Structural Concrete - Hassoun

22.9 Deflections (AASHTO 5.7.3.6) 917
MATERIAL PROPERTIES
PS Steel
Low relaxation, 0.5-in.-diameter seven-wire strands are used for the problem. Stress limits and properties
of prestressing tendons are to be taken as follows (AASHTO Table 5.9.3):
f pu = 270 ksi
Prestressed steel ultimate strength
f py = 0.9 f pu f py = 243 ksi Prestressed steel yield strength
f pe = 0.8 f py f pe = 194.4 ksi Strength at service limit state after all losses
f pbt = 0.9 f py f pbt = 218.7 ksi Strength at immediately prior to
seating—short-term f pbt may be allowed
f pi = 202.5 ksi
Strength at service limit state before losses
E ps = 28500 ksi
Modulus of elasticity of strands
A ps−single = 0.153 in. 2
Area of 0.5 ′′ diameter strand
e m = 27.59 in.
Eccentricity of PS force at midspan
e end = 14.17 in.
Eccentricity of PS force at end span
Reinforcing Steel
f y = 60 ksi
E S = 29,000 ksi
Yield strength of reinforcing steel
Modulus of elasticity of reinforcing steel
Bulb-Tee Girder (BT) (Section 22.1.4)
γ c = 150 pcf
Normal-weight concrete
f c_BT = 8.0 ksi
28-day compressive strength of bulb-tee
f ci_BT = 6.0 ksi
Initial strength at time of initial prestressing of bulb-tee
E ci_girder = 33,000(0.15)
√f 1.5 ′ ci_BT ksi′ Modulus of elasticiry of bulb-tees at time of initial
prestressing
E ci_girder = 4696 ksi
E c_girder = 33,000(0.15)
√f 1.5 ′ c_BT ksi′ Elastic modulus of bulb-tee after concrete hardening
E c_girder = 5422 ksi
Deck Slab (DS)
γ c = 150 pcf
Normal-weight concrete
f ′ c_deck = 4 ksi
28-day compressive strength of deck slab
f ci_deck = 3.6 ksi
Initial strength of deck slab
E ci_deck = 33000(0.15)
√f 1.5 ′ ci_deck ksi′ Modulus of elasticiry of deck slab
E ci_deck = 3637 ksi
E c_deck = 33000(0.15)
√f 1.5 ′ c_deck ksi′ Elastic modulus of deck slab after concrete hardening
E c_deck = 3834 ksi