lKAU: Eng. Sci.,
Vol. 2, pp. 95117
(1~1()
A.H. / IYY() A.D.)
ACI
Code Torsion Equations Modified for Rectangular
Concrete Beams with an Opening
ALIA. AKHTARUZZAMAN
Civil Engi11:eering Department, Faculty
ofEngineering,
King Abdulaziz University, Jeddah, Saudi Arabia.
ABSTRACf.
The ACI Code torsion equations for concrete beams of solid
crosssection have been modified to predict the torsional strength of rectan
gular beams with a transverse opening. The equations have also been
adapted to include the effect of torsionbending' interaction at low
TIM
ratios. A comparison with available test results offiftyone beams subjected
to different combinations of torsion, bending and shear shows excellent ag
reement between the predicted values and the experimental results at all
ranges of
ratios. Results oftorsion tests on twentythree plain concrete
and partially reinforced concrete beams with a rectangular opening are also
presented.
Introduction
Beams in multistoried buildings are often provided with transverse openings in the
webs. Such openings may significantly reduce their torsional strength. The ACT
Code
ll
]
equations which are based on Hsu's(21 research on reinforced concrete beams
of solid section, do not have any provisions for designing such beams. Some research
workers[37] have investigated torsional strength of beams with a transverse opening
of different profiles. But the equations developed by them are rather complex. It
may, however, be possible to modify the existing ACI Code equations suitably to
predict the torsional strength of a rectangular beam section with a transverse open
ing.
The ACI Code Equations and Proposed Modifications
According to the ACI Code
llJ
, the nominal torsional strength
Tn'
of a reinforced
concrete beam of solid crosssection is obtained as
(1)
95
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Ali A. Akhtaruzzaman
where
T
c
is the nominal torsional strength provided by concrete and
T
s
is the nominal
torsional strength provided by torsional reinforcement. Similarly, the nominal tor
sional strength of a beam containing an opening
T
nh
,
can also be written as
(2)
T
ch
and
T
sh
are the nominal torsional strengths provided by concrete section
containing the opening and by the torsional reinforcement in the hole section, re
spectively.
a.
Rectangular Beams
Subjected to
Torsion Only
i.
Solid beams
For a beam of solid crosssection, the ACI Code equations for
T
c
T
s
are
T
c
0.8
vr:
b
2
h
(3)
(4)
At
is the area ofone leg of a vertical stirrup, band
h
are the width and depth of
the beam section,
Ie
is the compressive strength ofconcrete,
f
y
is the yield strength of
steel,
s
is the stirrup spacing,
Xl
Yl
are the shorter and longer centertocenter di
mensions of the stirrups, and
at
is a coefficient as a function of
Yl.
According to Winter and Nilson[81,
T
c
in Eq. 3 represents 40 percent of the tor
sional strength of a plain concrete beam
T
pc
'
given by
T
=
2
Yj"
b
2
h
(5)
c
Equation 5 is similar to Hsu's[91 equation for torsional strength of a plain concrete
beam,
i.e.,
(6)
I,
is the modulus of rupture of concrete.
Equation 4 can be written as
T
s
=
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 Strength of materials, Tensile strength, Ali A. Akhtaruzzaman, torsional strength

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