ENGV 425
HOMEWORK: TORSION AND SHORT COLUMN TEMPLATE
1. A rectangular beam is 15 in. wide and 30 in. deep. For f c? = 4000 psi and f yt = 60,000 psi ,
determine the required spacing of No. 4 (No. 13) closed stirrups for a factored shear of 80 kips
and factored torsional moment of 50 ft-kips. The stirrup centroid is located 1.75 in. from each
concrete face. The effective depth is 26.5 in.
Given parameters:
?1 := 0.85 ,
Es := 29000000 psi ,
f c? ? psi = 3604997 psi
Ec := 57000 ?
fy
Vu := 80 kip
? f := 0.90
? y :=
Tu := 50 ft ? kip
?v := 0.75
? := 1.0
Es
= 0.002
Tip: To estimate the required spacing, the required steel area due to torsion and due to shear must
be combined. Therefore, 2???? + ???? = ???? ????.4 . Using the equations in the textbook, ???? shall be
??
estimated in function of ??. I.e., ???? = xxx. yy à??. In principle, ???? must be estimated from shear
????2
??
analysis, but to save time it will be given as ???? = 0.0355 ???? .
2. A beam of rectangular cross section has b = 22 in. and h = 15 in. It is to carry a total factored
load of 3600 lb/ft uniformly distributed over its 26 ft span, and in addition the beam will be
subjected to a uniformly distributed torsion of 1800 ft-lb/ft at factored loads. Closed stirrup-ties
will be used to provide for flexural shear and torsion, placed with the stirrup steel centroid 1.75
in. from each concrete face. The corresponding flexural effective depth will be approximately
12.5 in. Design the transverse reinforcement for this beam and calculate the increment of
longitudinal steel area needed to provide for torsion, using f c? = 4000 psi and f y = 60,000 psi .
Tip: For transverse reinforcement, use No. 4 bars.
??
????2
????
??
must be estimated from shear analysis, but
to save time it will be given as ???? = 0.0313 ???? . ???? =
???? ??
2
?? ??
and ???? = ??2 . To make the calculation
simple, just consider the spacing required to carry the maximum ???? and ???? at ?? from the support
(increasing spacing through the beam length can be skipped). The longitudinal reinforcement
also needs to be calculated.

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