+2 votes
in Finite Element Method by (110k points)
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

1 Answer

+2 votes
by (185k points)
selected by
Best answer
Right answer is (a) M=\(\frac{EI}{(le)^2}\)[6ξq1+(3ξ-1)leq2-6ξq3+(3ξ+1)leq4]

Explanation: The correct expression is given by


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. The value of shape function (ξ) varies between -1 to +1.

Related questions

We welcome you to Carrieradda QnA with open heart. Our small community of enthusiastic learners are very helpful and supportive. Here on this platform you can ask questions and receive answers from other members of the community. We also monitor posted questions and answers periodically to maintain the quality and integrity of the platform. Hope you will join our beautiful community