Structural Concrete - Hassoun

906 Chapter 22 Prestressed Concrete Bridge Design
where
M n = nominal resistance (kip ⋅ in)
φ = resistance factor as specified in AASHTO 5.5.4.2
22.6.3 Limits for Reinforcement (AASHTO 5.7.3.3)
22.6.3.1 Maximum Reinforcement (AASHTO 5.7.3.3.1). This provision was been deleted from
the AASHTO specification in 2005. The current provisions of LRFD eliminate this limit and unify
the design of prestressed and nonprestressed tension- and compression-controlled members. Below
a net tensile strain in the extreme tension steel of 0.005, as the tension reinforcement quantity
increases, the factored resistance of prestressed and nonprestressed sections is reduced in accordance
with AASHTO 5.5.4.2.1. This reduction compensates for decreasing ductility with increasing
overstrength. Only the addition of compression reinforcement can result in an increase in the
factored flexural resistance of the section.
22.6.3.2 Minimum Reinforcement (AASHTO 5.7.3.3.2). The amount of prestressed and noprestressed
tensile reinforcement shall be adequate to develop a factored flexural resistance, M r , at least
equal to the lesser of:
• 1.2 times the cracking moment, M cr , determined on the basis of elastic stress distribution and
the modulus of rupture, f r , of the concrete, where M cr may be taken as
( )
sc
M cr = S c (f r + f cpe )−M dnc − 1 ≥ S
s c f r (22.12)
nc
where
f cpe = compressive stress in concrete due to effective prestress forces only at extreme fiber of
section where tensile stress is caused by externally applied loads (ksi)
M dnc = total unfactored dead load moment acting on the monolithic or noncomposite section
(kip⋅ft)
S c = section modulus for the extreme fiber of composite section where tensile stress is
caused by externally applied loads (in. 3 )
S nc = section modulus for the extreme fiber of monolithic or noncomposite section where
tensile stress is caused by externally applied loads (in. 3 )
• 1.33 times the factored moment required by the applicable strength load combinations
specified in Table 22.8.
22.7 DESIGN FOR SHEAR (AASHTO 5.8)
The AASHTO specifications direct a designer to use the sectional model to design for shear and
torsion when it is reasonable to assume that plane sections remain plane after loading. The resistance
of members in shear or in shear combined with torsion may be determined by satisfying
the conditions of force equilibriums and strain compatibility by utilizing experimentally verified
stress–strain curves for reinforcement and for diagonally cracked concrete.
The sectional model is appropriate for the design of typical bridge girders, slab, and other
regions of components where the assumptions of traditional engineering beam theory are valid.
Components in which the distance from the point of zero shear to the face of the support
is less than 2d, or components in which a load causing more than 1 of the shear at a support is
2
closer than 2d from the face of the support, may be considered to be deep components and shall be
designed for shear and torsion using the strut-and-tie model (AASHTO 5.8.1.1).