Advanced Solid Mechanics I
<Home Assignment #3>
(Deadline: June 19, 2025)
1. (10 pt.) Two solid circular bars are joined and subjected to a load P at A, with both
ends clamped.
Figure 1. Two solid circular bars with both ends clamped.
(a) State the governing equation along with the boundary conditions
(b) Determine the displacement u(x).
(c) Sketch the axial force diagram (AFD).
2. (10 pt.) A cantilever beam is subjected to a uniformly distributed load q along its
length and a concentrated load P at the free end.
Using the Timoshenko beam theory,
(a) Derive an expression for the transverse displacement v(x).
(b) Compare the results with those obtained from Euler-Bernoulli beam theory.
Figure 2. A cantilever beam subjected to two loads.
3. (10 pt.) Consider a thin-walled rectangular cross-section beam subjected to a
torsional moment Mx.
(a) Determine the warping function by solving Saint-Venant’s torsion equation
(b) Calculate the torsional stiffness of the beam.
Figure 3. A thin section