Design of Pier Frame 172

8/12/2019 Design of Pier Frame 172

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MUMBAI MONORAIL PROJECT

Definitive Design Review Design Calculation fo r Pier

Struc tures of Pier 1A10a (Frame 4) & Pier 2G1 (Frame 172)

(Buffer Stop) Rev.A1

MM001-D-DR-VSB-LTSE-303182

21-Jun-10Page 1 / 72

LARSEN & TOUBRO LIMITED - SCOMI ENGG. BHD. CONSORTIUM

Contract No.: T/MONORAIL/WJWC/2008

Project Title: MUMBAI MONORAIL

Document Title:

Design Calculation for Pier Structures of Pier1A10a (Frame 4) & Pier 2G1 (Frame 172)

(Buffer Stop)

(Definitive Design Review)

Revision History

A1 21/6/2010 Initial Submission

MARK DATE DESCRIPTION SYSTEMS CIVIL

APPROVED BY (LTSE)Project Director M I S SainiJoint Project Director Suhaimi Yaacob

SCOMI ENGINEERING BERHAD LARSEN & TOUBRO LIMITED

Checked By (QA/QC Manager) Checked By (QA/QCManager)

Checked By (Civil Head)Checked By (Design &Engineering Manager)

Checked By (Project Manager)Checked By (ContractsManager)

Prepared By Prepared By

DATE DATE

CONTRACTORSDOCUMENT No.:

DOCUMENT No.:


REVISION

A1


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PRELIMINARY NOTE

This document is the exclusive property of PJSI Consultants Sdn. Bhd. (PJSI).

It is confidential and may not be used, reproduced or communicated either inwhole or in part, in any form or manner without the prior written agreement ofPJSI.

This document shall not be distributed to third parties except under the terms ofthe contract.

REVISION STATUS

A1 21/6/2010 Initial Submission LEEKL YAPKS AKI

Rev. Date Revision Note Designed by Checked by Approval by


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TABLE OF CONTENTS

TITLE

1. Summary

2. Design Criteria

3. Computer Model

4. Pier Type 12

a. Pier Stemb. Pier Headc. Pier Cap

PAGE

4

5

5

8


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1.0 SUMMARY

This report presents the design calculations for Pier 1A10a and 2G1 (Type 12) of frame 4 andframe 172 with the following parameters. A pair of buffer stops are mounted on the end spanbeam adjacent to pier 1A10a and 2G1 to absorb train impact load upon train overshot.

(a) Horizontal alignment of the guideway structure in planThe alignment is straight or very gently curved with a horizontal radius of greaterthan 1000m.

(b) Soil conditionThe pier base is founded on shallow foundation where the rock level is shallowerthan 5m from the ground level (or about 3m from the pile cut-off level). The base ofthe pier is modeled as fixed in this case.

(c) Span configuration of the guideway frame structure

-The spans are not to exceed 27m and each frame has not more than 4 spans hencelimiting the overall length between expansion joints not more than 108m. (Frame 4)- There is single span which is not exceeds 27m with a bearing end. (Frame 172)

(d) Pier height-Top surface of the guideway beam is about 15m from the top of pilecap.(Frame 4 and Frame 172)

Generally, the design of the pier in buffer stop consists of three sections; pier stem, pier headand pier cap (see Figure 3.1). the pier is of the typical Y pier (1700mm x 1200mm),

The dimensions and reinforcement bars for the piers are summarized as below:

(i) Pier Type 12 (for Pier 1A10a and 2GT) : (Refer drawings MB-GS-D-0557/0558)

- Pier Stem :o Size : 1700mm x 1200mm (Rectangular shape)o Main Bars : 48T32 (about 1.89% of Ac)o Links : T16-150 (Outer) + 8T12-150 (Ties)

- Pier Head :o Main Bars : 16T20 + 36T32o Links : T16-150 (Outer) + 15T12-150 (Ties)

- Pier Cap :o Main Bars : 12T20 + 34T25 (about 0.90% of Ac)o Links : 2T16-175 (Outer) + T16-100/150 (Ties)


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2.0 DESIGN CRITERIA

Refer to design criteria for guide way structure (Definitive Design Review) (MM002-D-DR-VSP-LTSE-303001) for details design criteria. Apart from the loads as applied in typicalanalysis models, these frames are subject to an additional impact load of 400kN, one at a

time, at the end of the frames adjacent to pier 1A10a & 2G1. This impact load of 400kN,derived from the accidental impact force caused by train overshot, is supplied by Scomi videits Letter LT-Gen-MM-L-220378. As it is a type of collision load, it is thus applied underadditional ULS5 load combinations.

Besides, as it is anticipated that these frames are to be connected with future monorail line atpier 1A10a and 2G1, these piers have thus been duly designed to take the loading from anisolated single span frame, which is to be supported by bearing on these piers. The verticaland lateral loads being considered are dead load, superimposed dead load, train live load,hunting force, and longitudinal traction & braking force, which are applied as point loads ontop of the piers.

3.0 COMPUTER MODEL

Fig 3.1 shows the finite element model of the structure. Elastic springs are included in themodel to simulate the soil-structure interaction in both longitudinal and transverse direction.The elements local axis and sign conventions of internal forces used in the computer modelare as shown in Fig. 3.2 and Fig. 3.3, respectively.

1A10a


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Fig. 3.1: Frame 4 and Frame 172 models

Fig. 3.2: Local axis of pier elements (right hand rule).

2G1


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PIER TYPE 12


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4.0 PIER TYPE 12

4.1 PIER STEM TYPE 12

This section documented all results and designs for Pier Stem of TYPE 12.

4.1.1 SUMMARY OF PIER STEM FORCES

The summary of the maximum element forces due to various load combinations aretabulated as below. The results are separated into two tables; first table presents thesummary solely due to service load combinations 1&5 for crackwidth check, and secondtable is of all ultimate load combinations for ultimate design. There are 12 summary cases ineach table, in which:

Case 1 - Maximum & Minimum Axial Force + Corresponding ResultsCase 2 - Maximum & Minimum My + Corresponding Results

Case 3 - Maximum & Minimum Mz + Corresponding ResultsCase 4 - Maximum & Minimum Vy + Corresponding ResultsCase 5 - Maximum & Minimum Vz + Corresponding ResultsCase 6 - Maximum & Minimum Torsion + Corresponding Results

Negative sign in axial force indicates compression and vice versa. As the global analysismodel does not include secondary effects on slender column, additional moment induceddue to slenderness of column shall be added to the initial moment extracted from theanalysis model. If it is short column, additional moment produced in considering a nominalallowance for eccentricity due to construction tolerance (20mm) shall be added to the initialmoment from the analysis model. The calculation is as shown below:

Notation :N = Axial force (kN)My_ct = Bending moment about local axis-y for construction tolerance (kNm)My_s = Bending moment about local axis-y due to column slenderness (kNm)Mz_ct = Bending moment about local axis-z for construction tolerance (kNm)Mz_s = Bending moment about local axis-z due to column slenderness (kNm)

(i) Column bending about local-y

- Shape of deflection:

z

N

lo = 15000mm


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- Column dimension: (shown with local axis)

- Check slenderness:ley= 1.5lo = 22.50mley /hz = 22.50m / 1.20m = 18.75 > 12 Slender column

- Additional moment due to construction tolerance (20mm), My_ct :My_ct = 0.02N

- Additional moment due to column slenderness, My_s :My_s = N [(hz /1750) (ley/ hz)2(1-0.0035ley/ hz)]

= 0.225N

(ii) Column bending about local-z

- Shape of deflection:

15000mm

X

Z

Top face of pilecap

N

y

lo = 15000mm

1700

z

y

1200


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- Column dimension: (shown with local axis)

- Check slenderness:lez = 2.3lo = 34.50m

lez /hy = 34.50m / 1.7m = 20.29 > 12 slender column

- Additional moment due to construction tolerance (20mm),Mz_ct :Mz_ct = 0.02N

- Additional moment due to column slenderness,Mz_s :Mz_s = N [(hy /1750) (lez/ hy)2(1-0.0035lez/ hy)]

= 0.372N

These additional moments due to the effects of construction tolerance or pier slenderness(whichever is greater) are then added to the Midas analysis output for final design forces.

15000mm

X

Y

Top face of pilecap

1700

z

y

1200


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Pier Stem Results

Table 4.1: Service Load Combinations 1&5 (S1&S5)

CASE Elem Load Part Axial My Mz Vy Vz T

(kN) (kNm) (kNm) (kN) (kN) (kNm)

1 (max) 1010 S1-64(max) I[1011] -2288 12 -3 7 -94 41

1 (min) 3010 S1-11 J[3012] -4507 -1251 -436 45 256 113

2 (max) 1010 S1-57(max) J[1012] -3197 1539 -972 19 -127 115

2 (min) 3010 S5.1-3 J[3012] -4276 -2834 -196 67 440 268

3 (max) 1010 S1-24(max) J[1012] -3442 919 2027 -28 -7 138

3 (min) 3010 S1-13 J[3012] -3754 -607 -1489 91 132 13

4 (max) 3010 S1-13 I[3011] -3357 602 -649 91 132 13

4 (min) 1010 S1-28(max) I[1011] -2828 837 624 -84 106 70

5 (max) 3010 S5.1-2 I[3011] -3878 1223 -384 -15 440 -252

5 (min) 1010 S1-57(min) I[1011] -2876 -697 -800 19 -243 115

6 (max) 1010 SLS5-2(max) I[1011] -3025 454 1354 -33 15 277

6 (min) 3010 S5.1-2 I[3011] -3878 1223 -384 -15 440 -252

Table 4.2: Ultimate Load Combinations 1 - 5 (U1-U5)

CASE Elem Load Part Axial My Mz Vy Vz T


1 (max) 1010 U4.1-256 I[1011] -2801 -1675 -1044 10 -577 65

1 (min) 3010 U3b_3.1-11 J[3012] -6381 -3501 -3629 20 -13 -120

2 (max) 1010 U4.1-129 J[1012] -4892 6370 -2384 54 -751 19

2 (min) 1010 U4.1-92 J[1012] -4613 -4831 3938 -134 635 111

3 (max) 1010 U2b.1-20 J[1012] -5143 -1408 7244 -224 132 214

3 (min) 1010 U3b_4.1-59 J[1012] -4753 1735 -5324 -35 -160 -189

4 (max) 3010 U2b.1-10 I[3011] -5157 2818 -2210 316 374 -93

4 (min) 1010 U2b.1-28 I[1011] -3890 1846 3875 -303 153 313

5 (max) 3010 U5.1-1 J[3012] -3738 -3938 -1451 5 1300 -50

5 (min) 1010 U4.1-129 I[1011] -4329 -2608 -1679 54 -751 19

6 (max) 1010 U2b.1-25 I[1011] -4190 1145 3118 -168 -59 591

6 (min) 1010 U3b_4.1-4 I[1011] -4235 -1023 -2064 -13 -180 -419


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4.1.2 PIER STEM ULTIMATE LIMIT STATE DESIGN

The ultimate limit state sectional analysis is carried out by AdSEC software, whereasultimate shear and torsion design is done by using spreadsheet.

4.1.2.1 Pier Stem Axial and Bending Design to IRS CBC - 1997

The table 4.3 shows the envelope of pier forces for ultimate axial and bending design. Theultimate limit state analysis is done by using AdSEC software. Figure 4.1 shows thearrangement of bars in the pier stem. 7 cases are studied, which are:

Case 1 - Max & Min Axial Force + Corresponding ResultsCase 2 - Max & Min My + Corresponding ResultsCase 3 - Max & Min Mz + Corresponding ResultsCase 6 - Absolute Max Torsion + Corresponding Results

Table 4.3: Ultimate Load Combinations 1 - 5 (U1-U5) Maximum Final Design Forces forAxial and Bending Design

CASE Elem Load Part Axial My Mz Vy Vz T(kN) (kNm) (kNm) (kN) (kN) (kNm)

1 (max) 1010 U4.1-256 I[1011] -2801 -1675 -1044 10 -577 65

1 (min) 3010 U3b_3.1-11 J[3012] -6381 -3501 -3629 20 -13 -120

2 (max) 1010 U4.1-129 J[1012] -4892 6370 -2384 54 -751 19

2 (min) 1010 U4.1-92 J[1012] -4613 -4831 3938 -134 635 111

3 (max) 1010 U2b.1-20 J[1012] -5143 -1408 7244 -224 132 214

3 (min) 1010 U3b_4.1-59 J[1012] -4753 1735 -5324 -35 -160 -189

6 (max) 1010 U2b.1-25 I[1011] -4190 1145 3118 -168 -59 591

Fig. 4.1: Pier Stem bar arrangement


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Definition

Name Pier Stem 12

Type Concrete

Material C45

Section Area 2.039E+6mmReinforcement Area 38600.mm

Reinforcement 1.894%

Properties

Area 2.039E+6mm

Geometric Centroid y 0.0mm

z 0.0mm

Second Moments of Area Iyy 244.4E+9mm4

Izz 490.4E+9mm4

Iyz -10760.mm4

Principal Second Moments of Area Iuu 490.4E+9mm4

Izz 244.4E+9mm4

Angle 90.00

Shear Area Factor ky 0

kz 0

Torsion Constant 0.0mm4

Section Modulus Zy 407.3E+6mm

Zz 577.0E+6mm

Plastic Modulus Zpy 611.3E+6mmZpz 865.9E+6mm

Radius of Gyration Ry 346.2mm

Rz 490.5mm

Maximum compressive force Nmax 53990.kN

Strain at Nmax 0

Moment at ref. pt. for Nmax Myy 0.0kNm

Mzz 0.0kNm

Note: Nmax is the maximum compressive force which can be carried by the section.This is calculated by applying a constant strain across the entire section, using

ultimate material properties.


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Section Material PropertiesType ConcreteName C45Weight Normal WeightDensity 2.300t/m

Cube Strength fcu 45MpaTensile Strength fct 3.22MpaElastic Modulus (short term) E 32500MPaPoisson's Ratio v 0.2Coeff. Thermal Expansion 12.00E-6/C

Partial Safety Factor mc,ULS 1.5

mc,SLS 1Maximum Strain 0.0035ULS Compression Curve Recto-parabolicULS Tension Curve No-tensionSLS Compression Curve Linear

SLS Tension Curve No-tensionAggregate Size 20.00mm

Reinforcement Properties

LoadingReference PointAll loading acts through the Reference Point.All strain planes are defined relative to the Reference Point.Definition Geometric CentroidReference Point Coordinates y 0.0mm

z 0.0mmTotal ULS Loads

Analysis N Myy Mzz M Case [kN] [kNm] [kNm] [kNm] []

1 2801 -1675 -1044 1974 148.12 6381 -3501 -3629 5042 134

3 4892 6370 -2384 6801 20.52

4 4613 -4831 3938 6233 -140.8

5 5143 -1408 7244 7380 -101

Name Fe500fy 500MPaModulus 200000MPa


mc,SLS 1Maximum Strain 0.05Stress/Strain Curve Fig 2


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6 4753 1735 -5324 5600 71.95

7 4190 1145 3118 3322 -69.84

Strength Analysis SummaryGoverning conditions are defined as:

A - reinforcing steel tension strain limitB - concrete compression strain limit

Effective centroid is reported relative to the reference point.Analysis Eff. Eff. N Nmax N/Nmax M Mu M/Mu Governing Neutral Neutral

Case Centroid Centroid Condition Axis Axis

(y) (z) Angle Depth

(NA)

[mm] [mm] [kN] [kN] [kNm] [kNm] [] [mm]

1 0.00 0.00 2801 53990 0.0519 1974.0 9965 0.1981 B: Node 7 160.5 559.6

2 0.00 0.00 6381 53990 0.1182 5042.0 11150 0.4521 B: Node 7 148.7 748.9

3 0.00 0.00 4892 53990 0.0906 6801.0 10400 0.6543 B: Node 2 13.33 517.6

4 0.00 0.00 4613 53990 0.0854 6233.0 10590 0.5883 B: Node 6 -154.3 665.8

5 0.00 0.00 5143 53990 0.0953 7380.0 13230 0.5580 B: Node 5 -111.7 691.16 0.00 0.00 4753 53990 0.0880 5600.0 12490 0.4483 B: Node 1 58.38 737.3

7 0.00 0.00 4190 53990 0.0776 3322 12160 0.2731 B: Node 4 -55.92 732.9

M/Mu < 1.0 OK!

4.1.2.2 Pier Stem Shear and Torsion Design to IRS CBC - 1997

The table 4.4 shows the most critical cases for shear and torsion design.

Table 4.4: Ultimate Load Combinations 1 - 5 (U1-U5) Maximum Final Design Forces forShear and Torsion Design

CASE Elem Load Part Axial My Mz Vy Vz T(kN) (kNm) (kNm) (kN) (kN) (kNm)

4 (max) 3010 U2b.1-10 I[3011] -5157 2818 -2210 316 374 -93

4 (min) 1010 U2b.1-28 I[1011] -3890 1846 3875 -303 153 313

5 (max) 3010 U5.1-1 J[3012] -3738 -3938 -1451 5 1300 -50

5 (min) 1010 U4.1-129 I[1011] -4329 -2608 -1679 54 -751 19

6 (max) 1010 U2b.1-25 I[1011] -4190 1145 3118 -168 -59 591

6 (min) 1010 U3b_4.1-4 I[1011] -4235 -1023 -2064 -13 -180 -419

The design calculations for ultimate shear and torsion are shown in the spreadsheet nextpages. 3 cases are studied, which are:

i) Absolute Maximum Vy + Corresponding Vz & Torsionii) Absolute Maximum Vz + Corresponding Vy & Torsioniii) Absolute Maximum Torsion + Corresponding Vz & Vy


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PIER SHEAR & TORSION DESIGN

to IRS CBC - 1997

Reference : Pier Stem for Buffer Stop

Case : Maximum Vy + corresponding Vz & Torsion

Input Data : Z

hy= 1700 mm Cover = 50 mm Ybz= 1200 mm Tension Reinf. F = 32 mm

fcu = 45 N/mm2

As provided,(z-dir) = 8040 mm2

fy = 415 N/mm2

As provided,(y-dir) = 14472 mm2

1200

fyv = 415 N/mm2

Shear Link, (z-dir) = 12 mm

Shear Link, (y-dir) = 12 mm 1700Torsion Link = 16 mm

Analysis Results :

Shear (z-dir) = 374 kN

Shear (y-dir) = 316 kN

N = 5157 kN

Torsion = 93 kNm

SHEAR DESIGN (Cl. 15.6.6 IRS CBC - 1997)

a) Shear in z- direction:

V = 374.0 kNb = 1700.0 mmd = 1118.0 mm

vz= 0.20 N/mm2

OK!

100As/bd = 0.76

vc = 0.67 N/mm2

depth factor, s= 0.82

1+0.05N/Ac = 1.13

Asv/sv = 1.88 mm2/mm

b) Shear in y- direction:

V = 316.0 kNb = 1200.0 mmd = 1618.0 mm

vy= 0.16 N/mm OK!

100As/bd = 0.41

vc = 0.55 N/mm2


1+0.05N/Ac = 1.13


c) Shear resistance of pier:

Vcz = 1181 kN [concrete capacity)Vsz = 2604 kN [link capacity = 0.87fy(As)d/(sv) ]Vcy = 843 kN [concrete capacity]Vsy= 2887 kN [link capacity = 0.87fy(As)d/(sv)]

Vz / Vuz + Vy / Vuy < 1

0.10 + 0.08 = 0.18 OK!


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TORSION DESIGN (Cl. 15.4.4 IRS CBC - 1997)

a) Torsional Shear Stress, vt

vt = 2T / [h2

min(hmax- hmin/3)] = 0.10 N/mm

hmin = 1200 mm

hmax = 1700 mm

c) Minimum Ultimate Torsional Shear Stress, vtmin

vtmin = 0.067 (fcu)0.5

= 0.42 N/mm No Torsional Reinf Required

d) Ultimate Torsional Shear Stress, vtu

vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 1568 mm

In z-dir : vz + vt = 0.30 N/mm (OK)

In y-dir: vy + vt = 0.26 N/mm (OK)

e) Torsional link, Ast/sv

Ast/sv = T / [0.8 x1y1(0.87fyv )] = 0.19 mm2/mm

COMBINED SHEAR AND TORSION DESIGN

a) Shear Links

Torsion Required 2 T 16 Links @ 2091

alone Provide 2 T 16 Links @ 150 (Asv/sv = 2.68mm2/mm )

(OK)

Torsion In z-dir: Total torsion + shear link required 2.08 mm2/mm

+ Provide 2 T 16 Links @ 150 + (outer legs)

Shear 5 T 12 Links @ 150 (inner legs) (Asv/sv = 6.45mm2/mm )

(OK)

Torsion In y-dir: Total torsion + shear link required 1.52 mm2/mm


Shear 3 T 12 Links @ 150 (inner legs) (Asv/sv = 4.94mm2/mm )

(OK)

b) Longitudinal Reinforcement, AsL/sL

AsL/sL= Ast/sv(fyv/fy) = 0.10 mm2/mm

AsL = 253 mm2

Required 1 T 32 EF (As = 804 mm2)


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to IRS CBC - 1997


Case : Maximum Vz + corresponding Vy & Torsion

Input Data : Z


fcu = 45 N/mm2


fy = 415 N/mm2


1200

fyv = 415 N/mm2



Analysis Results :



N = -3738 kN

Torsion = 50 kNm



V = 1300.0 kNb = 1700.0 mmd = 1118.0 mm

vz= 0.68 N/mm OK!

100As/bd = 0.76

vc = 0.67 N/mm2


1+0.05N/Ac = 0.91



V = 5.0 kNb = 1200.0 mmd = 1618.0 mm

vy= 0.00 N/mm2

OK!

100As/bd = 0.41

vc = 0.55 N/mm2


1+0.05N/Ac = 0.91





0.37 + 0.00 = 0.37 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 1700 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 1568 mm






a) Shear Links


alone Provide 2 T 16 Links @ 150 (Asv/sv = 2.68 mm2/mm )

(OK)



Shear 5 T 12 Links @ 150 (inner legs) (Asv/sv = 6.45 mm2/mm )

(OK)




(OK)


AsL/sL = Ast/sv(fyv/fy) = 0.05 mm2/mm

AsL = 136 mm2



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to IRS CBC - 1997


Case : Maximum Torsion + corresponding Vy & Vz

Input Data : Z


fcu = 45 N/mm2


fy = 415 N/mm2


1200

fyv = 415 N/mm2



Analysis Results :



N = 4190 kN

Torsion = 591 kNm



V = 59.0 kN

b = 1700.0 mmd = 1118.0 mm

vz= 0.03 N/mm2

OK!

100As/bd = 0.76

vc = 0.67 N/mm2


1+0.05N/Ac = 1.10



V = 168.0 kN

b = 1200.0 mmd = 1618.0 mm

vy= 0.09 N/mm2

OK!

100As/bd = 0.41

vc = 0.55 N/mm2


1+0.05N/Ac = 1.10



Vcz = 1156 kN [concrete capacity)Vsz = 2604 kN [link capacity = 0.87fy(As)d/(sv) ]

Vcy = 825 kN [concrete capacity]Vsy= 2887 kN [link capacity = 0.87fy(As)d/(sv)]


0.02 + 0.05 = 0.06 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 1700 mm


vtmin = 0.067 (fcu)0.5

= 0.42 N/mm Torsional Reinf Required


vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 1568 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 1610 mm2


Maximum torsion induced in pier stem required 3T32 each face or total 6T32, which is about0.1071 of total perimeter bar provided. The ultimate moment utilized 0.2731 correspondingto absolute maximum torsion, giving a total utilization ratio of 0.3802 < 1. Hence, it deemedsatisfactory.


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4.1.3 PIER STEM SERVICEABILITY LIMIT STATE CHECK

The crack width of the pier is checked against service load combinations 1&5, by usingAdSEC software. Table below shows the envelope of pier forces for serviceability check. Thearrangement of bars in the pier stem is shown in ultimate limit check. 6 cases are checked,

which are:

Case 1 - Max & Min Axial Force + Corresponding ResultsCase 2 - Max & Min My + Corresponding ResultsCase 3 - Max & Min Mz + Corresponding Results

Table 4.5: Serviceability Load Combinations 1&5 (S1 and S5) Maximum Final Forces forCombined Axial and Bending SLS check

CASE Elem Load Part Axial My Mz(kN) (kNm) (kNm)

1 (max) 1010 S1-64(max) I[1011] -2288 12 -3

1 (min) 3010 S1-11 J[3012] -4507 -1251 -4362 (max) 1010 S1-57(max) J[1012] -3197 1539 -972

2 (min) 3010 S5.1-3 J[3012] -4276 -2834 -196

3 (max) 1010 S1-24(max) J[1012] -3442 919 2027

3 (min) 3010 S1-13 J[3012] -3754 -607 -1489

LoadingReference PointAll loading acts through the Reference Point.All strain planes are defined relative to the Reference Point.Definition Geometric Centroid

Reference Point Coordinates y 0.0mmz 0.0mm

Applied loads

Load N Myy MzzCase [kN] [kNm] [kNm]

1 2288 12 -3

2 4507 -1251 -436

3 3197 1539 -972

4 4276 -2834 -196

5 3442 919 2027

6 3754 -607 -1489


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4 0.00 0.00 4276 53990 0.08 2841 10260 0.28 881

5 0.00 0.00 3442 53990 0.06 2226 11650 0.19 702

6 0.00 0.00 3754 53990 0.07 1608 11890 0.14 783

Crack Widths at SLS Loads

Crack widths calculated at 20mm intervalsAnalysis Face Point y z Strain Strain bt Control Acr Cmin Cmin h x Crack

Case Em E1 Bar From Width

[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm]

2 2 79 684.7 588 -64.90E-06 -64.90E-06 732.3 17 66 62 Face 2 1492 1241 0.0114

3 86 795.3 588 -71.32E-06 -71.32E-06 732.3 1 55.44 62 Face 2 1492 1241 0.0114

4 90 834 549.3 -61.99E-06 -61.99E-06 732.3 1 55.44 62 Face 2 1492 1241 0.0099

3 4 140 834 -450.7 -250.40E-06 -250.40E-06 878.9 8 81.19 62 Face 6 1688 1015 0.0558

5 149 795.3 -588 -304.70E-06 -304.70E-06 878.9 8 55.44 62 Face 6 1688 1015 0.0499

6 161 575.3 -588 -269.90E-06 -269.90E-06 878.9 27 73.64 62 Face 6 1688 1015 0.0557

7 231 -7.95E+02 -588 -52.70E-06 -52.70E-06 878.9 16 55.44 62 Face 6 1688 1015 0.0086

8 235 -8.34E+02 -549.3 -29.57E-06 -29.57E-06 878.9 16 55.44 62 Face 6 1688 1015 0.0048

4 1 4 -795.3 588.0 -414.20E-06 -414.20E-06 1701 9 55.44 62 Face 2 1264 714.1 0.0676

2 73 564.7 588.0 -460.90E-06 -460.90E-06 1701 18 80.2 62 Face 2 1264 714.1 0.0999

3 86 795.3 588.0 -468.90E-06 -468.90E-06 1701 1 55.44 62 Face 2 1264 714.1 0.0765

4 95 834 449.3 -349.20E-06 -349.20E-06 1701 1 82.16 62 Face 2 1264 714.1 0.0771

8 285 -834 450.7 -293.00E-06 -293.00E-06 1701 9 81.19 62 Face 2 1264 714.1 0.0641

5 1 1 -834 5.49E+02 -27.90E-06 -27.90E-06 655.6 9 55.44 62 Face 2 2040 1230 0.0046

2 5 -795.3 588 -5.24E-06 -5.24E-06 655.6 9 55.44 62 Face 2 2040 1230 0.0009

6 218 -564.7 -588 -249.70E-06 -249.70E-06 655.6 35 80.2 62 Face 6 2040 1230 0.0559

7 234 -8.34E+02 -549.3 -324.40E-06 -324.40E-06 655.6 16 55.44 62 Face 6 2040 1230 0.0532

8 240 -834 -449.3 -297.40E-06 -297.40E-06 655.6 16 82.16 62 Face 6 2040 1230 0.0679

6 2 85 7.95E+02 588 -131.20E-06 -131.20E-06 486.7 1 55.44 62 Face 2 2048 1499 0.0214

3 89 834 549.3 -133.00E-06 -133.00E-06 486.7 1 55.44 62 Face 2 2048 1499 0.0217

4 95 834 449.3 -117.30E-06 -117.30E-06 486.7 1 82.16 62 Face 2 2048 1499 0.0259 Max. Crack width = 0.0999 < 0.2mm OK!


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4.2 PIER HEAD TYPE 12

The methodology adopted for the computation of the forces acting on the solid pier-head isas described below. The corresponding member forces (for the same relevant loadcase/combination) in each of the two pier legs from the computer model are resolved and

statically combined to act at the centroid of the solid pier-head. The envelope of the resultantforces for all the relevant load cases and combinations are then used for section analysisusing the AdSec software to check for crack-width and ultimate strength capacity.

1. Find the member forces for each of the two pier legs corresponding to the relevantload case/combination.

2. Resolve the member forces to the line of cut taking into consideration of the geometryand inclination of the pier legs. Two horizontal cuts are made (See Fig 4.2): CUT-1 atthe top of the pier-head and just below the pier-cap, and CUT-2 at the mid-height ofthe pier-head i.e. mid-point between the pier-cap and the top of the pier stem.

3. The resolved member forces are statically combined to obtain the force resultant

acting at the centroid of the solid pier-head.4. The envelope of the force resultants from various relevant load combinations are then

used for section analyses to check for crack-width and ultimate strength capacity bymeans of the AdSec software.

Fig. 4.2: Figure Showing CUT-1 And CUT-2 Across The PierHead


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4.2.1 SUMMARY OF RESULTANT FORCES FOR TYPE 12 PIER-HEADS

The summary of the envelope of maximum resultant forces in the pier-heads TYPE 12 due tovarious load combinations are tabulated below. The results are separated into two tables.Tables 4.6 and 4.8 present the force summaries at CUT-1 (just below the pier-cap, see Fig4.2)

and CUT-2 (at pier-head mid height) due to service load combination 1 for the purpose ofcrack-width check. Tables 4.7 and 4.9 are of all ultimate load combinations for the purpose ofultimate limit state design. There are 12 summary cases in each table, namely:

Case 1 Maximum & minimum Axial Force + corresponding resultsCase 2 Maximum & minimum Axial Force + corresponding resultsCase 3 Maximum & minimum My + corresponding resultsCase 4 Maximum & minimum My + corresponding resultsCase 5 Maximum & minimum Mz + corresponding resultsCase 6 Maximum & minimum Mz + corresponding results

Negative sign in axial force indicates compression and vice versa.

Envelope Of Type 12 Pier-Head Resultant Forces

Table 4.6: Service Load Combinations 1&5 (SLS1 and SLS5) Along CUT-1

CASE

Leg 1

Elem

Leg 2

Elem Load Axial My Mz Vy Vz T


1 (max) 1008 1009 S1-32(max) -2328 -1000 62 -53 -60 189

1 (min) 3008 3009 S5.1-3 -3648 -629 -2589 440 67 268

2 (max) 1008 1009 S1-57(max) -2516 741 957 -185 19 105

2 (min) 1008 1009 S1-24(max) -2761 -1683 106 -66 -28 129

3 (max) 1008 1009 S1-57(max) -2516 741 957 -185 19 1053 (min) 3008 3009 S5.1-2 -3648 431 -2602 440 -15 -252

4 (max) 3008 3009 S5.1-3 -3648 -629 -2589 440 67 268

4 (min) 1008 1009 S1-57(max) -2516 741 957 -185 19 105

5 (max) 3008 3009 S5.1-3 -3648 -629 -2589 440 67 268

5 (min) 1008 1009 S1-32(max) -2328 -1000 62 -53 -60 189

6 (max) 3008 3009 S5.1-3 -3648 -629 -2589 440 67 268

6 (min) 3008 3009 S5.1-2 -3648 431 -2602 440 -15 -252


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Table 4.7: Ultimate Load Combinations 1 - 5 (U1-U5) Along CUT-1

CASE

Leg 1

Elem

Leg 2



1 (max) 3008 3009 U3a_2.1-1 -2885 1 -87 6 5 -150

1 (min) 3008 3009 U2b.1-11 -5463 -760 -3008 407 86 351

2 (max) 3008 3009 U3b_3.1-15 -4843 1362 -1884 181 26 216

2 (min) 1008 1009 U2b.1-22 -3869 -3312 -440 22 -130 384

3 (max) 1008 1009 U4.1-129 -4041 -99 3987 -751 54 19

3 (min) 3008 3009 U5.1-3 -4909 -1052 -3536 520 136 286

4 (max) 1008 1009 U4.1-94 -3339 -1543 -3095 525 -95 279

4 (min) 1008 1009 U4.1-129 -4041 -99 3987 -751 54 19

5 (max) 3008 3009 U5.1-3 -4909 -1052 -3536 520 136 286

5 (min) 3008 3009 U2b.1-8 -4154 -1158 -2547 326 -217 254

6 (max) 1008 1009 U4.1-153 -3741 -384 2565 -541 -77 433

6 (min) 1008 1009 U4.1-132 -3741 -291 2558 -540 -2 -304

Table 4.8: Service Load Combinations 1&5 (SLS1 and SLS5) Along CUT-2

CASELeg 1Elem

Leg 2Elem Load Axial My Mz Vy Vz T


1 (max) 1008 1009 S1-32(max) -2443 -1095 -21 -53 -60 189

1 (min) 3008 3009 S5.1-3 -3764 -524 -1899 440 67 268

2 (max) 1008 1009 S1-57(max) -2631 770 667 -185 19 105

2 (min) 1008 1009 S1-24(max) -2877 -1727 3 -66 -28 129

3 (max) 1008 1009 S1-57(max) -2631 770 667 -185 19 105

3 (min) 3008 3009 S5.1-2 -3763 408 -1912 440 -15 -252

4 (max) 3008 3009 S5.1-3 -3764 -524 -1899 440 67 268

4 (min) 1008 1009 S1-57(max) -2631 770 667 -185 19 105

5 (max) 3008 3009 S5.1-3 -3764 -524 -1899 440 67 268

5 (min) 1008 1009 S1-32(max) -2443 -1095 -21 -53 -60 189

6 (max) 3008 3009 S5.1-3 -3764 -524 -1899 440 67 268

6 (min) 3008 3009 S5.1-2 -3763 408 -1912 440 -15 -252


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Table 4.9: Ultimate Load Combinations 1 - 5 (U1-U5) Along CUT-2

CASE

Leg 1

Elem

Leg 2



1 (max) 3008 3009 U3a_2.1-1 -3029 9 -87 6 5 -191

1 (min) 3008 3009 U2b.1-11 -5608 -625 -2371 407 86 351

2 (max) 3008 3009 U3b_3.1-15 -4987 1403 -1598 181 26 226

2 (min) 1008 1009 U2b.1-22 -4013 -3516 -406 22 -130 384

3 (max) 1008 1009 U4.1-129 -4185 -14 2810 -751 54 19

3 (min) 3008 3009 U5.1-3 -5053 -839 -2721 520 136 286

4 (max) 1008 1009 U4.1-94 -3483 -1693 -2272 525 -95 279

4 (min) 1008 1009 U4.1-129 -4185 -14 2810 -751 54 19

5 (max) 3008 3009 U5.1-3 -5053 -839 -2721 520 136 286

5 (min) 3008 3009 U2b.1-8 -4298 -1498 -2036 326 -217 254

6 (max) 1008 1009 U4.1-153 -3885 -505 1717 -541 -77 433

6 (min) 1008 1009 U4.1-132 -3886 -294 1712 -540 -2 -304


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4.2.2 TYPE 12 PIER-HEADS Of PIER: ULTIMATE LIMIT STATE DESIGN

The ultimate limit state sectional analysis is carried out by AdSec software, whereas shearand torsion design is done by using spreadsheet.

4.2.2.1 Type 12 Pier-Heads Of Pier: Axial and Bending Design to IRS CBC 1997 AlongCUT-1

Table below shows the envelope of pier-head resultant forces along CUT-1 for ultimate axialand bending design. The ultimate limit state analyses are done by using AdSec software.Figure shows the arrangement of bars in the pier-head. 6 cases are studied, which are:

Case 1 Maximum & minimum Axial Force + corresponding resultsCase 2 Maximum & minimum My + corresponding resultsCase 3 Maximum & minimum Mz + corresponding results

Table 4.10: Ultimate Load Combinations 1 - 5 (U1-U5) Maximum And Minimum ResultantForces Of Pier-Head Type 12 At CUT-1 for Combined Axial and Bending Ultimate Design

CASE

Leg 1

Elem

Leg 2



1 (max) 3008 3009 U3a_2.1-1 -2885 1 -87 6 5 -150

1 (min) 3008 3009 U2b.1-11 -5463 -760 -3008 407 86 351

2 (max) 3008 3009 U3b_3.1-15 -4843 1362 -1884 181 26 216

2 (min) 1008 1009 U2b.1-22 -3869 -3312 -440 22 -130 384

3 (max) 1008 1009 U4.1-129 -4041 -99 3987 -751 54 19

3 (min) 3008 3009 U5.1-3 -4909 -1052 -3536 520 136 286

Fig. 4.3: Pier HEAD bar arrangement


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DefinitionName Pier HEAD 12Type ConcreteMaterial C45Section Area 5.693E+6mm

Reinforcement Area 33980.mmReinforcement 0.5969%

PropertiesArea 5.693E+6mmGeometric Centroid y 0.0mm

z 0.0mmSecond Moments of Area Iyy 682.8E+9mm4

Izz 10.68E+12mm4Iyz -436800.mm4

Principal Second Moments of Area Iuu 10.68E+12mm4

Izz 682.8E+9mm4Angle 90.00

Shear Area Factor ky 0kz 0

Torsion Constant 0.0mm4Section Modulus Zy 1.138E+9mm

Zz 4.500E+9mmPlastic Modulus Zpy 1.707E+9mm

Zpz 6.752E+9mmRadius of Gyration Ry 346.3mm

Rz 1369mm

Maximum compressive force Nmax 125900.kNStrain at Nmax 0Moment at ref. pt. for Nmax Myy 0.0kNm

Mzz 0.0kNmNote: Nmax is the maximum compressive force which can be carried by the section.This is calculated by applying a constant strain across the entire section, usingultimate material properties.

Section Material PropertiesType ConcreteName C45

Weight Normal WeightDensity 2.300t/mCube Strength fcu 45MpaTensile Strength fct 3.22MpaElastic Modulus (short term) E 32500MPa


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Poisson's Ratio v 0.2Coeff. Thermal Expansion 12.00E-6/C


mc,SLS 1Maximum Strain 0.0035

ULS Compression Curve Recto-parabolicULS Tension Curve No-tensionSLS Compression Curve LinearSLS Tension Curve No-tensionAggregate Size 20.00mm


LoadingReference PointAll loading acts through the Reference Point.All strain planes are defined relative to the Reference Point.Definition Geometric CentroidReference Point Coordinates y 0.0mm

z 0.0mmTotal ULS Loads


1 2885 1 -87 87.01 89.34

2 5463 -760 -3008 3103 104.2

3 4843 1362 -1884 2325 54.14

4 3869 -3312 -440 3341 172.4

5 4041 -99 3987 3988 -91.42

6 4909 -1052 -3536 3689 106.6

Name Fe500fy 500MPaModulus 200000MPa


mc,SLS 1

Maximum Strain 0.05Stress/Strain Curve Fig 2


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Effective centroid is reported relative to the reference point.

Analysis Eff. Eff. N Nmax N/Nmax M Mu M/Mu Governing Neutral NeutralCase Centroid Centroid Condition Axis Axis

(y) (z) Angle Depth

(NA)


1 0.00 0.00 2885 125900 0.0229 87.0 37880 0.0023 B: Node 1 84.22 572.5

2 0.00 0.00 5463 125900 0.0434 3103.0 33030 0.0939 B: Node 7 165.7 624.6

3 0.00 0.00 4843 125900 0.0385 2325.0 17080 0.1361 B: Node 2 3.018 280

4 0.00 0.00 3869 125900 0.0307 3341.0 10010 0.3339 B: Node 7 179.8 136

5 0.00 0.00 4041 125900 0.0321 3988.0 39950 0.0998 B: Node 5 -102.8 681.3

6 0.00 0.00 4909 125900 0.0390 3689.0 29920 0.1233 B: Node 7 169.1 539.1

M/Mu < 1.0

OK!

4.2.2.2 Type 12 Pier-Heads Of Pier: Axial and Bending Design to IRS CBC 1997 AlongCUT-2

Table below shows the envelope of pier-head resultant forces along CUT-2 for ultimate axialand bending design. The ultimate limit state analyses are done by using AdSec software.Figure shows the arrangement of bars in the pier-head. 6 cases are studied, which are:

Case 1 Maximum & minimum Axial Force + corresponding resultsCase 2 Maximum & minimum My + corresponding resultsCase 3 Maximum & minimum Mz + corresponding results

Table 4.11: Ultimate Load Combinations 1 - 5 (U1-U5) Maximum And Minimum ResultantForces Of Pier-Head Type 12 At CUT-2 for Combined Axial and Bending Ultimate Design

CASE

Leg 1

Elem

Leg 2



1 (max) 3008 3009 U3a_2.1-1 -3029 9 -87 6 5 -191

1 (min) 3008 3009 U2b.1-11 -5608 -625 -2371 407 86 351

2 (max) 3008 3009 U3b_3.1-15 -4987 1403 -1598 181 26 226

2 (min) 1008 1009 U2b.1-22 -4013 -3516 -406 22 -130 384

3 (max) 1008 1009 U4.1-129 -4185 -14 2810 -751 54 19

3 (min) 3008 3009 U5.1-3 -5053 -839 -2721 520 136 286


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Fig. 4.4: Pier HEAD Cut 2 bar arrangementDefinitionName Pier HEAD 12Type ConcreteMaterial C45Section Area 2.892E+6mmReinforcement Area 28950.mmReinforcement 1.001%

PropertiesArea 2.892E+6mmGeometric Centroid y 0.0mm

z 0.0mmSecond Moments of Area Iyy 346.7E+9mm4

Izz 1.400E+12mm4

Iyz -46030.mm4Principal Second Moments of Area Iuu 1.400E+12mm4

Izz 346.7E+9mm4Angle 90.00

Shear Area Factor ky 0kz 0

Torsion Constant 0.0mm4Section Modulus Zy 577.6E+6mm

Zz 1.161E+9mmPlastic Modulus Zpy 867.2E+9mm

Zpz 1.742E+9mm

Radius of Gyration Ry 346.3mmRz 695.7mm

Maximum compressive force Nmax 67890.kNStrain at Nmax 0


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Moment at ref. pt. for Nmax Myy 8.078E-6kNmMzz 0.0kNm

Note: Nmax is the maximum compressive force which can be carried by the section.This is calculated by applying a constant strain across the entire section, usingultimate material properties.

Section Material PropertiesType ConcreteName C45Weight Normal WeightDensity 2.300t/mCube Strength fcu 45MpaTensile Strength fct 3.22MpaElastic Modulus (short term) E 32500MPaPoisson's Ratio v 0.2Coeff. Thermal Expansion 12.00E-6/C

Partial Safety Factor mc,ULS 1.5mc,SLS 1

Maximum Strain 0.0035ULS Compression Curve Recto-parabolicULS Tension Curve No-tensionSLS Compression Curve LinearSLS Tension Curve No-tensionAggregate Size 20.00mm


LoadingReference PointAll loading acts through the Reference Point.All strain planes are defined relative to the Reference Point.Definition Geometric Centroid

Reference Point Coordinates y 0.0mmz 0.0mm

Name Fe500fy 500MPa

Modulus 200000MPaPartial Safety Factor mc,ULS 1.15

mc,SLS 1Maximum Strain 0.05Stress/Strain Curve Fig 2


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Total ULS Loads


1 3029 9 -87 87.46 84.09

2 5608 -625 -2371 2452 104.8

3 4987 1403 -1598 2127 48.724 4013 -3516 -406 3539 173.4

5 4185 -14 2810 2810 -90.29

6 5053 -839 -2721 2847 107.1



Effective centroid is reported relative to the reference point.

Analysis Eff. Eff. N Nmax N/Nmax M Mu M/Mu Governing Neutral NeutralCase Centroid Centroid Condition Axis Axis

(y) (z) Angle Depth

(NA)


1 0.00 0.00 3029 67890 0.0446 87.5 15790 0.0055 B: Node 1 70.99 601.3

2 0.00 0.00 5608 67890 0.0826 2452.0 16200 0.1514 B: Node 8 133.5 796.8

3 0.00 0.00 4987 67890 0.0735 2127.0 11440 0.1860 B: Node 2 14.7 545.5

4 0.00 0.00 4013 67890 0.0591 3539.0 8476 0.4176 B: Node 7 178.5 235.9

5 0.00 0.00 4185 67890 0.0617 2810.0 17070 0.1646 B: Node 5 -90.99 469.2

6 0.00 0.00 5053 67890 0.0744 2847.0 15450 0.1843 B: Node 7 138 778.8 M/Mu < 1.0 OK!


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to IRS CBC - 1997

Reference : Pier Head for Buffer Stop (CUT 1)


Input Data : Z


fcu = 45 N/mm2 As provided,(z-dir) = 6432 mm2

fy = 415 N/mm2 As provided,(y-dir) = 12160 mm2 1200

fyv = 415 N/mm2



Analysis Results :



N = 4041 kN

Torsion = 19 kNm



V = 54.0 kNb = 4745.0 mmd = 1118.0 mm

vz= 0.01 N/mm2

OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.04


b) Shear in y- direction:V = 751.0 kNb = 1200.0 mmd = 4663.0 mm

vy= 0.13 N/mm2

OK!

100As/bd = 0.11

vc = 0.36 N/mm2


1+0.05N/Ac = 1.04



Vcz = 2031 k N [concrete capacity)

Vsz = 4734 kN [link capacity = 0.87fy(As)d/(sv) ]Vcy = 2081 k N [concrete capacity]Vsy= 8322 kN [link capacity = 0.87fy(As)d/(sv)]


0.01 + 0.07 = 0.08 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 4745 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 4613 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 38 mm2



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to IRS CBC - 1997



Input Data : Z




fyv = 415 N/mm2



Analysis Results :



N = 4154 kN

Torsion = 254 kNm



V = 217.0 kNb = 4745.0 mmd = 1118.0 mm

vz= 0.04 N/mm2

OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.04



vy= 0.06 N/mm2

OK!

100As/bd = 0.11

vc = 0.36 N/mm2


1+0.05N/Ac = 1.04






0.03 + 0.03 = 0.06 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 4745 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 4613 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 507 mm2



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to IRS CBC - 1997



Input Data : Z

hy= 4745 mm Cover = 50 mmY

bz= 1200 mm Tension Reinf. F = 32 mm



fyv = 415 N/mm2



Analysis Results :



N = 3741 kN

Torsion = 433 kNm



V = 77.0 kNb = 4745.0 mmd = 1118.0 mm

vz= 0.01 N/mm OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.03



vy= 0.10 N/mm2

OK!

100As/bd = 0.11

vc = 0.36 N/mm2


1+0.05N/Ac = 1.03






0.01 + 0.05 = 0.06 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 4745 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 4613 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 864 mm2



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4.2.2.3 Type 12 Pier-Heads Of Pier: Shear And Torsion Design to IRS CBC 1997 AlongCUT-2

The table 4.13 shows the most critical cases for shear and torsion design.

Table 4.13: Ultimate Load Combinations 1 - 5 (U1-U5) Maximum Final Design Forces forShear and Torsion Design

CASE

Leg 1

Elem

Leg 2



4 (max) 1008 1009 U4.1-94 -3483 -1693 -2272 525 -95 279

4 (min) 1008 1009 U4.1-129 -4185 -14 2810 -751 54 19

5 (max) 3008 3009 U5.1-3 -5053 -839 -2721 520 136 286

5 (min) 3008 3009 U2b.1-8 -4298 -1498 -2036 326 -217 254

6 (max) 1008 1009 U4.1-153 -3885 -505 1717 -541 -77 433

6 (min) 1008 1009 U4.1-132 -3886 -294 1712 -540 -2 -304

The design calculations for ultimate shear and torsion are shown in the spreadsheet nextpages. 3 cases are studied, which are:

i) Absolute Maximum Vy + Corresponding Vz & Torsionii) Absolute Maximum Vz + Corresponding Vy & Torsioniii) Absolute Maximum Torsion + Corresponding Vz & Vy


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to IRS CBC - 1997

Reference : Pier Stem for Buffer Stop (Cut 2)


Input Data : Z




fyv = 415 N/mm2



Analysis Results :



N = 4185 kN

Torsion = 19 kNm



V = 54.0 kNb = 2411.0 mmd = 1118.0 mm

vz= 0.02 N/mm2

OK!

100As/bd = 0.36

vc = 0.52 N/mm2


1+0.05N/Ac = 1.07



vy= 0.27 N/mm2

OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.07



Vcz = 1240 k N [concrete capacity)Vsz = 2908 kN [link capacity = 0.87fy(As)d/(sv) ]

Vcy = 1357 k N [concrete capacity]Vsy= 4156 kN [link capacity = 0.87fy(As)d/(sv)]


0.01 + 0.14 = 0.15 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 2411 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 2279 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 45 mm2



47/72






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to IRS CBC - 1997



Input Data : Z


fcu = 45 N/mm2


fy = 415 N/mm2


1200

fyv = 415 N/mm2



Analysis Results :



N = 4298 kN

Torsion = 254 kNm



V = 217.0 kNb = 2411.0 mmd = 1118.0 mm

vz= 0.08 N/mm2

OK!

100As/bd = 0.36

vc = 0.52 N/mm2


1+0.05N/Ac = 1.07



V = 326.0 kNb = 1200.0 mmd = 2329.0 mm

vy= 0.12 N/mm2

OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.07





0.05 + 0.06 = 0.11 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 2411 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 2279 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 605 mm2



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21-Jun-10Page 49 / 72



to IRS CBC - 1997



Input Data : Z


fcu = 45 N/mm2


fy = 415 N/mm2


1200

fyv = 415 N/mm2



Analysis Results :



N = 3885 kN

Torsion = 433 kNm



V = 77.0 kNb = 2411.0 mmd = 1118.0 mm

vz= 0.03 N/mm2

OK!

100As/bd = 0.36

vc = 0.52 N/mm2


1+0.05N/Ac = 1.07



vy= 0.19 N/mm OK!

100As/bd = 0.23

vc = 0.45 N/mm2


1+0.05N/Ac = 1.07





0.02 + 0.10 = 0.12 OK!


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vt = 2T / [h2


hmin = 1200 mm

hmax = 2411 mm


vtmin = 0.067 (fcu)0.5



vtu = 0.75 (fcu)0.5

= 4.74 N/mm

x1 = 1068 mm

y1 = 2279 mm






a) Shear Links



(OK)




(OK)




(OK)



AsL = 1031 mm2



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4 2761 -1683 106

5 2516 741 957

6 3648 431 -2602

SLS Cases Analysed

Name Loading Pre-stress Creep Mq/Mg Cnom Crack Eqn.Long Interm. Short Factor Coeff.Term Term Term A [mm]

1 L1 - - 0 2 1 50 Eqn. 24

2 L2 - - 0 2 1 50 Eqn. 24

3 L3 - - 0 2 1 50 Eqn. 24

4 L4 - - 0 2 1 50 Eqn. 24

5 L5 - - 0 2 1 50 Eqn. 24

6 L6 - - 0 2 1 50 Eqn. 24

Total SLS Loads


1 2328 -1000 62 1002 -176.5

2 3648 -629 -2589 2664 103.7

3 2516 741 957 1210 -52.25

4 2761 -1683 106 1686 -176.4

5 2516 741 957 1210 -52.25

6 3648 431 -2602 2637 80.59

SLS Loads Analysis - Summary

Analysis Secant Neutral Neutral k at M0Case EI Axis Axis

Angle Depth(NA)

[kNm] [] [mm] [/m]

1 6.36E+06 -179.8 744.9 2.41E-12

2 34.01E+06 165.2 1848 1.16E-12

3 12.92E+06 -5.109 1175 1.65E-12

4 4.78E+06 -179.8 570.2 2.41E-12

5 12.92E+06 -5.109 1175 1.65E-12

6 48.96E+06 21.09 2391 1.23E-12


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Moment summary for SLS axial loadsEffective centroid is reported relative to the reference points

Case Eff. Centroid N Nmax N/Nmax M Mu M/Mu Mcr

y z[mm] [mm] [kN] [kN] [kNm] [kNm] [kNm]

1 0.00 0.00 2328 125900 0.02 1002 9177 0.1092 4712 0.00 0.00 3648 125900 0.03 2664 31410 0.0848 1560

3 0.00 0.00 2516 125900 0.02 1210 14720 0.0822 637

4 0.00 0.00 2761 125900 0.02 1686 9386 0.1797 558

5 0.00 0.00 2516 125900 0.02 1210 14720 0.0822 637

6 0.00 0.00 3648 125900 0.03 2637 35230 0.0749 1822

Crack Widths at SLS LoadsCrack widths calculated at 20mm intervalsAnalysis Face Point y z Strain Strain bt Control Acr Cmin Cmin h x Crack



1 1 4 -2276 584 -72.33E-06 -72.33E-06 4745 9 55.44 66 Face 2 1220 744.9 0.01182 94 -496.3 584 -71.13E-06 -71.13E-06 4745 43 130.5 72 Face 2 1220 744.9 0.0208

3 234 2276 584 -69.26E-06 -69.26E-06 4745 1 55.44 66 Face 2 1220 744.9 0.0113

4 243 2315.0 445.3 -47.38E-06 -47.38E-06 4745 1 82.16 66 Face 2 1220 744.9 0.0103

8 586 -2315 545.3 -66.26E-06 -66.26E-06 4745 9 55.44 66 Face 2 1220 744.9 0.0108

2 2 226 2144 584 -34.86E-06 -34.86E-06 961 1 108.3 66 Face 2 2360 1848 0.0092

3 234 2276 584 -37.51E-06 -37.51E-06 961 1 55.44 66 Face 2 2360 1848 0.0061

4 243 2.32E+03 445.3 -27.79E-06 -27.79E-06 961 1 82.16 66 Face 2 2360 1848 0.0061

3 5 297 2.28E+03 -584 -1.03E-06 -1.03E-06 2096 8 55.44 66 Face 6 1613 1175 0.0002

6 519 -2144 -584.0 -37.90E-06 -37.90E-06 2096 16 108.3 66 Face 6 1613 1175 0.0097

7 527 -2276 -584.0 -39.00E-06 -39.00E-06 2096 16 55.44 66 Face 6 1613 1175 0.0063

8 531 -2315 -545.3 -35.72E-06 -35.72E-06 2096 16 55.44 66 Face 6 1613 1175 0.0058

4 1 4 -2276 584.0 -223.20E-06 -223.20E-06 4745 9 55.44 66 Face 2 1219 570.2 0.0365

2 94 -496.3 584 -220.70E-06 -220.70E-06 4745 43 130.5 72 Face 2 1219 570.2 0.0692

3 234 2276 584 -216.80E-06 -216.80E-06 4745 1 55.44 66 Face 2 1219 570.2 0.0355

4 243 2315 445.3 -167.80E-06 -167.80E-06 4745 1 82.16 66 Face 2 1219 570.2 0.0376

8 581 -2315 4.55E+02 -177.60E-06 -177.60E-06 4745 9 75.48 66 Face 2 1219 570.2 0.03735 5 297 2276 -584 -1.03E-06 -1.03E-06 2096 8 55.44 66 Face 6 1613 1175 0.0002

6 519 -2144 -584 -37.90E-06 -37.90E-06 2096 16 108.3 66 Face 6 1613 1175 0.0097

7 527 -2.28E+03 -584 -39.00E-06 -39.00E-06 2096 16 55.44 66 Face 6 1613 1175 0.0063

8 531 -2315 -545.3 -35.72E-06 -35.72E-06 2096 16 55.44 66 Face 6 1613 1175 0.0058

6 4 293 2315 -545.3 -19.14E-06 -19.14E-06 641.9 8 55.44 66 Face 6 2809 2391 0.0031

5 297 2.28E+03 -584 -20.33E-06 -20.33E-06 641.9 8 55.44 66 Face 6 2809 2391 0.0033

6 305 2136 -584 -17.62E-06 -17.62E-06 641.9 8 114.6 66 Face 6 2809 2391 0.0046 Max. Crack width = 0.0692 < 0.2mm OK!


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4.2.3.2 Type 12 Pier-Heads Of Piers: SLS1&5 Crack-Width Check Along CUT-2

The crack width of the pier is checked against service load combinations 1&5, by usingAdSEC software. Table below shows the envelope of pier forces for serviceability check. Thearrangement of bars in the pier head is shown in ultimate limit check. 6 cases are checked,

which are:

Case 1 - Max & Min Axial Force + Corresponding ResultsCase 2 - Max & Min My + Corresponding ResultsCase 3 - Max & Min Mz + Corresponding Results

Table 4.15: Serviceability Load Combinations 1&5 (S1 and S5) Maximum Final Forces ofPier-Head Type 12 At CUT-2 for Combined Axial and Bending SLS check

CASELeg 1Elem

Leg 2Elem Load Axial My Mz

(kN) (kNm) (kNm)

1 (max) 1008 1009 S1-32(max) -2443 -1095 -21

1 (min) 3008 3009 S5.1-3 -3764 -524 -1899

2 (max) 1008 1009 S1-57(max) -2631 770 667

2 (min) 1008 1009 S1-24(max) -2877 -1727 3

3 (max) 1008 1009 S1-57(max) -2631 770 667

3 (min) 3008 3009 S5.1-2 -3763 408 -1912

LoadingReference PointAll loading acts through the Reference Point.

All strain planes are defined relative to the Reference Point.Definition Geometric CentroidReference Point Coordinates y 0.0mm

z 0.0mm

Applied loads

Load N Myy MzzCase [kN] [kNm] [kNm]

1 2443 -1095 -21

2 3764 -524 -1899

3 2631 770 667

4 2877 -1727 3

5 2631 770 667

6 3763 408 -1912


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SLS Cases Analysed

Name Loading Pre-stress Creep Mq/Mg Cnom Crack Eqn.

Long Interm. Short Factor Coeff.Term Term Term A [mm]

1 L1 - - 0 2 1 50 Eqn. 24

2 L2 - - 0 2 1 50 Eqn. 243 L3 - - 0 2 1 50 Eqn. 24

4 L4 - - 0 2 1 50 Eqn. 24

5 L5 - - 0 2 1 50 Eqn. 24

6 L6 - - 0 2 1 50 Eqn. 24

Total SLS Loads


1 2443 -1095 -21 1095 178.9

2 3764 -524 -1899 1970 105.4

3 2631 770 667 1019 -40.94 2877 -1727 3 1727 -179.9

5 2631 770 667 1019 -40.9

6 3763 408 -1912 1955 77.95

SLS Loads Analysis - Summary

Analysis Secant Neutral Neutral k at M0Case EI Axis Axis

Angle Depth(NA)

[kNm] [] [mm] [/m]

1 3.75E+06 179.7 763.2 2.26E-12

2 12.50E+06 138.6 1854 1.94E-12

3 5.75E+06 -12.91 1226 1.95E-12

4 3.16E+06 -180 626.7 2.27E-12

5 5.75E+06 -12.91 1226 1.95E-12

6 14.23E+06 48.61 2007 1.94E-12

Moment summary for SLS axial loadsEffective centroid is reported relative to the reference points

Case Eff. Centroid N Nmax N/Nmax M Mu M/Mu Mcr

y z[mm] [mm] [kN] [kN] [kNm] [kNm] [kNm

1 0.00 0.00 2443 67890 0.04 1095 7792 0.1406 502

2 0.00 0.00 3764 67890 0.06 1970 15010 0.1313 1058

3 0.00 0.00 2631 67890 0.04 1019 9517 0.1070 507


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21-Jun-10Page 56 / 72


4 0.00 0.00 2877 67890 0.04 1727 7982 0.2164 596

5 0.00 0.00 2631 67890 0.04 1019 9517 0.1070 507

6 0.00 0.00 3763 67890 0.06 1955 15530 0.1259 1134

Crack Widths at SLS Loads

Crack widths calculated at 20mm intervalsAnalysis Face Point y z Strain Strain bt Control Acr Cmin Cmin h x Crack



1 1 4 -1155 584 -122.90E-06 -122.90E-06 2411 1 55.44 61.5 Face 8 1212 763.2 0.0200

2 63 4.661 584 -124.70E-06 -124.70E-06 2411 33 123.9 66 Face 2 1212 763.2 0.0349

3 122 1155 584 -126.40E-06 -126.40E-06 2 411 35 55.44 61.5 Face 4 1212 763.2 0.0205

4 126 1194 545.3 -115.20E-06 -115.20E-06 2411 35 55.44 61.5 Face 4 1212 763.2 0.0187

8 362 -1194 545.3 -111.60E-06 -111.60E-06 2411 1 55.44 61.5 Face 8 1212 763.2 0.0181

2 2 114 1025 584 -77.75E-06 -77.75E-06 557.5 27 101 66 Face 2 2462 1854 0.0202

3 122 1.16E+03 584 -91.38E-06 -91.38E-06 557.5 35 55.44 61.5 Face 4 2462 1854 0.0149

4 131 1.19E+03 445.3 -79.03E-06 -79.03E-06 557.5 35 82.16 61.5 Face 4 2462 1854 0.0176

3 6 295 -1025 -584.0 -74.60E-06 -74.60E-06 1001 18 101 66 Face 6 1697 1226 0.0186

7 303 -1155 -584.0 -79.77E-06 -79.77E-06 1001 2 55.44 61.5 Face 8 1697 1226 0.0130

8 312 -1194 -445.3 -57.34E-06 -57.34E-06 1001 2 82.16 61.5 Face 8 1697 1226 0.0124

4 1 4 -1155 584 -305.20E-06 -305.20E-06 2411 1 55.44 61.5 Face 8 1201 626.7 0.04982 63 4.661 584 -304.90E-06 -304.90E-06 2411 33 123.9 66 Face 2 1201 626.7 0.0901

3 122 1155 5.84E+02 -304.60E-06 -304.60E-06 2411 35 55.44 61.5 Face 4 1201 626.7 0.0497

4 131 1194 445.3 -228.80E-06 -228.80E-06 2411 35 82.16 61.5 Face 4 1201 626.7 0.0507

8 357 -1194 454.7 -234.50E-06 -234.50E-06 2411 1 75.48 61.5 Face 8 1201 626.7 0.0488

5 6 295 -1.03E+03 -584 -74.60E-06 -74.60E-06 1001 18 101 66 Face 6 1697 1226 0.0186

7 303 -1155 -584 -79.77E-06 -79.77E-06 1001 2 55.44 61.5 Face 8 1697 1226 0.0130

8 312 -1.19E+03 -445.3 -57.34E-06 -57.34E-06 1001 2 82.16 61.5 Face 8 1697 1226 0.0124

6 4 176 1194 -454.7 -65.10E-06 -65.10E-06 523.4 36 75.48 61.5 Face 4 2569 2007 0.0135

5 182 1194 -545.3 -73.34E-06 -73.34E-06 523.4 36 55.44 61.5 Face 4 2569 2007 0.0120

6 192 1035 -584 -60.49E-06 -60.49E-06 523.4 36 97.76 61.5 Face 4 2569 2007 0.0152 Max. Crack width = 0.0901 < 0.2mm OK!


57/72



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