Graphical Solution for Shear Deflection of Flexural Members

Shear deflections are often required in flexural members of wood and wood based materials because of the high ratios of modulus of elasticity to modulus of rigidity and depth to span frequently encountered. This research note presents a simple, graphical method for calculating shear deflection at any point in a simple or cantilever span under general loading. The shear deflection at an arbitrary point b is equal to k[(1 p) Aab PAbc] where k is a parameter depending upon the shape of the cross section, p is the fraction of the span from the left and, a to b, Aab is the area of the V/GA diagram between a and b and Abc is the area of the remainder of the V/GA diagram. The features of the formula are: 1) it is analogous to the moment-area concepts for computing bending stress deflections; 2) it is applicable to all materials for which the shear modulus is known; 3) it yields shear deflections for all loading conditions; 4) it yields the shear deflection for any point in the member; 5) it involves no differentiation or integration; 6) it may be used in conjunction with shear diagrams already developed for many types of loading and which are available in handbooks.

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