Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 81

3.7.3.1 Example: Design of Torsion Reinforcement

Determine the required combined shear and torsion reinforcement for the E-W spandrel beam of Building #2,
Alternate (1) - slab and column framing with spandrel beams.

For E-W spandrels:

Spandrel size = 12 20 in.

d = 20 -2.5 = 17.5 in. = 1.46 ft.
˜ n = 24 - (12/12) = 23.0 ft.
Beam weight = 1.2(12 0.150/144) = 0.30 kips/ft

q u from slab = 1.2(136) + 1.6(50) = 243 psf

20

Tributary load to spandrel (1/2 panel width) = 243 (20/2) = 2.43 kips/ft

Beam = 0.30 kips/ft

Total w u = 2.73 kips/ft

M o = q u ˜ 2 ˜ n 2 /8 = 0.243(24)(18.83) 2 /8 = 254.5 ft-kip

where

12 16

2(12) =

+

n = 20 − 18.83 ft.

T u = 0.30M o /2 = 0.3(254.5) = 38.8 ft-kip
T u at distance d = 38.8 - 38.8/24(1.46) = 36.4 ft-kip
V u (at the face of support) = 2.73(23)/2 = 31.4 kips
V u at distance d = 31.4-2.73(1.46) = 27.4 kips

(1) Check if torsion can be neglected

A cp = 20(12) + (20-8.5)(8.5) = 337.8 in 2

p cp = 20(2) + 12(2) + (20-8.5)(2) = 87 in

⎛

A cp
P cp

⎞

= 0.004 = 0.004(337.8) 2 /87 = 5.25 ft - kip < 36.4 Torsion must be considered

⎜ ⎟

⎝ ⎠

(2) Calculate the maximum factored torsional moment at the critical section to be considered:

⎛

A cp
p cp

⎞

0.75(4) 4000(337.8) 2

T u =φ 4 f c ʹ

⎟ =

/ 87 /12,000 = 20.7ft − kips < 36.4

⎜

⎝ ⎠

Note: The difference in torsional moments 36.4-20.7 must be redistributed (ACI 11.5.2.2).
This redistribution will result in an increase of the positive midspan moment is slab.