AAE 221 – Structures II – Spring 2004
Chapter 3.2 – Analytical solutions of static problems using energy methods
1.
Consider the beam problem illustrated in fig. 1.
fig. 1
The beam is homogenous and symmetric, has length L, a moment of inertia I and a
Young’s modulus E.
To simplify your computations, write the stiffness K of the
rotational spring as
L
EI
K
a
=
where alpha is a nondimensional parameter.
(a) Obtain the beam deflection using EulerBernoulli beam theory.
How does the
deflection at the free end of the beam change when the length of the beam is doubled
(assuming that
a
remains constant)?
(b) Obtain the deflection at the free end of the beam using Castigliano’s second theorem.
Compare with the solution found in (a).
(c) Plot (schematically) the variation of the displacement of the end of the beam with
respect to the parameter
a.
What happens when the stiffness of the torsional element
tends to infinity?
What about when
a
tends to zero?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 Lambros
 EulerBernoulli beam theory

Click to edit the document details