On the Effect of Shearing Force Upon the Beam Theory

Abstract

In studying the strength and stiffness of a beam which is subjected to lateral loading, we usually apply the so-called "beam theory". But, when we deal with a deep beam, the beam theory often gives insufficient answers, because, in this case, the deflection of the beam due to shear should not be disregarded. Moreover, if the beam is statically indeterminate, the bending moment curve of the beam should also be altered by shear. I propose to show how the effect of the shear may be taken into account in calculating the statically indeterminate quantities and the deflection of the beam, and I deduce the general expression of those quantities, from which the results of the "beam theory" may be obtained as special cases.