Structural Concrete - Hassoun

936 Chapter 22 Prestressed Concrete Bridge Design
M u corresponding to V u at this section is calculated as below:
M DC = w DC x2
= 1.841(3)2 = 2.071 kip ⋅ ft M
8 8
DW = w DW_int x2
= 0.28(3)2 = 0.315 kip ⋅ ft
8 8
Maximum moment due to uniform lane load of 0.64 klf:
(0.64 klf)x(L − x) 0.64(3)(100 − 3)
M uniformLL = = = 93.1 kip⋅ ft
2
2
Maximum moment due to design truck of HL-93 without dynamic load allowance:
[ (
M HL93 = 16 K 4.5 1 − x ) ] [ (
42 ft
− = 16 4.5 1 − 3 )
− 42 ]
= 189.4 kip⋅ ft
L L
100 100
Maximum moment due to design tandem without dynamic load allowance:
(
M Tandem =(50 K)x 1 − x L − 2ft ) (
= 50(3) 1 − 3
L
100 − 2 )
= 142.5 kip⋅ ft
100
Controlling maximum live load moment:
M Truck = max(M HL93 , M Tandem )=max(189.4, 142.5) =189.4 kip⋅ ft
The maximum moment due to live load, including the effects of dynamic load allowance and
load distribution factor is calculated below:
M LL = DM int {M uniformLL +[(1 + IM)M truck ]} = 0.845[93.1 +(1 + 0.33)189.4]
= 291.6 kip⋅ ft
The factored maximum moment demands corresponding to the maximum shear demands:
M u = 1.25M DC + 1.5M DW + 1.75M LL = 1.25(2.1)+1.5(0.3)+1.75(291.6)
= 513.4 kip⋅ ft
2. Norminal Shear Resistance
The nominal shear resistance V n shall be the lesser of:
V n = V c + V s + V p (AASHTO 5.8.3.3 − 1)
V n = 0.25f ′ c_BT b v d v + V p (AASHTO 5.8.3.3 − 2)
The shear resistance provided by concrete:
√
V c = 0.0316β f ′ c_BT b v d v (AASHTO 5.8.3.3 − 3)
The shear resistance provided by transverse reinforcement:
V s = A v f y d v (cotθ + cotα)sinα
s
where
b v = 6.5 in. Minimum web width, measured parallel to the neutral axis,
between the resultants of the tensile and compressive forces
due to flexure
L cr = x = 36 in. Critical section for shear design