Structural Concrete - Hassoun

552 Chapter 15 Design for Torsion
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75 (October 1978).
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Civil Engineers75 (March 1983).
15. Alan H. Mattock. “How to Design for Torsion.” In Torsion of Structural Concrete. Special Publication
18. American Concrete Institute, Detroit, MI, 1968.
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ACI Journal 66 (January 1969).
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ACI, Detroit, MI, 2014.
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pp. 209–285.
PROBLEMS
For each problem, compute the cracking moment φT cr and the maximum factored torque φT n that can be
applied without using torsional web reinforcement. Use f c ′ = 4ksiandf y = 60 ksi.
15.1 A rectangular section with b = 16 in. and h = 24 in.
15.2 A rectangular section with b = 12 in. and h = 20 in.
15.3 A T-section with b = 48 in., b w = 12 in., t = 4 in., and h = 25 in. Assume flanges are confined with
closed stirrups.
15.4 A T-section with b = 60 in., b w = 16 in., t = 4 in., and h = 30 in. Assume flanges are confined with
closed stirrups.
15.5 An inverted L-section with b = 32 in., b w = 14 in., t = 6 in., and h = 24 in. The flange does not have
closed stirrups.
15.6 An inverted L-section with b = 40 in., b w = 12 in., t = 6 in., and h = 30 in. The flange contains confined
closed stirrups.
15.7 Determine the necessary web reinforcement for a simple beam subjected to an equilibrium factored
torque T u = 220 K ⋅ in. and V u = 36 K. The beam section has b = 14 in., h = 22 in., and d = 19.5 in., and
is reinforced on the tension side by four no. 9 bars. Use f c ′ = 4ksiandf y = 60 ksi.
15.8 Repeat Problem 15.7 using f c ′ = 5ksi and f y = 60 ksi.
15.9 The section of an edge (spandrel) beam is shown in Fig. 15.17. The critical section of the beam is
subjected to an equilibrium torque T u = 300 K ⋅ in. and a shear V u = 60 K. Determine the necessary
web reinforcement using f c ′ = 4ksi and f y = 60 ksi. Consider that the flange is not reinforced with
closed stirrups.
15.10 Repeat Problem 15.9. Considering that the flange is effective and contains closed stirrups.
15.11 The T-section shown in Fig. 15.18 is subjected to a factored shear V u = 28 K and a factored equilibrium
torque T u = 300 K ⋅ in. and M u = 250 K⋅ft. Design the necessary flexural and web reinforcement. Use
f c ′ = 4ksiandf y = 60 ksi.
15.12 Repeat Problem 15.11 if V u = 36 K, T u = 360 K ⋅ in., M u = 400 K⋅ft, and h = 24 in.
15.13 Repeat Problem 15.11 using f c ′ = 3ksiandf y = 60 ksi.