Question

From the Euler-Bernoulli beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1^st element of the stiffness matrix?

(a) \(\frac{12EI}{h^3}\)

(b) \(\frac{12EA}{h^3}\)

(c) \(\frac{12EA}{h}\)

(d) \(\frac{12AI}{h^3}\)

This question was posed to me during an internship interview.

Origin of the question is Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

Answer 1

Right option is (a) \(\frac{12EI}{h^3}\)

Explanation: In the formulation of the Euler-Bernoulli beam theory, there are two degrees of freedom at a point, w and \(\frac{dw}{dx}\). Typically, the finite element model of this theory uses cubic polynomial. The first element of the stiffness matrix is \(\frac{12EI}{h^3}\), where E is Young’s modulus, I is the area moment of inertia and h is the length of the element.