Bridge Ch 5 Example on Slab Bridge

Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

Chapter 5 SUPERSTRUCTURES Example on Design of Slab Bridge Design Data and Specifications Superstructure consists of 10m slab, 36m box girder and 10m T-girder all simply supported. Only the design of Slab Bridge will be used for illustration.

Roadway Grade = 1660.00 m, amsl HWM = 1643.56 - Roadway grade dictates elevation of superstructure and not minimum free board requirement. I. Slab Clear span = 10m Road way width = 7.32m Curb width = 0.8m

II. T-Girder Clear span 10m Road way width = 7.32m Curb width = 0.80m

-Materials Concrete: Class ‘A’ concrete: Cylinder strength

III.Box-Girder Clear span = 36m Road way width = 7.32m Curb width = 0.80m

f c’ = 28MPa

[A5.4.2.1] [A5.4.2.4]

Steel: fy = 400MPa Es = 200GPa 

Design method is Load and Resistance Factor Design (LRDF)

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Chapter 5- Superstructures Design Example on Slab Bridge



Fundamentals of Bridge Structures

Reference: AASHTO LRFD Bridge Design Specifications, SI units, 2nd Edition, 2005.

Slab Bridge Design

1.

Depth Determination

[A2.5.2.6.3]

Minimum recommended depth for slabs with main reinforcement parallel to traffic is

Where S is the span, S=c/c of supports ≤ clear span + d, S=10+0.4/2+0.43/2=10.415m

Use D = 540 mm, d= 540- F/2-25 = 499mm S=10.415m≤Clear span + d = 10000 + 499 = 10.499m Ok! 2.

(Cover)

Live Load Strip Width

a) Interior Strip i) One lane loaded: multiple presence factor included

[Art.4.6.2.3]

[C.4.6.2.3]

L1 is smaller of 10415 or 18000. W1 is the smaller of 8920 or 9000 L1 = 10415 W1 = 8920

ii) Multiple lanes loaded

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Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

W=Actual edge to edge width = 8920mm NL = Int(clear roadway width/3600)

Use E=3256.63mm Equivalent concentrated and distributed loads Truck: P1’=35/3.2566=10.75; P2’ = 145/3.2566 = 44.52 Tandem: P3’=110/3.2566 = 33.78 Lane: w’ = 9.3/3.2566 = 2.856 b) Edge Strip Longitudinal edge strip width for a line of wheels

[Art.4.6.2.1.4]

E= distance from edge to face of barrier + 300+1/4* strip width E= 800 + 300+3256.63/4 = 1914.08mm > 1800mm E=1800mm 3.

Influence Lines for Shear Force and Bending Moment

Slab bridges shall be designed for all vehicular live loads specified in AASHTO Art 3.6.1.2, including the lane load [Art.3.6.1.3.3]

a) Inter Strip i) Maximum Shear Force

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Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

Impact factor = 1+IM/100 = 1+33/100 = 1.33, not applied to lane load [Art.3.6.2.1] VLL+IM=1.33*72.52+14.87 = 111.32 ii) Maximum bending Moment Truck: MTr = 44.52(0.703+2.553) + 10.75(0.103) = 146.06 kNm Tandom: MTa = 33.78(2.304*2) =155.66 kNm this →governs Lane: MLn = 2.856*(1/2)*2.604*10.415 MLL+Im = 1.33*155.66+38.73 = 245.76kNm

=38.73kNm

b) Edge Strip Because E= 1800mm, one lane loaded with a multiple presence factor of 1.2 will be critical

4.

Select resistance factor, φ

[Art. 5.5.4.2.1] φ 0.90 0.90

Strength Limit States (RC) Flexure & Tension Shear & Torsion Axial Compression Bearing On concrete Compression in strut and tie model 5.

Select Load Modifiers, η1 Strength i) Ductility η0 0.95 ii) Redundancy ηR 1.05 iii) Importance ηI 1.05

0.75 0.70 0.70

service 1.0 1.0 1.0

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fatigue 1.0 1.0 1.0

[Art. 1.3.3] [Art. 1.3.4] [Art. 1.3.5] Page 4

Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

η0 = ηR = ηI = 1.0 6.

Select Applicable Load Combinations [Table 3.4.1-1] Strength I U=η (1.25DC + 1.50DW + 1.75(LL+1M)+1.0FR+γTG TG Service I U=1.0(DC+DW) +1.0(LL+IM) + 0.3(WS+WL+1.0FR Fatigue U=0.75*(LL+IM)

7.

Dead Load Force Effects a)

Interior Strip:- Consider a 1m Strip, ρcon=2400 kg/m3 WDC= (2400*9.81)* 10-3 kN/m3 * 0.54 m = 12.71kN/m2 WDW = (2250*9.81)* 10-3 kN/m3 * 0.075m = 1.66kN/m2

[Table 3.5.1-1]

75mm bituminous wearing surface, ρbit = 2250kg/m3 [Table 3.5.1-1] VDC = ½ * 12.71*10.415 = 66.21kN/m VDW = ½ * 1.66*10.415 = 8.64kN/m

b)

Edge Strip:

VDC = ½* 16.06*10.415 = 83.63kN/m 8.

Investigate Service Limit State

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Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

i) Durability: Cover for main reinforcement steel for 

[Art. 5.12]

deck surface subjected to tire wear = 60mm

 bottom of cast in-place slab = 25 mm ηD = ηR = ηI = 1.0 η = 1.0 a)

Moment –Interior Strip

M=1.0(172.34 + 22.51 + 245.76) = 440.61 kNm Reinforcement: Assume j=0.875 and fs = 0.6 fy = 0.6*400 = 240

b)

Moment – Edge strip:

M=1.0(217.76 + 0 + 533.56) = 751.32kNm

ii)

Control of Cracking

[Art.5.7.3.4]

Components shall be so proportioned that the tensile stress in the mild steel Reinforcement at the service limit state, fs, does not exceed fsa

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Chapter 5- Superstructures Design Example on Slab Bridge

Fundamentals of Bridge Structures

Z – crack width parameter (N/mm) = 23000N/mm for severe exposure dc depth of concrete measured from extreme tension fiber to center of bar located closest there to. Clear cover used to compute dc≤50mm

a)

Interior strip

190