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ứng dung midas civil trong phân tích kết câu ( bằng tiếng anh)

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


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