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

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 tor

for midas Civil

DESIGN GUIDE

AASHTO LRFD

Prestressed Concrete Girder Design

Steel Composite Girder Design

Steel Composite Bridge Load Rating

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

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DISCLAIMER

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.

ŚĂƉƚĞƌϭƉƌŽǀŝĚĞƐĚĞƚĂŝůĞĚĚĞƐĐƌŝƉƟŽŶƐŽĨƚŚĞĚĞƐŝŐŶƉĂƌĂŵĞƚĞƌƐ͕h>^ͬ^>^ĐŚĞĐŬƐ͕ĚĞƐŝŐŶŽƵƚƉƵƚƐƵƐĞĚĨŽƌƉƌĞƐƚƌĞƐƐĞĚĐŽŶĐƌĞƚĞ

ŐŝƌĚĞƌĚĞƐŝŐŶƚŽ^,dK>Z&͘

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ĚĞƐŝŐŶƚŽ^,dK>Z&͘

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Organization

dŚĞŽďũĞĐƟǀĞŽĨƚŚŝƐĚĞƐŝŐŶŐƵŝĚĞŝƐƚŽŽƵƚůŝŶĞƚŚĞĚĞƐŝŐŶĂůŐŽƌŝƚŚŵƐǁŚŝĐŚĂƌĞĂƉƉůŝĞĚŝŶŵŝĚĂƐŝǀŝůĮŶŝƚĞĞůĞŵĞŶƚĂŶĂůLJƐŝƐĂŶĚĚĞƐŝŐŶƐLJƐƚĞŵ͘dŚĞŐƵŝĚĞĂŝŵƐƚŽƉƌŽǀŝĚĞƐƵĸĐŝĞŶƚŝŶĨŽƌŵĂƟŽŶĨŽƌƚŚĞƵƐĞƌƚŽƵŶĚĞƌƐƚĂŶĚƚŚĞƐĐŽƉĞ͕ůŝŵŝƚĂƟŽŶƐĂŶĚĨŽƌŵƵůĂƐĂƉƉůŝĞĚŝŶƚŚĞĚĞƐŝŐŶfeatures 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 ƚƵƚŽƌŝĂůƐ͕ǁŚŝĐŚĂƌĞĨŽƵŶĚŽŶŽƵƌǁĞďƐŝƚĞ͕ŚƩƉ͗ͬͬǁǁǁ͘DŝĚĂƐhƐĞƌ͘ĐŽŵ͕ďĞĨŽƌĞĚĞƐŝŐŶŝŶŐ͘ĚĚŝƟŽŶĂůŝŶĨŽƌŵĂƟŽŶĐĂŶďĞĨŽƵŶĚŝŶƚŚĞŽŶůŝŶĞhelp available in the program’s main menu

Foreword

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

Chapter 1.

Strength Limit States

Serviceability Limit States

5 Principal stress at service loads

6 Principal stress at service loads

03 16 28

34 40 44 47 49 51

67

Contents

Prestressed Concrete

Girder Design

Chapter 1.

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

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, M u : Factored moment at the section due to strength load combination

ΦM n : Factored flexural resistance

1.1 Resistance Factor

Resistance factor Φ shall be taken as follow

[Fig.1 1] Resistance Factor

Where,

d t : 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

ε t : Net tensile Strain

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

fiber

AASHTO LRFD14 (5.5.4.2.1)

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

೛ Model>Properties>Section Manager>Reinforcements

[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

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

[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

f : Specified compressive strength of concrete for design

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

೛ PSC>PSC Design Data> PSC Design Material…

[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

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

Concrete

AASHTO LRFD14 (5.7.2.2)

(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

Where,

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

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

f s , f s ’: 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

Where,

ε s : the strain of tensile reinforcement

ε s ’ : the strain of compressive reinforcement.

ε cu : the ultimate compressive strain in the concrete (ε cu = 0.003)

c : the neutral axis depth

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

d c : 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 “ε s x E s”

E s : Modulus of elasticity in reinforcement

F y : 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

ps p ps

Where,

A p : the cross sectional area of tendon

f ps : the stress of tendon

೛ 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

[Fig.1 8] Tendon Property Dialog

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

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 Bond Type

Internal (Pre-tension) Bonded

Internal (Post-tension) Unbonded Bonded

▪ 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

▪ f pu , f py

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 Bond Type Tensile Stress

Code Bonded fps for Bonded Type

Unbonded fps for Unbonded Type

Unbonded* 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

f py : Yield strength of prestressing steel

f pu : Specified tensile strength of prestressing steel

d p : 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

AASHTO LRFD14 (5.7.3.1.1) (Eq 5.7.3.1.1-2)

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)

Where,

l i : length of tendon between anchorages

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

is always applied as “0” in midas Civil

(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:

)(

001.00

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

[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

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

AASHTO LRFD14 (5.7.3.2.1) (Eq 5.7.3.2.1-1)

AASHTO LRFD14 (5.7.3.3.2)

AASHTO LRFD14 (5.7.3.3.2) (Eq 5.7.3.3.2-1)

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

3 ( 1 2 )

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, J2 will be applied as 1.0

which is more conservative value

γ3 : 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, J3wil be applied as 1.0

f r : modulus of rupture of concrete specified in Article 5.4.2.6

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

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

externally applied loads (in 3 )

In midas Civil, section modulus under tension is applied.

f cpe : 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

ps e ps e p cpe

A : 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

AASHTO LRFD14 (5.4.2.6) (C5.4.2.6)

೛ 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

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

AASHTO LRFD14 (3.4.1)

೛Results>Load combinations>Concrete Design tab

[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

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

Active:

Serviceability

Active:

Strength/Stress

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

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

b v : 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

AASHTO LRFD14 (5.5.4.2.1)

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

▪ Non-Segmental Box Girder

d v : 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 0.9d e or 0.72h(in.)

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

Where,

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

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

AASHTO LRFD14 (5.8.2.9)

[Fig.1.18] Effective shear depth

▪ Segmental Box Girder

dv : 0.8h or the distance from the extreme compression fiber to the centroid of the prestressing

reinforcement , whichever is greater (in.)

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

h = Total height of a section

d t = Distance from extreme compression fiber to the centroid of the prestressing tendons

s s p ps

M

N V V A f d

d v : 0.8h or the distance from the extreme compression fiber to the centroid of the prestressing

reinforcement , whichever is greater (in.)

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

AASHTO LRFD14 (5.8.6.5) (Eq 5.8.3.4.2-4)

Where,

h : Total height of a section

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

[Fig 1.19] Net longitudinal tensile strain

For non-segmental box girders, the nominal shear resistance, Vn, shall be determined as the

V c : shear resistance component that relies on tensile stresses in the concrete

V s : shear resistance component that relies on tensile stresses in the transverse reinforcement

V p : 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

b v : Effective web width taken as the minimum web width within the depth, dv (refer to the clause

1.2.2.1 Effective web width)

d v : Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

For segmental box girders, the nominal shear resistance, Vn, shall be determined as the lesser

V c : shear resistance component that relies on tensile stresses in the concrete

V s : shear resistance component that relies on tensile stresses in the transverse reinforcement

V p : 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

AASHTO LRFD14 (5.8.3.3) (Eq 5.8.3.3-1) (Eq 5.8.3.3-2)

AASHTO LRFD14 (5.8.6.5) (Eq 5.8.6.5-1) (Eq 5.8.6.5-2)

load combinations

b v : Effective web width taken as the minimum web width within the depth, dv (refer to the clause

1.2.2.1 Effective web width)

d v : Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

Design for shear may utilize any of the two methods (simplified and general procedure) for

prestressed sections identified in AASHTO-LRFD12 In midas Civil, sections can be designed

as per the general procedure

b v : Effective web width taken as the minimum web width within the depth, dv (refer to the clause

1.2.2.1 Effective web width)

d v : Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

β : Factor indicating ability of diagonally cracked concrete to transmit tension and shear as

specified in Article 5.8.3.4

For the sections containing at least the minimum amount of transverse reinforcement :

4.8 (1 750 )s

E

H

  1.38 0.63

S x : The lesser of either d v or the maximum distance between layers of longitudinal

crack control reinforcement, where the area of the reinforcement in each layer is

not less than 0.003bvsx, as shown in Figure 5.8.3.4.2-3(in.) In midas Civil, it is applied as dv

a g : maximum aggregate size(in.)In midas Civil, it is applied as “1in.”

ε s : net longitudinal tensile strain in the section at the centroid of the tension reinforcement.Refer to the

clause 1.2.2.3 Net longitudinal tensile strain

2.4.2 Vc (Segmental Box Girder)

c c v v

Where,

b v : Effective web width taken as the minimum web width within the depth, dv (refer to the clause

1.2.2.1 Effective web width)

d v : Effective shear depth (Refer to the clause 1.2.2.2 Effective shear depth)

K: S tress variable K shall not be taken greater tham 1.0 for any section where the stress in the

extreme tension fiber, calculated on the basis of gross section properties, due to factored load

and effective prestress force after losses exceeds 0.19√f’ c in tension

AASHTO LRFD14 (5.8.3.4)

AASHTO LRFD14 (5.8.3.3) (Eq 5.8.3.3-3)

AASHTO LRFD14 (5.8.3.4.2)

AASHTO LRFD14 (5.8.3.4.2) (Eq 5.8.6.5-3)

0.0632 '

pc c

f K

f

In midas Civil, the value of K is calculated as below

1) Calculate the tensile stress of tendon, ft, after losses Tendon based on the

f pc : Unfactored compressive stress in concrete after prestress losses have occured either at the

centroid of the cross-section resisting transient loads or at the junction of the web and flange

where the centroid lies in the flange (ksi)

In midas Civil, fpc is calculated as follows

Where, y joint is a distance from the centroid to the junction of the web and flange

When the centroid lies in the web, verify the stress at the centroid of the cross-section

ps e u pc

2.5 The nominal shear resistance by shear reinforcement, Vs

The nominal shear resistance by shear reinforcement, Vs, is calculated as follows:

2.5.1 Vs (Non-Segmental Box Girder)

(cot cot ) sin

d v :Refer to 1.2.2.2 Effective shear depth (for Non-Segmental Box Girders)

θ: angle of inclination of diagonal compressive stresses as determined in Article 5.8.3.4 (degrees)

; if the procedures of Article 5.8.3.4.3 are used, cotθ is defined therein

AASHTO LRFD14 (5.8.6.3) (Eq 5.8.6.3-3)

AASHTO LRFD14 (5.8.6.3)

AASHTO LRFD14 (5.8.3.3.3) (Eq 5.8.3.3-4)

[Fig.1.20] angle of inclination of transverse Compressive stress

H :Refer to 1.2.2.3 Net longitudinal tensile strain

α: Angle of inclination of transverse reinforcement to longitudinal axis (degrees)

Enter the Angle of transverse reinforcement as shown in Fig1.22

s: Spacing of transverse reinforcement

Enter the Pitch of transverse reinforcement as shown in Fig1.22

೛Model>Properties>Section Manager>Reinforcements

[Fig.1.21] Transverse Reinforcement

The required input data for transverse reinforcement are as follows:

- Pitch: Enter the spacing of transverse reinforcement

- Angle: Enter the angle of inclination of transverse reinforcement

- Aw: Enter the total area of all transverse reinforcements in the web

2.5.2 Vs (Segmental Box Girder)

midas Civil applies the following equation where the angle of inclination (α) of transverse

reinforcement is taken into account:

AASHTO LRFD14 (5.8.3.4.2) (Eq 5.8.3.4.2-3)

Transverse Reinforcement

d v : refer to 1.1.2.2 Effective shear depth (for Segmental Box Girders)

α: angle of inclination of transverse reinforcement to longitudinal axis (degrees)

Enter the Angle of transverse reinforcement as shown in Fig1.22

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

1) Calculate the shear stress (vu) acting on the concrete



(1.41)

Where,

Φ = Use the shear strength reduction factor of 0.9

b v : refer to 1.1.2.1 Effective web width

d v : refer to 1.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

2) Calculate smax differently, depending on whether the section is Segmental Box Girder or

not and on the range of vu

3) Compare the entered spacing of transverse reinforcement with smax

d v : refer to 2.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

d v : refer to 1.2.2.2 Effective shear depth (for Segmental Box Girders)

midas Civil calculates vu using Eq 5.8.2.9-1 for the shear check and using Eq 5.8.6.5-5

for the torsion check

AASHTO LRFD14 (5.8.3.3.3) ((Eq 5.8.6.5-4)

AASHTO LRFD14 (5.8.2.7)

AASHTO LRFD14 (5.8.2.7) (Eq 5.8.2.9-1)

AASHTO LRFD14 (5.8.2.7)

AASHTO LRFD14 (5.8.6.6) AASHTO LRFD14 (5.8.2.7)

2.7 Minimum required transverse reinforcement (Av,min)

The minimum required transverse reinforcement can be checked according to the following

steps:

1) Calculate the minimum required reinforcement, Av,min , differently dependng on

whether the section is Segmental Box Girder or not

▪ For Non-Segmental Box Girders

' ,min 0.0316 v

In midas Civil bw=bv

2) Calculate the shear strength of the section, and then verify the transverse

reinforcement using the following equations:

If the area of transverse reinforcement (Av) is greater than or equal to Av,req , it says OK

The area of transverse reinforcement (Av) is Aw which is entered from Fig.1.22

AASHTO LRFD14 (5.8.2.4) (Eq 5.8.2.5-1) 







(Eq 5.8.2.5-2)

2.8 Interface Shear

For the composite sections, the Shear Friction caused during construction sequences needs

to be considered Therefore, the Interface Shear check function is activated for the

pre-composite section design check

2.8.1 Calculate Vni

The Vni value is calculated based on the above calculation The Acv is the Interfacial Shear

section area The Acf value is the cross section of the shear reinforcement of the Interfacial

Shear section The following equation (5.8.4.4-1) needs to be satisfied about the minimum

shear reinforcement rea

The Pc value is the compressive force acting on the interface In the program, the Pc value is

calculated based on the selfweight of slab

The program suggests the factors used in design In midas Civil, they are applied as shown

below:

Table The design factors used in midas Civil

AASHTO-LRFD12 Standard

In Acv = bci x Lvi, bci value is taken from the Bvi input by the user and the Lvi value is taken

from the girder length of the program model

The Avf is the cross section of the reinforcement rebars in the interfacial shear plane (Acv) The calculator is activated when the button is clicked So that the cross section is calculated based on the rebar diameter, number and gap inputted by the user

The Vri value is calculated based on the above equation (5.8.4.1-1) Also, the Vri value should be equal to or greater than Vui

For PSC design check, the Ż is taken as 1.0

The Interface Shear calculation can be reviewed in the MS Excel Report

The Interface Shear check result can be also checked in the Shear Resistance Results table

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 Fig.1.12 Load Combinations dialog

2.10 Check the shear resistance results

2.10.1 by Result Tables

The results can be checked as shown in the table below

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

[Fig.1.22] 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

Vu : Maximum shear force among Strength/Stress load combinations

Mu : Bending moment for the LCom which has Vu

Vn : Nominal Shear resistance

Phi : Resistance factor for shear

Vc : Shear resistance of concrete

Vs : Shear resistance of shear reinforcement

Vp : Shear force of the effective prestressing force

PhiVn : Design Shear resistance

de : Effective web width

dv : Effective depth for shear

ex : Longitudinal Strain

theta : Angle of inclination of transverse compressive stresses

beta : Factor indicating ability of transversely cracked concrete to transmit tension

and shear

Avs : Area of shear reinforcement

Ast : Area of longitudinal reinforcement

Al : Area of longitudinal torsional reinforcement

bv : Effective width

Avs_min : Minimum required transverse reinforcement

Avs_req : Required transverse reinforcement

Al_min : Minimum longitudinal torsional reinforcement

bv_min : Minimum effective web width

Vri : Nominal interface shear resistance

Vui : factored interface shear force due to total load based on the applicable strength and extreme

event load combinations

2.10.2 by Excel Report

The detailed results, which contain the calculations, are produced in the Excel Report

೛ Design>PSC Design>PSC Design Calculation…

[Fig.1.23] Excel Report for shear resistance

3 Torsion resistance

Check the combined shear and torsional resistance

3.1 Dimension of section for torsion

The dimensions of section that are required for checking torsion are as follows:

Ao : Area enclosed by the shear flow path, including any area of holes therein (in2)

midas Civil uses the area of the closed section enclosed by the torsion reinforcement, instead of the shear flow path

Ph : Perimeter of the centerline of the closed transverse torsion reinforcement (in)

Acp : Total area enclosed by outside Perimeter of the concrete section (in2)

P : The length of the outside perimeter of concrete section (in)

[Fig.1.24] Dimension of section for torsion

**Additional information for the torsional area Ac and circumference Ph calculation of the composite section

In midas Civil, when Ao section is applied for the composite section, the girder and slab sections (section areas with the Torsion Thk Offset applied in the Section Manager) are calculated separately and then added The Ph circumference is calculated based on the same approach but the value of bw*2 is substracted in order to consider the contact area between the girder and slab

ex)



3.2 Calculate torsional resistance

Torsional resistance can be checked according to the following steps:

1) Calculate the torsional cracking moment (Tcr) differently, depending on whether the section is Segmental Box Girder or not

2) Compare the factored torsional moment (Tu) with the limit, which differs depending on the type of girder (segmental box girder or non-segmental box girder), in order to decide whether the effect of torsion should be considered or not

3) In case where the torsional effect should be considered, calculate the design torsional strength and compare it with T

$FSSF

$RSK

3.2.1 Torsional cracking moment (Tcr)

▪ For Non-Segmental Box Girders

2 '

f pc : compressive stress in concrete after prestress losses have occurred at either the centroid of

the cross-section resisting transient loads or at the junction of the web and flange where the centroid

lies in the flange (ksi)

midas Civil calculates fpc as follows:

If the centroid lies in the flange: calculate at the junction of the web and flange

Where, y joint is the distance from the centroid to the junction of the web and flange.

If the centroid lies in the web: calculate at the centroid of the corss-section

ps e pc

g

A f f

p shall be less than or equal to 2Aobv for a box section

▪ For Segmental Box Girders

b e : effective width of shear flow path, but not exceeding the minimum thickness of the webs

or flanges comprising the closed box section (in.) be shall be adjusted to account for

presence of ducts as specified in Article 5.8.6.1 midas Civil uses bv

3.2.2 Condition for torsion check

▪ For Non-Segmental Box Girders

AASHTO LRFD14 (5.8.6.3) (Eq 5.8.6.3-2)

AASHTO LRFD14 (5.8.2.1) (Eq 5.8.2.1-3)

AASHTO LRFD14 (5.8.6.3) (Eq 5.8.6.3-1)

3.2.3 Torsional resistance

In accordance with AASHTO-LRFD12, the torsional resistance should meet the condition

Tu≤ΦTn for the cases of segmental box girders and non-segmental box girders

▪ For Non-Segmental Box Girders

2 o t ycot

n

A A f T

s

T

(1.51)

Where,

A t : area of one leg of closed transverse torsion reinforcement in solid menbers, or total area of

transverse torsion reinforcement in the exterior web of cellular members (in 2 ) Awt of Torsional

Reinforcement entered in Fig.1 26 will be used

s :Pitch of Torsional Reinforcement entered in Fig.1 26 will be used

Θ: angle of crack as determined in accordance with provisions of Article 5.8.3.4 with the

modifications to the expressions for v and V u herein (degrees) The same equation, which was used for

the shear check, will be used:

29 3500 s

(1.52)

s

H : Refer to 1.2.2.3 Net longitudinal tensile strain

▪ For Segmental Box Girders

2 o t y

n

A A f T

Where,

A t : Awt of Torsional Reinforcement entered in Fig.1 26 will be used

s : Pitch of Torsional Reinforcement entered in Fig.1 26 will be used

The reinforcement data used for the torsion check are as follows:

೛ Model>Properties>Section Manager>Reinforcements

[Fig.1.25] Transverse Reinforcement

- Pitch : spacing of transverse torsional reinforcement

- Awt : area of transverse torsional reinforcement

AASHTO LRFD14 (5.5.4.2.1)

AASHTO LRFD14 (5.8.3.6.2) (Eq 5.8.3.6.2-1)

AASHTO LRFD14 (5.8.3.4.2) (Eq 5.8.3.4.2-3)

AASHTO LRFD14 (5.8.6.4) (Eq 5.8.6.4-2)

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 longitudinal reinforcement

Check the longitudinal reinforcement to resist torsion Check it for box sections and for

solid sections, respectively

▪ For Solid sections

Aps is the area of tensile tendon and As is the area of tensile reinforcement

d v : refer to 2.1.2.2 Effective shear depth (for Non-Segmental Box Girders)

▪ For Box sections

The Code suggests that the reinforcement for resisting torsion is limited to the

following equation for box sections:

midas Civil incorporates the above equation to check the longitudinal torsional

reinforcement The Alt of Torsional Reinforcement entered in Fig.1 26 will be used Alt is

only for resisting warping torsion and is used only for box sections

3.4 Check combined torsional and shear stress

For Segmental Box Girders, check the combined shear and torsional stress

'

0.474 2

b v : refer to 1.1.2.1 Effective web width

d v : refer to 1.1.2.2 Effective shear depth (for Segmental Box Girders)

b e : effective thickness of the shear flow path of the elements making up the space truss model

resisting torsion calculated in accordance with Article 5.8.6.3 (in) midas Civil uses b v

midas Civil calculates the maximum combined stress using the equation below

'

0.474 2

AASHTO LRFD14 (5.8.3.6.3) (Eq 5.8.3.6.3-2)

AASHTO LRFD14 (5.8.6.4) (Eq 5.8.6.4-3)

AASHTO LRFD14 (5.8.6.5) (Eq 5.8.6.5-5)

3.5 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.1.12 Load Combinations dialog

3.6 Check the torsional resistance results

3.6.1 by Result Tables

The results can be checked as shown in the table below

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

[Fig.1.26] 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

Vu : shear force for the corresponding LCom

Mu : bending moment for the corresponding LCom

Tu : torsional moment for the corresponding LCom

Vn : Nominal Shear resistance

Tn : Nominal Torsional resistance

Phi : strength reduction factor for shear

Phi_t : strength reduction factor for torsion

Vc : Shear resistance of concrete

Vs : Shear resistance of shear reinforcement

Vp : Shear force of the effective prestressing force

PhiVn : Design Shear resistance

Phi_tTn : Design Torsional resistance

de : Effective web width

dv : Effective depth for shear

ex : Longitudinal Strain

theta : Angle of inclination of transverse compressive stresses

beta : Factor indicating ability of transversely cracked concrete to transmit tension and shear

Avs : Area of shear reinforcement

Ast : Area of longitudinal reinforcement

Al : Area of longitudinal torsional reinforcement

bv : Effective width

Avs_min : Minimum required transverse reinforcement

Avs_req : Required transverse reinforcement

Al_min : Minimum longitudinal torsional reinforcement

bv_min : Minimum effective web width

At : Area of transverse torsional reinforcement

At_req : Required transverse torsional reinforcement

3.6.2 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.1.27] Excel report for torsional resistance

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

Serviceabiltiy Limit States



1 Stress for cross section at a construction stage

The allowable stress at a construction stage differs depending on the generated stress

because the precompressed 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 (1.59)

Where, the definition of f’ci is stated in 2.1.2

(2) Allowable tensile stress of concrete

[Fig.1.28] Allowable tensile stress of concrete

AASHTO LRFD14 (5.9.4.1.1)

AASHTO LRFD14 (5.9.4.1.2)