can maybe use for 334 project

can maybe use for 334 project - l KAU: Eng. Sci., Vol. 2,...

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lKAU: Eng. Sci., Vol. 2, pp. 95-117 (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 cross-section 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 torsion-bending' interaction at low TIM ratios. A comparison with available test results offifty-one 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 twenty-three 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[3-7] 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 cross-section is obtained as (1) 95
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96 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 cross-section, 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 center-to-center 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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can maybe use for 334 project - l KAU: Eng. Sci., Vol. 2,...

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