of section where tensile stress is caused by externally applied

loads (ksi)

It is obtained in elastic state (uncracked section) and the following equation has been

applied in midas Civil.

f cpe

¦A

f

ps e

Ag

¦A

fe

ps e p

S

(1.18)

Where,

f e : Effective prestress forces of prestressing tendons

e p : Distance from the neutral axis to the centroid of the prestressing tendons

Aps : Area of prestressing tendon

Ag : Gross area of cross-section

S : Sectional modulus in compression

In midas Civil, construction type of PSC section is determined in PSC design parameter dialog

box.

12

Design Guide for midas Civil

PSC> Design Parameter> Parameters…

[Fig.1. 4] PSC Design parameter Dialog - Construction Type

Construction type: Segmental, Non-Segmental

The selected construction type will affect the calculation of cracked moment, shear and

torsional resistance, and tensile stress limit of concrete.

1.6 Check moment resistance

In midas Civil, factored moment is obtained from load combinations specified in Load

Combinations dialog box. In AASHTO LRFD specification, load combinations need to be

generated as shown in the fig 1.12.

AASHTO LRFD14

(3.4.1)

[Fig.1. 5] Load Combinations and Load factors for strength limit state

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

13

Results>Load combinations>Concrete Design tab

Active:

Strength/Stress

Active:

Serviceability

[Fig.1. 6] Load Combinations dialog

In midas Civil, load combinations can be automatically generated by clicking [Auto

Generation…] button. The load combinations need to be generated in concrete design tab.

The most critical load combination among Strength/Stress type load combinations will be

used to obtain factored moment, factored shear force, and factored torsional moment. The

Service type load combinations will be used to verify the serviceability limit state.

The verification of flexural moment obtained from Strength/Stress type load combination

can be divided into two following cases.

1) No need to satisfy minimum reinforcement

M r t Mu

(1.19)

2) Need to satisfy minimum reinforcement

M r t M u and M r t M cr

1.7 Moment resistance verification

1.7.1 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. 7] Result table for moment resistance

14

Design Guide for midas Civil

(1.20)

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

Muy : Design moment

Mcr : Crack Moment

Mny : Nominal moment resistance.

PhiMny : Design moment resistance.

Ratio : Muy/ PhiMny : Flexural resistance ratio, The verification is satisfied when it is less than 1.0.

PhiMny /min(1.33Muy, Mcr) : Verification of minimum reinforcement. The verification is satisfied when

it is less than 1.0. If the verification of minimum reinforcement is not required, it will be displayed as

1.0.

1.7.2 by Excel Report

Detail verification results can be checked in MS Excel report as shown in the figure below.

Design>PSC Design>PSC Design Calculation…

[Fig.1. 8] Excel report for moment resistance

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

15

2. Shear resistance

Shear resistance without consideration of effects of torsion shall be verified to satisfy the

following condition.

M u d IVn

AASHTO LRFD14

(5.5.4.2.1)

(1.21)

Where, strength reduction factor, Φ=0.9.

Refer to the clause 2.3 Torsion Resistance for the verification of shear resistance where the

effects of torsion are required to be considered. In AASHTO-LRFD (2012), the design for

shear and torsion will be performed for segmental and non-segmental box girders.

2.1 Classification of Segmental Box Girder

The program will consider a section is segmental box girder when the following 2 conditions

are satisfied.

1. In PSC Design Parameter dialog box, Construction Type is specified as Segment.

2. When a section is defined with PSC box section (ex. PSC-1CELL, 2CELL, 3CELL, nCELL,

cCELL2, PLAT, and Value type)

Property > Section Property > Section >PSC

[Fig.1.16] PSC section data dialog

2.2 Parameters for shear

2.2.1 Effective web width (bv)

bv : effective web width taken as the minimum web width within the depth d v as determined in Article

5.8.2.9 (in.)

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.

16

Design Guide for midas Civil

AASHTO LRFD14

(5.8.3.3.3)

Property > Section Property > Section >PSC

[Fig 1.17] Consideration of 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.

2.2.2 Effective shear depth (dv)

▪ Non-Segmental Box Girder

dv

: effective shear depth takem as the distance , measured perpendicular to the neutral axis,

between the resultants of the tensile and compressive forces due to flexure; it need not be

taken less than the greater of 0.9de or 0.72h(in.)

In midas Civil, the value of effective shear depth, dv, is calculated as shown in the equation

below.

dv

de

§

·

Mn

min ¨

, 0.9de , 0.72h ¸

¨ As f s Aps f ps

¸

©

¹

AASHTO LRFD14

(5.8.2.9)

(1.22)

Aps f ps d p As f s d s

(1.23)

Aps f ps As f s

Where,

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

ds : Distance from extreme fiber to the centroid of nonprestressed tensile reinforcement

Chapter 1. Prestressed Concrete Girder Design - AASHTO LRFD 2014

17

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