MAE 131A
Practice Final Exam
Problem 1.
A vertical compressive force FA = 19 kN is applied at point A of the top cross section of a column
supported by the ground. For a cross section sufficiently away from the load, determine:
(a) the moments of inertia Ix and Iy of the cross section,
(b) the intercepts of the neutral axis with the x and y axes, and draw the neutral axis,
(c) the maximum tensile and compressive stresses in the section.
Problem 2.
Forces are applied at points A and B of the alloy frame as shown. (a) Determine the (i) normal force,
(ii) shear force, (iii) bending moment, and (iv) torque carried by section C. (b) For section C, draw
the diagrams of (i) normal stress due to normal force, (ii) normal stress due to bending moment,
(iii) shear stress due to torque, (iv) shear stress due to shear force, and evaluate the maximum of
each stress. (c) Compute the principal stresses for point K in section C. (d) Identify the most critical
point in section C, and compute the principle stresses for that point.
Problem 3.
A 19.5-kN force is applied at point D of the cast-iron post shown. Knowing that the post has a
diameter of 60 mm, determine the principal stresses and the maximum shearing stress at points H
and K.
Problem 4.
For the T-profile beam shown below (a) find the centroid of the cross section and (b) calculate the moment
of inertia Ix for the horizontal principle axis. Then, by applying the superposition principle and making use of
the Deflections and Slopes Table, determine (c) the reactions at A and B and (d) the deflection and slope at
C. Finally, determine the (e) maximum normal stress in the beam, and (f) the maximum shear stress at the
centroid of the cross section. The Young’s modulus of the beam is E = 50 GPa.
Problem 5.
By applying the superposition principle and making use of the deflections table below, for the
beam and loading shown in the figure, determine:
(a) the reactions at A and C,
(b) the deflection at B,
(c) the slope at B.
You are given that w = 15 kN/m, L = 1.2 m, h = 14 cm, and that the Young’s modulus of the
beam is E = 195 GPa.