Structural Concrete - Hassoun

22.9 Deflections (AASHTO 5.7.3.6) 933
where
(
k = 2 1.04 − f py
= 0.28
A ps = 5.625 in. 2
A ′ s = 0
A s = 0
f pu
)
( )
= 2 1.04 − 243
270
Area of prestressing strands
Area of compressive steel
Area of reinforcing steel at the bottom of girder;
assume fully prestressed
f pu = 270 ksi f y = 60 ksi f s ′ = 60 ksi
b = b eff_int = 8.5 ft
Width of compression face of member
d p = D s − y m = 67.474 in.
d s = D s − 3in.= 69 in.
d ′ s = 0 in.
h f = t s = 8 in.
β 1 = 0.85 − 0.05(f ′ c_BT − 4ksi) 1
ksi
= 0.85 − 0.05(8 − 4) = 0.65
Distance from extreme fiber to cg of PS strands
Distance from extreme fiber to cg of mild
reinforcement
Distance from extreme fiber to cg of compression
reinforcement, assume no compression steel
Depth of compression flange = thickness of deck
Assume rectangular section behavior, b = b w :
Use
Therefore,
b w = b = 102 in.
c rec =
=
A ps f pu + A s f y − A ′ sf ′
s
0.85f ′ c_BT β 1 b w + kA ps (f pu ∕d p )
(5.625)(270)+0 + 0
= 3.322 in.
0.85(8)(0.65)(102)+0.28(5.625)(270∕67.47)
if (c rec ≤ h f , “Assumption − correct”, “NG, try” T − Section − behavior”)
= “Assumption − correct”
C T = A ps f pu + A s f y − A′ sf ′
s − 0.85f ′ c_BT (b − b w )h f
0.85f ′ c_BT β 1 b w + kA ps (f pu ∕d p )
= 3.322 in. (Assume T − section behavior)
c = c rec = 3.322 in.
(
f ps = f pu 1 − kc ) (
rec
= 270 1 −
d p
2. Factored flexural resistance—flanged section
)
0.28 (3.322)
= 266.3 ksi
67.47
φ f = 1.0
For tension-controlled prstrestressed concrete section, AASHTO
Table 5.5.4.2.2-1