Structural Concrete - Hassoun

146 Chapter 3 Flexural Analysis of Reinforced Concrete Beams
1. Calculate ρ = A s /bd, ρ ′ = A s /bd, and (ρ − ρ ′ ).
2. Calculate ρ b , ρ max ,andρ min as given above (or see Section 3.10).
3. Calculate K = 0.85β 1 (f c∕f ′ y )(d ′ ∕d)[87∕(87 − f y )]. (f c ′ and f y are in ksi.)
4. When compression steel yields,
a. Check that ρ ≥ ρ min .
b. Check that ρ − ρ ′ ≥ K for compression steel to yield. If not, then compression steel does
not yield.
c. If compression steel yields, then f s ′ = f y .
d. Check that ρ≤(ρ max + ρ ′ )or(ρ − ρ ′ ) ≤ ρ max .
e. a =(A s − A ′ s)f y ∕(0.85f cb).
′ ( )
f. Calculate φM n = φ(A s − A ′ s)f y d − 1 a + φA ′ 2 s f y (d − d ′ ).
g. If ρ − ρ ′ >ρ max but