Which of the following equations is the correct expression for bending moment (M) in an element, given the modulus of elasticity (E), moment of inertia (I), element length (le), shape function (ξ) and displacement (q) in a uniformly distributed load on a simply supported beam?

(a) M=\(\frac{EI}{(le)^2}\)[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]

(b) M=\(\frac{EI}{(le)^3}\)[6ξq1-(3ξ-1)leq2-6ξq3-(3ξ+1)leq4]

(c) M=\(\frac{EI}{(le)^2}\)[6ξq1+(3ξ-1)leq2-6ξq3-(3ξ+1)leq4]

(d) M=\(\frac{EI}{(le)^3}\)[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]

The question was posed to me in my homework.

My question comes from Shear Force & Bending Moment in chapter Beams and Frames of Finite Element Method