BRG-S-T-D-RD 105+545

PRESTRESSED CONCRETE GIRDER BRIDGEAT KM 105 + 545

ON TOPI DARBAND ROAD

INTRODUCTION

This document is prepared for the Prestressed Pre – Cast Girders and R.C.C. deck slab bridge situated on SWABI – TOPI – DARBAND road at KM 105 + 545. This document is submitted as part of the Contract Agreement between the Consultants M/S KHYBER CONSULTING ENGINEERS (KCE) and the Client NATIONAL HIGHWAY AUTHORITY (NHA) for design of the SWABI–TOPI–DARBAND road. AASHTO LRFD 1994, (BRIDGE DESIGN SPECIFICATIONS), is the governing code.

1. GENERAL INFORMATION

1.1DESIGN SPECIFICATION

1.1.11.1.1 AASHTO LRFD code 1994 (BRIDGE DESIGN SPECIFICATIONS)

1.1.21.1.2 AASHTO Standard specifications 1996.

1.1.31.1.3 Pakistan Code of Practice for Highway Bridges (PCPHB) 1967.

1.2DESIGN PHILOSOPHY (Limit states, of AASHTO LRFD 1994)

1.2.11.2.1 Service limit state (Flexural design of PC Girders and stability check of the abutments).

1.2.21.2.2 Strength limit state (Design of all the structural components except PC girders).

1.2.31.2.3 Fatigue limit state (Design of PC girders).

Note: The bridge is a single span simply supported so it does not need to be investigated for the Extreme Event Limit States (Sec. 4.7.4.2).

1.3LIVE LOADS

1.3.11.3.1 Single Lane of Military Class 70 Loading (PCPHB, 1967.).

1.3.21.3.2 Class A Loading (PCPHB).

1.3.31.3.3 HS20-44 Truck (AASHTO standard 1996).

1.3.41.3.4 Design Lane Load plus Design Truck (HL – 93, AASHTO LRFD 1994).

1.3.51.3.5 Design Lane Load plus Design Tandem (HL – 93, AASHTO LRFD 1994).

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1.4HYDROLOGICAL INFORMATION (Ref: AASHTO LRFD)

1.4.11.4.1 Catchment area = 2.02 Km2.

1.4.21.4.2 Discharge (100 years) = 29.33 m3/sec.

1.4.31.4.3 Time of concentration = 1.31 hrs.

1.4.41.4.4 Scour Depth with respect to H.F.L. = 1.35 meters.

1.4.51.4.5 Coefficient of run – off = 0.6

1.4.61.4.6 Lacey ‘s silt factor = 1.25

Note: The finished road elevations determine height of the Bridge; H.F.L. shown on the drawings is the flood that can pass easily under the Bridge.

1.5 GEOTECHNICAL INFORMATION

1.5.11.5.1 Unit weight of the soil under the abutment foundation soil = 17300 N/m3.

1.5.21.5.2 Angle of internal friction of the granular backfill = 35

1.5.31.5.3 Presumptive allowable bearing capacity (Ref: AASHTO LRFD code) 2.9 to 3.8 MPa.

1.5.41.5.4 Recommended value to be used for the general geology anticipated at the bridge site (Foliated metamorphic rock: Slate, Schist) = 3.4 MPa.

Note: Presumptive allowable bearing capacity is by no mean a substitute for proper soil investigation. Detailed geotechnical investigation must be carried out, to finalize the bearing capacity, at the time of construction (Based on the agreed proposition) and the Sub – Structure will be updated accordingly.

Rational formula for discharges (Hydrology in Practice by Elezabeth M. Shaw pp/297). Hydrology in Practice by Elizabeth M. Shaw pp/298). Ref: Lacey ‘s scour depth equation for regime channels.


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2. SUPER STRUCTURE DESIGN

2.1 GENERAL IFORMATIONS ABOUT BRIDGE GEOMETRY (Ref: AASHTO LRFD)

2.1.12.1.1 No. of Spans = 1

2.1.22.1.2 Each Span Length = 30 meters.

2.1.32.1.3 Total Span Length = 30 meters.

2.1.42.1.4 Effective Span Length = 29.3 meters.

2.1.52.1.5 Skew Angle = 0

2.1.62.1.6 Type of Superstructure Pre – Cast Prestressed ConcreteGirders and RCC Deck Slab.

2.1.72.1.7 No. of Girders per Span = 4

2.1.82.1.8 Clear Width of the Bridge = 8500 mm.

2.1.92.1.9 Total Width of the Bridge = 10100 mm.

2.1.102.1.10 No. of Diaphragms per Span = 5

2.1.112.1.11 Type of guardrail R.C.C. Guard Rail Post and Pre-castGuard Rails.

Note: Detailed dimensions of the PC girders, diaphragms, deck slab, footpaths (safety curbs) and railings are shown in the drawings whereas a General Cross – Section of the Bridge is shown below:


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2.2 GENERAL IFORMATIONS ABOUT DESIGN PARAMETERS (Ref: AASHTO LRFD)

2.2.12.2.1 Resistance factors, , are:

2.2.1.12.2.1.1 Flexure and tension of reinforced concrete = 0.90

2.2.1.22.2.1.2 Shear and torsion in normal density concrete = 0.90

2.2.1.32.2.1.3 Axial compression with spirals and ties = 0.75

2.2.1.42.2.1.4 Bearing on concrete = 0.70

2.2.22.2.2 Load modifiers are :Strength Service Fatigue

2.2.2.12.2.2.1 Ductility, nD 1.0 1.0 1.0

2.2.2.22.2.2.2 Redundancy, nR 1.0 1.0 1.0

2.2.2.32.2.2.3 Operational importance, nI 1.0 N/A N/A

2.2.32.2.3 Load combinations and Load factors: Following limit states are investigated.

2.2.3.12.2.3.1 Service – I limit state

2.2.3.22.2.3.2 Strength – I Limit State

2.2.3.32.2.3.3 Fatigue Limit State

2.2.42.2.4 Live load distribution factors (per lane) are:

2.2.4.12.2.4.1 For bending moment in interior girders = 0.744

2.2.4.22.2.4.2 For bending moment in exterior girders = 0.744

2.2.4.32.2.4.3 Factor for shear in interior girders = 0.846

2.2.4.42.2.4.4 Factor for shear in exterior girders = 0.846

Note: Load factors relative to moment and shear AASHTO LRFD code 1994 are used.

2.2.52.2.5 Dynamic load allowance (not applied to the design lane load) are:

2.2.5.1 For Fatigue Limit State IMFati- = 15 %

2.2.5.2 For all HL – 93 loading (AASHTO LRFD code 1994) IM = 33 %

2.2.5.3 For Class A loading of the PCPHB IM = 13 %

2.2.5.4 For Military Class 70 Ton loading of the PCPHB IM = 10 %


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2.3 STRUCTURAL BEHAVIOR

2.3.12.3.1 Type of the Structure Simply supported

2.3.22.3.2 Interaction between the Girder and Deck Slab Acting as I-Beam for self weight of the girder, weightof the deck slab &weight of the diaphragms and acting as a composite section for the Live Load & superimposed dead loads of the wearing coarse, curbs and guard railings.

2.3.32.3.3 Interaction between Diaphragm, Girder and The diaphragms are primarily acting Deck Slab as bracing element.

2.3.42.3.4 Structural model for bridge design Beam line method: The use of Distribution Factors recommended by AASHTO LRFD takes into account structural interaction among variousgirders and deck slab. The D.F’s. are either based on 2 – D Grillage modelor 3 - D Finite Element analysis of eccentrically stiffened shell assembly.

2.4 MATERIAL PROPERTIES

2.4.12.4.1 Concrete used in the PC girders Class D concrete of 28 days cylinder compressive strength of 350 kg/cm2

(35 MPa.).

2.4.22.4.2 Strength of concrete at transfer Minimum 280 kg/cm2 (28 Mpa.).

2.4.32.4.3 Concrete used in the deck slab, diaphragms, Class A concrete of 28 days Curbs, railings, back walls, wing walls, cylinder compressive strength oftransom/girder seat, rollovers and footings. 210 kg/cm2 (21 MPa.).

2.4.42.4.4 High strength steel used in the PC girders Stress relived low relaxation Grade 270 (1860 MPa.) 7 – wire strands, conforming to ASTM A-416

2.4.52.4.5 Stress in the high strength steel at mid section 69 % of the ultimate strength immediately after transfer (excluding F. Losses) (i.e. 0.69 * fpu)

2.4.62.4.6 Normal reinforcement steel Grade 60 (414 MPa) deformed roundbars confirming to ASTM A-615.

2.4.72.4.7 Modulus of elasticity of prestressing steel strands Ep = 197,000 MPa.

2.4.82.4.8 Modulus of elasticity of reinforcing steel Es = 200,000 MPa.

2.4.92.4.9 Modulus of elasticity of concrete Ec = 4800* MPa.


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2.5 GEOMETRICAL PROPERTIES OF THE PC GIRDERS

2.5.12.5.1 Height of the Girder = 1850 mm.

2.5.22.5.2 Top flange width = 500 mm.

2.5.32.5.3 Bottom flange width = 600 mm.

2.5.42.5.4 Web thickness = 170 mm.

2.5.52.5.5 Effective flange width Beff = 2525 mm.

2.5.62.5.6 Cross sectional area of the I – Beam Ag = 580525 mm2.

2.5.72.5.7 Distance of Neutral Axis of I-Section from Bot- fibers Yb-I = 788.136 mm.

2.5.82.5.8 Distance of Neutral Axis of I-Section from Top fibers Yt-I = 1061.864 mm.

2.5.92.5.9 Distance of N.A of Comp- section from Bot-fibers Yb-c = 1255.86 mm.

2.5.102.5.10 Distance of N.A of Comp- section from Top-fibers Yt-c = 794.14 mm.

2.5.112.5.11 Moment of inertia of the I-Section II-Sec = 2.235 E+11 mm4.

2.5.122.5.12 Moment of inertia of the Composite section Ic-Sec = 5.403 E+11 mm4.

Note: X – Section at the mid section, End Block and Tendon arrangement at the end are shown in the figures on the next page.

Tendon arrangement at End Block, End Block Details and X – Section at mid section


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2.6 APPLIED MOMENTS ON THE PC GIRDERS

2.6.12.6.1 Service dead load moment due to self-weight of the girder Mgirder = 1.495 x 106 N – m.

2.6.22.6.2 Service dead load moment due to weight of the deck slab Mslab = 1.301 x 106 N – m.

2.6.32.6.3 Service dead load moment due to weight of the diaphragms Mdiaph = 0.248 x 106 N – m.

2.6.42.6.4 Service dead load moment due to weight of the wearing coarse, safety curbs and railings. Ms.i.d. = 0.438 x 106 N – m.

2.6.52.6.5 Service live load moment ML.L. = 2.706 x 106 N – m

Note: HL – 93, AASHTO LRFD 1994 code provisions for max- live load moment governs.

2.72.7 PRESTRESSED CONCRETE GIRDER DESIGN INFORMATION.

2.7.12.7.1 Type of prestressing steel used 7 – wire strands of Grade 270(1860 MPa.)

2.7.22.7.2 Diameter of the strand = 12.7 mm (0.5”)

2.7.32.7.3 Area of the prestressing steel (3 tendons/36 strands) Ap = 3554 mm2.

2.7.42.7.4 No. of tendons per girder = 3

2.7.52.7.5 No. of strands per tendon = 12

2.7.62.7.6 Diameter of the grooved rigid metallic sheath pipe = 69 mm

Note: Stressing/Jacking shall be performed form both ends with STRONGHOLD or equivalent system. Net stresses (at mid section) in all the tendons immediately after transfer of prestress force to girders is 0.69*fpu. Also, net jacking force in each tendon is:

Fo = 1.522 x 106 N.

2.82.8 NET JACKING FORCE IN THE TENDONS BEFORE RELEASE AND CORRESPONDING ELONGATION OF THE TENDONS.

Tendon No. Force in the Tendons Elongation of steel in each tendon (mm)N Kg

1 1.652 x 106 168460 2152 1.664 x 106 169702 2163 1.676 x 106 170940 218

Note: The loads and elongation given are the total quantities. Half of the elongation shall be achieved at each end.

Weigh in motion records at various bridge sites of Pakistan indicates a truck configuration of 3-Axle 45 –Ton (Abbreviated as PK3A45 by Khyber Consulting Engineers) will cause 2.561 x 106 N – m including an Impact of 13 %.


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2.92.9 PRESTRESS LOSSES IN THE TENDONS

2.9.12.9.1 Loss due to elastic shortening of concrete = 2.58 %.

2.9.22.9.2 Loss due shrinkage of concrete = 3.931 %.

2.9.32.9.3 Loss due to creep of concrete = 7.579 %

2.9.42.9.4 Loss due to relaxation of steel = 1.380 %.

2.9.52.9.5 Loss due to anchorage set/take – up/Anchorage PULL – IN = 3.062 %.

2.9.62.9.6 Frictional losses Frictional losses are different for each Tendon due to difference in length and angular change of the tendons.

Wobble coefficient k = 4.92X10-6 per mm (0.0015 per ft)

Curvature coefficient = 0.25

Frictional losses in the tendons are given below:

Frictional loss in Tendon No. 1 8.568 %Frictional loss in Tendon No. 2 9.370 %Frictional loss in Tendon No. 3 10.167 %

Note: Losses, jacking force and elongation given here are valid only for ½” 7-wire strands.

2.102.10 STRESSES IN THE PC GIRDERS AT DIFFERENT STAGES OF LOADING.

2.10.12.10.1 Stresses in the Girder Immediately after Transfer (at mid section).

Type of Stresses Applied Stresses MPa

Code Limiting Stress ValuesMPa.

Extreme fiber stresses in tension - 0.259 +1.313Extreme fiber stresses in compression -13.507 -15.169

2.10.22.10.2 Stresses in the Girder at Working Load Condition/Service Load Condition (at mid section).

Type of Stresses Applied StressesMPa

Code Limiting Stress ValuesMPa

Extreme fiber stresses in tension + 2.702 + 2.936Extreme fiber stresses in compression - 13.344 -15.514

Note: All the stresses are checked at the mid-section (span) of the girder

Sec. 9.16.1, AASHTO standard 1996. Note: Value of the Wobble coefficient given in Sec. 5.9.5.2.2b of AASHTO LRFD 1994 code is 7.45 times less than the value given by AASHTO standard 1996 code. We have adopted the Conservative (AASHTO standard) value.


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2.112.11 SHEAR DESIGN OF THE PC GIRDERS (Ref: AASHTO LRFD)

2.11.12.11.1 Ultimate applied shear force Vu = 1.295 x 106 N.

2.11.22.11.2 Ultimate moment corresponding to the ultimate shear Mu = 0.879 x 106 N – m.

2.11.32.11.3 Effective depth for shear dv = 1566 mm.

2.11.42.11.4 Effective width of the web bv = 135.5 mm.

2.11.52.11.5 Angle of the tendon force with the C.L. of the girder (average) = 6

2.11.62.11.6 Area of concrete at the end block Ag = 580525 mm2.

2.11.72.11.7 Depth of neutral axis at the end block Yb-I = 788.136 mm.

2.11.82.11.8 Moment of inertia of the girder at the end Ig = 2.35 x 1011 mm4.

2.11.92.11.9 Angle of inclination of diagonal compressive stresses = 23.5

2.11.102.11.10 Factor indicating ability of diagonally cracked concrete totransmit tension = 2.935

2.11.112.11.11 Shear capacity of the concrete Vc = 305810 N.

2.11.122.11.12 Shear capacity of the girder due to Prestress force in the girder Vp = 470380 N.

2.11.132.11.13 Transverse reinforcement 10 stirrups @ 200 mm c/c.

2.11.142.11.14 Shear carried by the transverse reinforcement Vs = 705560 N.

2.11.152.11.15 Nominal shear capacity of the girder Vn = Vc+Vs+ Vp = 1481950 N.

2.11.162.11.16 Effective shear resisting capacity of the girder Vr = * Vn = 1333755 N.

2.11.172.11.17 Ratio of the shear resisting capacity to ultimate applied shear = 1.03

2.11.182.11.18 Horizontal shear flow at the interface of Girder and Deck slab = 374736 N/m.

2.11.192.11.19 Area of concrete engaged in shear transfer Acv = 500000 mm2.

2.11.202.11.20 Permanent net compressive force normal to the shear plane Pc = 14223 N/m.

2.11.212.11.21 Area of shear reinforcement crossing the shear plane Avf = 1065 mm2/m.

2.11.222.11.22 Cohesion factor c = 0.52 MPa.

2.11.232.11.23 Friction Factor = 0.6

2.11.242.11.24 Nominal horizontal shear resistance of the interface plane Vn = 444898 N/m.

2.11.252.11.25 Effective horizontal shear resistance of the interface plane Vr = 400408 N/m.

2.11.262.11.26 Ratio of the horizontal shear resistance to the applied shear flow = 1.074


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2.122.12 DESIGN OF POST – TENSIONED ANCHORAGE ZONE (Ref: AASHTO LRFD)

2.12.1 Design of General Zone

2.12.1.12.12.1.1 Load factor for the jacking force P/S = 1.2

2.12.1.22.12.1.2 Distance from the end at which stress is to be measured = 175 mm.

2.12.1.32.12.1.3 Distance of the center of the bursting force parallel to the vertical face of the girder dburst1 = 925 mm.

2.12.1.42.12.1.4 Distance of the center of the bursting force parallel to the lateral face of the girder dburst2 = 250 mm.

2.12.1.52.12.1.5 Net stresses in the top fibers at distance of 175 mm ft = -4.724 N/mm2.

2.12.1.62.12.1.6 Net stresses in the bottom fibers at distance of 175 mm fb = -5.990 N/mm2.

2.12.1.72.12.1.7 Ultimate jacking force per tendon/bearing plate Pu = 1.826 x 106 N.

2.12.1.82.12.1.8 Thickness of the member t = 500 mm.

2.12.1.92.12.1.9 Center to center spacing of anchorage plates s = 500 mm.

2.12.1.102.12.1.10 Number of tendons in a row n = 3

2.12.1.112.12.1.11 Limiting stress from the approximate analysis fca = -15.445 N/mm2.

2.12.1.122.12.1.12 Ratio of the limiting stress to applied stresses in top fibers = 3.27

2.12.1.132.12.1.13 Ratio of the limiting stress to applied stresses in bottom fibers = 2.58

2.12.1.142.12.1.14 Bursting force corresponding to dburst1 Tburst1 = 1.475 x 106 N.

2.12.1.152.12.1.15 Bursting force corresponding to dburst2 Tburst2 = 1.004 x 106 N.

2.12.1.162.12.1.16 Bursting reinforcement for Tburst1 16 12 bars @ 110 mm (both faces)

2.12.1.172.12.1.17 Bursting reinforcement for Tburst2 12 12 bars @ 110 mm (B.F.) two layers of 6 bars each)

2.12.2 Design of Local Zone

2.12.2.12.12.2.1 Maximum area of the supporting surface A = 250,000 mm2.

2.12.2.22.12.2.2 Gross area of the bearing plate Ag = 90,000 mm2.

2.12.2.32.12.2.3 Effective net area of the bearing plate Ab = 82,146 mm2.

2.12.2.42.12.2.4 Factored bearing resistance of the anchorage Pr = 1.85 x 106 N.

2.12.2.52.12.2.5 Ratio of the bearing resistance Pr to ultimate jacking force Pu = 1.013


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2.132.13 DEFLECTION IN THE PC GIRDERS

2.13.12.13.1 Deflection due to live load and its dynamic effect = + 14.53 mm.

2.13.22.13.2 Deflection due to initial pretress force = - 42.14 mm.

2.13.32.13.3 Deflection due to weight of the girder and deck slab = + 37.57 mm.

2.13.42.13.4 Deflection due to weight of the diaphragms = + 5.07 mm.

2.13.52.13.5 Deflection due to weight of the curbs, railings and wearing coarse = + 3.21 mm.

2.13.62.13.6 Net deflection at working load condition = + 19.35 mm.

2.13.72.13.7 Allowable deflection due to total loads for simply supported structures = + 61.04 mm.

2.13.82.13.8 Allowable deflection due to live load and its dynamic effect = 36.63 mm.

2.13.92.13.9 Ratio of allowable net deflection to applied net deflection = 3.15

2.13.102.13.10 Ratio of allowable live load deflection to applied live load deflection = 2.52

Note: Net deflection is within the allowable limits.

2.142.14 DESIGN OF DECK SLAB (Ref: AASHTO LRFD)

2.14.1 Minimum depth of the deck slab (Sec. 9.7.1.1, AASHTO LRFD 1994) = 175 mm.

2.14.2 Thickness of the deck slab = 200 mm.

2.14.3 Width of strip for positive moment (+M) = 2049 mm.

2.14.4 Width of strip for negative moment (-M) = 1851 mm.

2.14.5 Primary Reinforcement steel used Grade 60 steel (ASTM A – 615)

2.14.6 Secondary Reinforcement steel used Grade 40 steel (ASTM A – 615)(Distribution and shrinkage steel)

2.14.7 Total service load positive moment = 30769 N – m.

2.14.8 Total service load negative moment = 38721 N – m.

2.14.9 Ultimate positive moment = 52544 N – m.

2.14.10 Ultimate negative moment = 64392 N – m.

2.14.11 Main positive reinforcement 16 @ 140 mm c/c.

2.14.12 Main negative reinforcement 16 @ 140 mm c/c.

2.14.13 Ultimate positive moment capacity of the deck slab Md(+ve) = 72480 N – m.

Sec.8.9.3.1, AASHTO standard 1996 & Sec. 2.5.2.6.2, AASHTO LRFD 1994.


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2.14.14 Ultimate negative moment capacity of the deck slab Md (-ve) = 79186 N – m.

2.14.15 Ratio of positive moment capacity to ultimate applied positive moment = 1.38

2.14.16 Ratio of negative moment capacity to ultimate applied negative moment = 1.23

Note: Strip method is used for design of the deck slab (Sec. 4.6.2.1 AASHTO LRFD 1994). Moments are given for a unit width of a meter.

2.15 DIAPHRAGMS

2.15.12.15.1 Height of the diaphragm = 1850 mm.

2.15.22.15.2 Width of the diaphragm = 200 mm.

2.15.32.15.3 Structural action : Primarily used as bracing element for stability and nominal Longitudinal and transverse reinforcement is provided.

3. SUB – STRUCTURE DESIGN

3.1 GENERAL INFORMATION

3.1.13.1.1 Type of abutment Coarse Rubble Masonry.

3.1.23.1.2 Width of the abutment at the top = 975 mm.

3.1.33.1.3 Width of the CRM wall at the bottom = 4575 mm.

3.1.43.1.4 Length of the CRM wall = 10100 mm.

3.1.53.1.5 Height of the CRM wall = 8700 mm.

3.1.63.1.6 Total Height of abutment (to the deck Level) = 12420 mm.

3.1.73.1.7 Type of footing R.C.C. Open/Spread footing.

3.1.83.1.8 Width of footing = 6575 mm.

3.1.93.1.9 Length of footing = 10700 mm.

3.1.103.1.10 Depth of footing = 1000 mm.

3.1.113.1.11 Type of pads Elastomeric Bearing Pads

Note: Detailed dimensions of the abutment, abutment footing, wing walls, back wall, transom, and rollover are shown on the drawings whereas a Cross – Section of the Abutment is shown below.


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Cross – Section of the Abutment Wall

3.2 STABILITY ANALYSIS OF THE ABUTMENTS.

3.2.13.2.1 Weight of the structure (including weight of the footing and backfill)on the footing = 12.13 x 106 N.

3.2.23.2.2 Total stabilizing force (weight of footing is not included) = 5.46 x 106 N.

3.2.33.2.3 Total stabilizing moment about toe of the CRM wall = 38.54 x 106 N – m.

3.2.43.2.4 Total sliding force = 3.53 x 106 N.

3.2.53.2.5 Total overturning moment about toe of the CRM wall = 16.61 x 106 N – m.

3.2.63.2.6 Coefficient of friction between the CRM wall and footing = 0.45

3.2.73.2.7 Factor of safety against sliding (F.O.S.)Sliding = 1.55

3.2.83.2.8 Factor of safety against overturning (F.O.S.)O.T. = 2.32


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3.2.1 PRESSURE DISTRIBUTION AT BASE OF THE FOOTING.

3.2.1.13.2.1.1 Stresses at toe of the footing (minus sign shows compression) qmax = - 0.31 MPa.

3.2.1.23.2.1.2 Stresses at heel of the footing qmin = - 0.06 MPa.

3.2.1.33.2.1.3 Presumptive allowable bearing capacity (Ref: AASHTO LRFD) 2.9 to 3.8 MPa.

3.2.1.43.2.1.4 Recommended value of use = 3.4 MPa.

3.2.1.53.2.1.5 Ratio of presumptive allowable bearing capacity to max stress at toe of footing = 10.97

PRESSURE DISTRIBUTION DIAGRAM FOR THE ABUTMENT FOOTING


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3.3 STRUCTURAL DESIGN OF SUB – STRUCTURE ELEMENTS

3.3.1 DESIGN OF BEARING PADS (Ref: AASHTO LRFD)

3.3.1.1 Total service load on the bearing pad PTotal = 0.987 x 106 N.

3.3.1.2 Service live load on the bearing pad PL.L. = 0.491 x 106 N.

3.3.1.3 Thermal coefficient for normal density concrete = 10.8 x 10-6 /C.

3.3.1.4 Shrinkage coefficient/Strain = 3.00 x 10-4.

3.3.1.5 Width of bearing pad W = 400 mm.

3.3.1.6 Length of bearing pad L = 300 mm.

3.3.1.7 Thickness of interior layers of Elastomer hri = 15 mm.

3.3.1.8 Number of interior layers of the Elastomer n = 2

3.3.1.9 Total thickness of the Elastomer hrt = 45 mm.

3.3.1.10 Shape factor of each layer Si = 5.71

3.3.1.11 Shear modulus of the Elastomer G = 1.2 MPa.

3.3.1.12 Applied compressive stress due to total load s = 8.2 MPa.

3.3.1.13 Applied compressive stress due to live load L = 4.09 MPa.

3.3.1.14 Limiting compressive stress for the total load = 11.0 MPa.

3.3.1.15 Limiting compressive stress for the live load = 4.52 MPa.

3.3.1.16 Factor of safety against failure due to total load compressive stress = 1.34

3.3.1.17 Factor of safety against failure due to live load compressive stress = 1.11

3.3.1.18 Compressive strain i = 5.2 %

3.3.1.19 Compressive deflection = 2.25 mm.

3.3.1.20 Total shear deformation s = 14.89 mm.

3.3.1.21 Net rotation due to dead and live loads s = 4.51 x 10-3 RAD.

3.3.1.22 Required thickness of the steel plate based on Service Limit State hS = 1.3 mm.

3.3.1.23 Required thickness of the steel plate based on Fatigue Limit State hFat- = 0.7 mm.

3.3.1.24 Thickness of the steel plate provided in the Bearing Pad = 1.5 mm.

3.3.2 DESIGN OF GIRDER SEAT/TRANSOM

3.3.2.13.3.2.1 Width of the transom = 975 mm.

3.3.2.23.3.2.2 Depth of the transom = 600 mm.


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3.3.2.33.3.2.3 Effective depth of the transom = 544 mm.

3.3.2.43.3.2.4 Minimum area of steel = 1705 mm2.

3.3.2.53.3.2.5 Moment of inertia of the transom I = 1.755 x 1010 mm4.

3.3.2.63.3.2.6 Modulus of elasticity of the transom concrete E = 21831 MPa.

3.3.2.73.3.2.7 Flexural rigidity of the transom EI =3.83 x 1014 N-mm2

3.3.2.83.3.2.8 Reinforcement steel 16 12 bars uniformly distributed.

Note: The transom is provided as a rigid element to distribute the load of super structure at top of the abutment wall (CRM wall). Its flexural rigidity is more than sufficient to distribute the load uniformly over the abutment and to take care for any localized differential settlement in CRM wall.

3.3.3 DESIGN OF WING WALLS

3.3.3.13.3.3.1 Thickness of the wing wall = 300 mm.

3.3.3.23.3.3.2 Effective depth of wing wall = 244 mm.

3.3.3.33.3.3.3 Ultimate moment on the interface of wing wall and backwall = 91150 N – m.

3.3.3.43.3.3.4 Area of steel provided = 1922 mm2.

3.3.3.53.3.3.5 Moment capacity of the wing wall with As-mini = 113744 N – m.

3.3.3.63.3.3.6 Ratio of ultimate moment capacity to ultimate applied moment = 1.25

3.3.3.73.3.3.7 Shrinkage and temperature steel = 1100 mm2.

3.3.3.83.3.3.8 Main flexural reinforcement 12 @ 150 mm c/c (B.F.)

3.3.3.93.3.3.9 Shrinkage and temperature reinforcement 10 @ 140 mm c/c (B.F.)

3.3.3.103.3.3.10 Ultimate shear at the interface of wing wall and backwall = 91150 N.

3.3.3.113.3.3.11 Ultimate shear capacity of the wing wall = 447640 N.

3.3.3.123.3.3.12 Ratio of the shear capacity and ultimate applied shear = 4.91

3.3.4 DESIGN OF BACKWALL

3.3.4.13.3.4.1 Thickness of the Backwall = 300 mm.

3.3.4.23.3.4.2 Effective depth of the backwall = 244 mm.

3.3.4.33.3.4.3 Ultimate moment at base of the Backwall Mu = 28971 N – m/m

3.3.4.43.3.4.4 Minimum area of steel = 665 mm2/m

3.3.4.53.3.4.5 Moment capacity of the section = 39420 N – m/m.


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3.3.4.63.3.4.6 Ratio of ultimate moment capacity and ultimate applied moment = 1.36

3.3.4.73.3.4.7 Main reinforcement steel 12 @ 170 mm c/c. (B.F.)

3.3.4.83.3.4.8 Shrinkage steel 10 @ 150 mm c/c. (B.F.)

3.3.4.93.3.4.9 Ultimate shear at base of the Backwall = 30830 N.

3.3.4.103.3.4.10 Ultimate shear capacity of the backwall = 165794 N.

3.3.4.113.3.4.11 Ratio of the ultimate shear capacity to ultimate applied shear = 5.4

3.3.5 DESIGN OF THE ABUTMENT FOOTING

3.3.5.13.3.5.1 Width of the footing = 6575 mm.

3.3.5.23.3.5.2 Length of the footing = 12100 mm.

3.3.5.33.3.5.3 Depth of the footing = 1000 mm.

3.3.5.43.3.5.4 Clear cover for the flexural steel = 75 mm.

3.3.5.53.3.5.5 Effective depth of the footing = 917 mm.

3.3.5.63.3.5.6 Applied punching shear on the footing = 12.21 x 106 N.

3.3.5.73.3.5.7 Punching shear capacity of the footing = 38.31 x 106 N.

3.3.5.83.3.5.8 Ratio of the punching shear capacity to applied punching shear = 3.14

3.3.5.93.3.5.9 Applied beam shear = 0.464 x 106 N.

3.3.5.103.3.5.10 Beam shear capacity of the footing = 7.54 x 106 N.

3.3.5.113.3.5.11 Ratio of the beam shear capacity to the applied beam shear = 16.24

3.3.5.123.3.5.12 Ultimate moment, in shorter direction, at face of the support Mu1 = 0.231 x 106 N-m/m.

3.3.5.133.3.5.13 Reinforcement steel provided in shorter direction (As-mini) 16 @ 180 mm c/c.

3.3.5.143.3.5.14 Ultimate moment capacity in shorter direction Mr1 = 0.252 x 106 N–m/m.

3.3.5.153.3.5.15 Ratio of the ultimate moment capacity to ultimateapplied moment In shorter direction = 1.09

3.3.5.163.3.5.16 Ultimate moment, in longer direction, at face of the support Mu2 = 0.231 x 106 N-m/m.

3.3.5.173.3.5.17 Reinforcement steel provided longer direction (As-mini) 16 @ 180 mm c/c.

3.3.5.183.3.5.18 Ultimate moment capacity in longer direction Mr2 = 0.316 x 106 N–m/m.

3.3.5.193.3.5.19 Ratio of the ultimate moment capacity to ultimate applied moment in longer direction = 1.37


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BRG-S-T-D-RD 105+545

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Transcript of BRG-S-T-D-RD 105+545