Torsion - Design of Reinforced Concrete - page 486

bottom reinforcing in spandrel beams subjected to torsion 6 in. into the supports. Usu-
ally this is insufficient.

15.8 ADDITIONAL ACI REQUIREMENTS

Before we present numerical examples for torsion design, it is necessary to list several
other ACI requirements. These are:

1. Sections located at a distance less than d from the face of support may be designed
for the torque at a distance d . Should, however, a concentrated torque be present
within this distance, the critical design section will be at the face of the support
(ACI 11.6.2.4).
2. The design yield strength of torsion reinforcing for nonprestressed members may
not be greater than 60,000 psi. The purpose of this maximum value is to limit the
width of diagonal cracks (ACI 11.6.3.4).
3. The longitudinal tension created by torsion moments is partly offset in the flex-
ural compression zones of members. In these zones the computed area of longi-
tudinal torsional reinforcing may be reduced by an amount equal to ,
according to ACI Section 11.6.3.9. In this expression, M u is the factored mo-
ment acting at the section in combination with T u . The reinforcing provided,
however, may not be less than the minimum values required in ACI Sections
11.6.5.3 and 11.6.6.2.
4. The longitudinal reinforcing must be distributed around the inside perimeter of the
closed stirrups and must be spaced no farther apart than 12 in. At least one bar
must be placed in each corner of the stirrups to provide anchorage for the stirrup
legs. These bars have to be #3 or larger in size and they must have diameters no
less than 0.042 times the stirrup spacings (ACI 11.6.6.2).
5. Torsional reinforcing must be provided for a distance no less than b t

M u / 0.9 d f y

d beyond
the point where it is theoretically no longer required. The term b t represents the
width of that part of the member cross section which contains the closed torsional
stirrups (ACI 11.6.6.3).

15.9 EXAMPLE PROBLEMS USING U.S. CUSTOMARY UNITS

In this section the design of torsional reinforcing for a beam is presented using U.S. cus-
tomary units; an example using SI units is presented in the next section.

EXAMPLE 15.1

c Design the torsional reinforcing needed for the beam shown in Figure 15.13 if 4000 psi, f y

60,000 psi, T u 30 ft-k, and V u 60 k. Assume 1.5 in. clear cover, #4 stirrups, and a required A s
for M u of 3.52 in. 2 Select #8 bars for flexural reinforcing.

f