Structural Concrete - Hassoun

910 Chapter 22 Prestressed Concrete Bridge Design
The initial value of ε x should not be taken greater than 0.002. If the value of ε x from Eq. (22.15) or
(22.16) is negative, the strain shall be taken as
ε x = (|M u|∕d v ) 0.5N u + 0.5|V u − V p | cot θ − A ps f po
2(E c A c + E s A s + E p A ps )
(22.17)
where
A c = area of concrete on flexural tension side of member as shown in Fig. 22.9 (in. 2 )
A ps = area of prestressing steel on flexural tension side of member, as shown in Fig. 22.7 (in. 2 )
A s = area of nonprestressed steel on flexural tension side of member at section under consideration,
as shown in Fig. 22.7 (in. 2 )
f po = parameter taken as modulus of elasticity of prestessing tendons multiplied by the locked-in
difference in strain between the prestessing tendons and the surrounding concrete (ksi). For
usual levels of prestressing, a value of 0.7 f pu will be appropriate for both pretensioned and
posttensioned members (ksi)
N u = factored axial force, taken as positive if tensile and negative if compressive (kip)
M u = factored moment, not to be taken less than V u d v (kip-in.)
V u = factored shear force (kip)
In order to determine θ and β in members with no transverse steel reinforcement or with web
reinforcement less than the minimum required, the crack spacing parameter in Table 22.16, s xe ,is
needed; it can be estimated as
1.38
12 ≤ s xe = s x ≤ 80 in. (22.18)
a g + 0.63
where
a g = maximum aggregate size (in.)
s x = lesser of either d v or maximum distance between layers of longitudinal crack control
reinforcement, where the area of the reinforcement in each layer is not less than 0.003b v s x ,as
shown in Fig. 22.9 (in.)
22.7.5 Approach 2: Simplified MCFT
AASHTO LRFD 2014 introduces a more simplified version of MCFT, which is explained in this
section. In this method, the shear design will follow the same procedure described in Section 22.7.2
with the exception that β and θ in steps 3 and 4 to be calculated directly as described next.
For sections containing at least the minimum amount of transverse reinforcement required by
the AASHTO code, the values of β shall be specified as follows:
4.8
β =
(22.19)
1 + 750ε s
For sections containing less than the minimum amount of transverse reinforcement required
by the AASHTO code, the values of β shall be specified as follows:
4.8 51
β =
(22.20)
1 + 750ε s 39 + S xe
where S xe can be calculated from Eq. (22.18).