Transverse Shear Effect on Deflection of Tapered Beam under Uniformly Distributed Load

Abstract

Abstract The effect of transverse shear as well as bending on deflection of tapered beams is considered with comparison to that of prismatic beams . It is noticed that the deflection due to transverse shear is usually small . An approximate solution is suggested for deflection of tapered beams by assuming the taper beam as a prismatic beam of uniform cross section equal to the smaller cross section of the taper beam to simplify the solution . A simply supported taper beam with circular or square cross section and loaded with uniformly distributed load is considered . The suggested approximate solution gives 6 % higher deflection ratio with respect to that by exact integration . The deflection ratio along a taper beam is presented by curves in logarithmic scales for different taper ratios ( 1.5 to 10 ) due to shear and bending . The deflection ratio due to the effect of transverse shear alone is also presented . The logarithmic scale is used for clearer presentation of the results . Both exact integration solution and approximate solution are used . The suggested approximate solution by using the smaller cross section area of a taper beam as an equivalent uniform area is found to be useful to deal with taper beams of different cross sectional shapes and also for beams under axial forces .

Keywords

• key words: bending moment
• deflection
• prismatic beam
• taper beam
• transverse shear