Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 52

0.85f' c

0.003

C

a= β 1 c

c

d

d - a
2

T

ε t

b

Strain Stress

ε t ≥ 0.005 Tension control φ = 0.9

ε t = 0.004 Minimum for beams and slabs φ = 0.817

ε t = 0.002 Balanced condition φ = 0.65 (See chapter 5 Columns)

ε t ≤ 0.002 Compression controls φ = 0.65 (See chapter 5 Columns)

0.005 > ε t < 0.002 Transition

C = 0.85 f' c

T = F s A s ≤ F y A s

T = C

M n = C [d -a/2] = T (d-a/2)

Figure 3-2 Code Strain Distribution and Stress Block for Nominal Strength Calculations

3.4 DESIGN FOR FLEXURAL REINFORCEMENT

Similar to developing the sizing equation, a simplified equation for the area of tension steel A s can be derived
using the strength design approach developed in Chapter 6 of Reference 3.8. An approximate linear relationship
between R n and ρ can be described by an equation in the form M n /bd 2 = ρ (constant), which readily converts to

A s = M u / φ d(constant). This linear equation for A s is reasonably accurate up to about two-thirds of the maximum

ρ . For › = 4000 psi and ρ = 0.0125 (60% ρ max ), the constant for the linear approximation is :