Department of Civil Engineering, University of Engineering and Technology Peshawar

Types of Bridges

 Main Structure Coinciding with Deck line

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 23

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Loads to be considered in bridge design can be divided
into two broad categories:
 Permanent loads,

 Transient loads.

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Permanent Loads
 Self weight of girders and deck, wearing surface, curbs and
parapets and railings, utilities and luminaries and pressures
from earth retainments.

 Two important dead loads are:

 DC: Dead load of structural components and non structural
attachments.

 DW: Dead load of wearing surface.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 25

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Permanent Loads
 Material Properties for Pavement
 γbitumen = 140 lb/ cft

 γconcrete = 150 lb/ cft

 Load factors for Pavement Dead Loads

 The maximum load factor for DC = 1.25

 The maximum load factor for DW = 1.5

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Transient Loads
 Gravity (Live) loads due to vehicular, railway and pedestrian
traffic.

 The automobile is one of the most common vehicular live

load on most bridges; it is the truck that causes the critical
load effects.

 Lateral loads due to water, wind, earthquake and ship

collisions etc.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 27

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Transient Loads
 Following effects caused by Live load are also very
important and must be considered in the design of a bridge.
 Impact (dynamic effects),

 Braking forces,

 Centrifugal forces (if present) and

 The effects of other trucks simultaneously present.

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
 The AASHTO design loads model consists of three distinctly
different loads:
 Design Truck,

 Design Tandem,

 Design Lane.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 29

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
 The vehicle combination as described in AASHTO (1994)
LRFD Bridge specifications are designated as HL-93 for
Highway Loading accepted in 1993.

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
• Design Truck

8 kips 32 kips 32 kips

8 kips 32 kips 32 kips
14 ft 14 ft to 30 ft

14 ft 14 ft to 30 ft

24 in 6 ft
12 in
12 ft

HL-93 Truck Load

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 31

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
 Design Tandem

24 kips 24 kips

4 ft

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
 Design Lane Load
 The AASHTO design lane loading is like a caravan of trucks.
 It is 0.064 k/ft2 and is assumed to occupy a region of 10 ft.
 It is applied as 0.064 k/ft2 (64 lb/ft2) of pressure to a width of 10 ft over the entire length
of bridge for FEM.

(0.64 kip/ ft)

10 ft
Bridge

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 33

Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Vehicular Design Loads
 In summary three design loads should be considered:

the design truck, design tandem, and the design lane.

 These loads are superimposed by two ways to yield the live

load effects, which are combined with the other load effects.

 The two ways of superposition are:

 Truck + lane

 Tandem + lane

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Loads for Bridge Design

 Load Modifier
 A factor accounting for ductility, redundancy and the
operational importance of the bridge.

 It is taken as 1.05 for simply supported bridges and is

applied on already factored values of bending moments.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 35

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of

Simply Supported RC
Slab Bridges

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Simply Supported RC Slab Bridge

 This type of bridge consist of only a slab (without any other

supporting member such as girders).

 A slab bridge is widely used when the bridge crosses a

minor road or small river.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 37

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design lane

 Slab bridges can be analyzed as 3D, 2D and 1D models.

 If it is to be analyzed as 1D model (line analysis), the bridge

width will be divided into various strips.

 These strips with a strip width of “E” are called design lanes.

E E E E E

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design lane
 The design lanes are then
transformed to line elements (1D
model) for line analysis. The moment
are calculated from line analysis.

 These moments (M) are then divided

by the design lane width (E) to get
moment per foot (M/E) for the slab.

Moment Obtained from 1D analysis

M/E M/E M/E M/E M/E

• Design lane widths can be calculated using equations given as follows.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 39

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design Lane Width
 For single lane loaded:

 E (inches) = 10.0 + 5.0 √ (L1W 1) …….. (1)

L1 = Modified span length = Minimum of (S) and 60 ft

W1 = Modified edge to edge width = Minimum of (Overall width of

bridge, W 1) or 30 ft

W
W1
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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design Lane Width
 For multilane loaded:

 E (inches) = 84 + 1.44√ (L1W 1) ≤ W 1/NL ……… (2)

L1 = Same as single lane loaded case = Minimum of (S) and 60 ft

W 1 = Minimum of (overall width of bridge, W 1) or 60 ft

NL = No. of design lanes= INT (W/12)

 Design Lane Width E, is the smallest value of (1) & (2)

W1
Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 41

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design of RC Slab Bridge
 Depth, h (ft) = 1.2(S + 10)/30
S
(S = span of bridge)

 ØMn ≥ Mu

 Mu = 1.05 [1.25MDC + 1.5MDW + 1.75MLL+IM ] (per foot)

 MDC = W DCS2/8 (ft-kip/ft) (W DC = hγconcrete )

Dead Loads
 MDW = W DWS /8 2
(ft-kip/ft) (W DW = hγwearing surface )

 MLL+IM = 1.33(MTandem OR MTruck) + Mlane (ft-kip) Live Load

 Convert MLL+IM to ft-kip/ft, Divide MLL+IM by “E”, design lane width.

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design of RC Slab Bridge
 Slab moments due to live loads:

1. Moment due to HL-93 Truck load, MTruck

(Max. moment due to truck load can be obtained by placing the middle axle at mid span of
the bridge and rear axle load at a distance of 14 ft from the middle axle load)

32 kips 32 kips
8 kips

14 ft 14 ft

S/2

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 43

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design of RC Slab Bridge
 Slab moments due to live loads:

2. Moment due Tandem Load, MTandem

(Max. moment due to tandem load can be obtained by placing the two loads at a distance
of 2 ft from the mid span)

24 kips 24 kips

2 ft 2 ft

S/2

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design of RC Slab Bridge
 Slab moments due to live loads:

3. Moment due design lane load, MLane

 MLane = 0.64 S2/8

0.64 kip/ft

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 45

Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Design of RC Slab Bridge
a) Distribution reinforcement (bottom transverse reinforcement) {A5.14.4.1}:
 Atransverse = (100/√S or 50 %) of As (whichever is less, But It should not be less
than As(Shrinkage)

 Astmin (shrinkage)= 0.0018Ag

b) Shrinkage and temperature reinforcement in top face of slab (long and

transverse both): For grade 60 steel,
• Ast = 0.0018Ag

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Reinforcement Detail in Slab Bridge:

As per shrinkage and A′

temperature reinforcement
requirements

Transverse Bottom reinforcement

As, Main reinforcement
(least of 100/√S % or 50 %) of As
(to be designed)
Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II
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Department of Civil Engineering, University of Engineering and Technology Peshawar

Analysis and Design of Simply

Supported RC Slab Bridges
 Reinforcement Detail in Slab Bridge:
 Bridge Reinforcement Animation

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Design Problem: Design of
simply supported slab bridge
for HL-93 live load.
 Span length of 35 ft centre to
centre of bearings.

 Roadway width is 44 ft curb to

curb.

 Allow for a future wearing

surface of 3 inch thick
bituminous overlay.

 Use fc′ = 4000 psi and fy = 60

ksi.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 49

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 1: Sizes.

 Span length of bridge (S) = 35 ft c/c

 Clear roadway width (W) = 44 ft (curb to curb)

 For a curb width of 15 inches, total width of the bridge (W 1) =

44 + (2 × 15/12) = 46.5 ft

 Minimum thickness of bridge slab is given by formula:

hmin = 1.2(S + 10)/30 = 1.2 (35 + 10)/30 = 1.8 ft = 21.6″ ≈ 22″

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 2: Loads.

 Slab load (wDC) = hγconc

= (22/12) × 0.15 = 0.275 ksf

 Wearing surface load (wDW ) = hγwearing surface

= (3/12) × 0.14 = 0.035 ksf

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 51

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Dead load moments:

Slab moments (MDC) = wDCS2/8

= 0.275 × (352)/8 = 42 ft-kip/ft

Wearing surface moment (MDW) = wDW S2/8

= 0.035 × 352/8 = 5.3 ft-kip/ft

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Live load moments:

 Truck Load moments:

MTruck = 350 ft-kip

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 53

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Live load moments:

 Tandem moment:

Mtandem = 372 ft-kip

 Lane moment:

Mlane = 0.64 × 352/8 = 98 ft-kip

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Live load moments:

 Mtandem > Mtruck, therefore we will use Mtandem

 MLL+IM (Including impact) = 1.33Mtandem + Mlane

= 1.33 × 372 + 98 = 593 ft-kip

 To convert MLL+IM to moment/ft, Divide MLL+IM by “E” design lane width.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 55

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Design Lane width “E” :

 For single lane loaded:

 E (inches) = 10.0 + 5.0 √ (L1W 1)

L1 = Modified span length = Minimum of (S = 35 ft) and 60 ft = 35 ft

W 1 = Modified edge to edge width = Minimum of (W1 = 46.5 ft) or 30

ft = 30 ft

 Therefore, E = 10.00 + 5.0√ (35 × 30.00) = 172 in = 14.3 ft

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Design Lane width “E” :

 For multilane loaded:

 E (inches) = 84 + 1.44√ (L1W 1) ≤ W 1/NL
L1 = 35 ft
W 1 = Minimum of (W 1 = 46.5 ft) or 60 ft = 46.5 ft
NL = No. of design lanes.= INT (W/12) =INT (44/12) = 3
 E = 84 + 1.44 √ (35 × 46.5) ≤ 46.5/3
= 142 inch or 11.84 ft ≤ 15.5
 Therefore, E = 11.84 ft (Least of all)

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 57

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 3: Analysis.

 Moment (per foot)

 MLL +IM per foot = 593/11.84 = 50 ft-kip/ft

Now,

 Mu = 1.05 [1.25MDC + 1.5MDW + 1.75MLL+IM (per foot)]

 Mu = 1.05 (1.25 × 42 + 1.5 × 5.33 + 1.75 × 50)

 Mu = 155.3 ft-kip/ft = 1863.6 in-kip/ft

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 4: Design.

 (a) Design :
 Moment (Mu) = 155.3 ft-kip/ft = 1863.6 in-kip/ft
 Effective depth of bridge slab (d) = h – cover – ½ × Dia of bar
used
 Using #8 bar, effective depth is bottom cover for slab is taken
equal to 1″.
 d = 22 – 1 – ½ × 1 = 20.5 inch
 Asmin = 0.0018 × 12 × 22 = 0.47 in2
 As = Mu/{Φfy (d – a/2)}
 After trials, As = 1.80 in2,(#8 @ 4 inches c/c)

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 59

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 4: Design.

 (b) Distribution reinforcement (bottom transverse

reinforcement) {A5.14.4.1}:
 The amount of bottom transverse reinforcement may be taken as
a percentage of the main reinforcement required for positive
moment as follows but not less than Shrinkage reinforcement:
 Atransverse = (100/√S or 50 %) of As (whichever is less)
100/√L = 100/√35 = 16.9 % < 50 %
 Therefore, Atransverse = 0.169 × 1.80 = 0.304 in2
 Astmim (shrinkage)= 0.0018Ag = 0.0018 × 12 × 22 = 0.47 in2 (#5 @
8 inches c/c)

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 4: Design.

 (b) Distribution reinforcement (bottom transverse reinforcement)

{A5.14.4.1}:
 Maximum spacing for temperature steel reinforcement in one way
slab according to ACI 7.7.6.2.1 is minimum of:
 5hf =5 × 22 = 110″

 18″

 Therefore #5 @ 8 inches c/c is OK.

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 61

Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 4: Design.

 (e) Shrinkage and temperature reinforcement in top face of slab

(long and transverse both): For grade 60 steel,
 Ast = 0.0018Ag = 0.0018 × 12 × 22 = 0.47 in2 (#5 @ 8 inches c/c)

 Finally use #5 @ 8 inches c/c.

 Final Recommendation:
 Main steel (bottom) = #8 @ 4″ c/c.

 Transverse bottom reinforcement = #5 @ 8″ c/c throughout.

 Top steel (long and transverse) = #5 @ 8″ c/c.

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 Department of Civil Engineering, University of Engineering and Technology Peshawar

Example
 Solution:
 Step No 5: Drafting

(Shrinkage reinforcement)
(Shrinkage reinforcement)

(Bottom transverse reinforcement)

(Main reinforcement)

Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II 63

Department of Civil Engineering, University of Engineering and Technology Peshawar

Some Famous Bridges

 Longest Bridge
 Danyang–Kunshan Grand Bridge in China (164800 m)

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