Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 70

3.7.1 Beam Sizing to Neglect Torsion

⎛

A cp
p cp

⎞

Torsion can be neglected if the factored torque T u (threshold torsion) is less than (ACI 11.5.1(a))

φλ ʹ f c ⎜ ⎟

⎝ ⎠

where:

A cp = area enclosed by outside perimeter of concrete-cross section, in 2 .

p cp = outside perimeter of concrete cross-section, in.

φ = 0.75

λ = modification factor for lightweight concrete

For normal weight concrete with compressive strength = 4000 psi, torsion can be neglected if:

⎛

A cp
p cp

⎞

T u < 0.004

⎜ ⎟

⎝ ⎠

where A cp and p cp are in in. 2 and in., respectively, and T u in ft-kips.

Section properties A cp and p cp are presented in Table 3-11 for rectangular and L shaped beams. Table 3-12
presents values for threshold torsion for › = 4 ksi

For a rectangular sections having width and height equal to b and h, respectively, the torsion can be neglected if:

h 2 b 2
2(h

⎡
⎢

⎤
⎥

T u <φ ʹ f c

+ b)

for concrete with › = 4000 psi:

h 2 b 2
h

⎡
⎢

⎤
⎥

T u < 0.002

+ b

where h and b are in inches, and T u ft-kip

Figure 3-14 shows values for threshold torsion for rectangular sections.