Question

Which of the following equations is the correct expression for shear force (V) in an element, given the modulus of elasticity (E), moment of inertia (I), element length (le), displacement (q) in a uniformly distributed load on a simply supported beam?

(a) V=\(\frac{EI}{(le)^3}\)(2q1+leq2-2q3+leq4)

(b) V=\(\frac{EI}{(le)^2}\)(2q1+leq2-2q3+leq4)

(c) V=\(\frac{EI}{(le)^2}\)(2q1+leq2+2q3+leq4)

(d) V=\(\frac{EI}{(le)^3}\)(2q1+leq2+2q3+leq4)

I got this question in exam.

Question is taken from Shear Force & Bending Moment topic in division Beams and Frames of Finite Element Method

Answer 1

Right answer is (a) V=\(\frac{EI}{(le)^3}\)(2q1+leq2-2q3+leq4)

Explanation: The correct expression is given by

V=\(\frac{EI}{(le)^3}\)(2q1+leq2-2q3+leq4)

Here E is the ratio of normal stress to normal strain. Here q1, q2, q3, q4 are the four displacements at the two supported nodes of the simply supported beam.