Structural Concrete - Hassoun

Summary 781
Section 19.5
The nominal moment of a rectangular prestressed concrete member is
(
M n = T d − a ) (
= A
2 ps f ps d p 1 − ρ )
p f ps
1.7 f c
′
The values of f ps are given by Eqs. 19.39 to 19.41. For flanged sections,
(
M n = A pw f ps d p − a ) (
+ A
2 pf f ps d p − h )
f
2
If nonprestressed reinforcement is used in the flexural member, then
(
M n = A ps f ps d p − a ) (
+ A
2 s f y d − a )
2
(Eq. 19.37)
(Eq. 19.43)
(Eq. 19.44)
where a =(A ps f ps + A s f y )∕0.85 f ′ cb. ForM n of flanged and rectangular sections with compression
reinforcement, refer to Eqs. 19.46 and Eqs. 19.47, respectively.
Sections 19.6 and 19.7
1. The cracking moment is
M cr = I
[
7.5λ √ f c ′ + F y b A + (Fe) y ]
b
I
2. Midspan deflections of simply supported beams are summarized in Table 19.3.
(Eq. 19.48)
Section 19.8
Shear strength of concrete (V c )=
(
0.6λ √ f c ′ + 700 V )
ud p
b
M w d (Eq. 19.50)
u
Minimum V c = 2λ √ f ′ cb w d p
Maximum V c = 5λ √ f ′ cb w d p
The shear strength, V ci , based on flexural shear, is given by Eq. 19.47, and the web-shear
strength, V cw , is given by Eq. 19.53:
Section 19.9
V s = 1 φ (V u − φV c ) and A v = A ps
80 × f pu
f y
× S d × √
d
b w
(Eq. 19.59)
Empirical practical dimensions for the preliminary design of prestressed concrete members are
suggested in this section.
Section 19.10
The development length of three- to seven-wire strands is
(
l d = f ps − 2 )
3 f se d b (Eq. 19.65)