Structural Concrete - Hassoun

Summary 147
Note that (A s f y − A ′ s f y )=A s1 = A s − A s2 = A s −(A ′ s f ′
s ∕f y ) and A s2 f y = A ′ s f ′
s . Also, a =
A s1 f y ∕(0.85f ′ cb).
Sections 3.15–3.17: Analysis of T-Sections
Given: f ′ c, f y , A s , and section dimensions. Required: design moment strength, φM n . Two possible
cases may develop. (Determine the effective flange width, b e ,first.)
Case 1
1. If a ≤ t (the slab thickness), then it is a T-section shape but acts as a singly reinforced rectangular
section using b = b e (the flange effective width) to calculate φM n .
a ′ =
A s f y
0.85f ′ cb e
≤ t
Or, check that A c (the area of concrete in compression) = A s f y ∕(0.85f c) ′ ≤ bt. IfA c ≥ bt,
then it is a T-section analysis.
2. If a ′ ≤ t or A c ≤ bt, then a ′ = a and φM n = φA s f y (d − a/2).
3. Check that ρ w (steel ratio in web) = A s /b w d ≥ ρ min .
4. Check that A s ≤ Max A s from Eq. 3.71. (Normally, this is OK for this case.)
( 0.85f
′
)
Max A s = c
[(b
f e − b w )t + 0.375β 1 b w d]
y
5. Check that ε t ≥ 0.005 for φ = 0.9. (Normally this is OK for this case.)
6. The effective flange width b = b e is the smallest of
a. Span/4
b. Center to center of adjacent slabs
c. b w +16 t,wheret = slab thickness
Case 2
1. When a > t or A c > bt, it is a T-section analysis.
2. For the flange, C f = 0.85f ′ ct(b − b w )=A sf f y , calculate A sf = C f /f y .
3. For the web,
A sw = tensionsteelintheweb = A s − A sf
a = (A s − A sf )f y
0.85f ′ cb w
4.
C w (web) =0.85f cab ′ w = A sw f y
φM n = φ[M w (web)+M f (flange)] = φ
[C w
(d − 1 )
2 a + C f
(d − 1 )]
2 t .
= φ
[0.85f cab ′ w
(d − 1 )
2 a + 0.85f ct(b ′ − b w )
(d − 1 )]
2 t .
[ (As )
= φ − A sf fy
(d − 1 )
2 a + A sf f y
(d − 1 )]
2 t