Structural Concrete - Hassoun

934 Chapter 22 Prestressed Concrete Bridge Design
a = β 1 c =(0.65)(3.322) =2.159 in.
(
M n = A ps f ps d p − 1 ) (
2 a + A s f y d s − 1 )
2 a − A ′ sf
(d ′
s ′ − 1 )
2 a
+ 0.85f ′ c_BT (b − b w )h f
(
=(5.625)(266.3)
( 1
2 a − 1 2 h f
)
67.47 − 2.159
2
φM n = φ f M n =(1.0)(8287) =8287 kip ⋅ ft
s
)
+ 0 + 0 + 0 = 8287 kip ⋅ ft
Check_flexure = if (φM n ≥ M u , “OK”, “NG”) =“OK”
3. Check maximum and minimum reinforcement
a. Maximum reinforcement (AASHTO 5.7.3.3.1): Provision deleted in 2005.
b. Minimum reinforcement (AASHTO 5.7.3.3.2): At any section of a flexural component,
the amount of prestressed and non-prestressd tensile reinforcement shall be adequate to
devleop a factored flexural resistance, M r , at least equal to the lesser of:
i. 1.2M cr :
where
f cpe = −F f
A g
− F f e m
S bg
= −942
713 − 942(27.59)
12,224
=−3.488 ksi
√
f r = 0.37 (f ′ c_BT
M dnc = M DC1 = 2045.6 kip ⋅ ft
S c = S bc = 17407 in. 3
S nc = S bg = 12224 in. 3
( )
Sc
M cr = S c (f r + f cpe )−M dnc − 1 ≥ S
S c f r
nc
Compressive stress in concrete due to effective
prestress forces only at extreme fiber of section
where tensile stress is caused by extremely applied
loads
ksi = 1.047 Modulus of rupure, AASHTO 5.4.2.6
[[
(
( ) Sc
M cr = max S c fr + f cpe − Mdnc
Total unfactored dead-load moment acting on the
noncomposite section
Section modulus for the extreme fiber of the
composite section where tensile stress is caused by
extrernally applied loads
Section modulus for the extreme fiber of the
monolithic or noncomposite section where tensile
stress is caused by externally applied loads
)]
− 1
S nc
, S c f r
]
[[
= max (17,405) (1.047 − 3.498)−2045.6(12)
1.2M cr = 1821.6 kip⋅ ft
]
(17,407) (1.047) = 1518 kip ⋅ ft
( ) ]
17,407
− 1 ,
12,224