SMTL 246 Strength of Materials
Assignment #1
Due date: As shown in Brightspace
Submit complete solutions for the following questions. Show all calculations and underline or
highlight intermediate and final answers. Include FBDs when required. Marks are awarded for
work shown.
1. Two solid cylindrical rods support a load of P = 27 kN as shown in Figure below. Rod (1)
has a diameter of 16 mm and the diameter of rod (2) is 12 mm. Determine the axial
stress in each rod.
2. The steel pipe column shown in the following Figure has an outside diameter of 8.625
in. and a wall thickness of 0.25 in. The timber beam is 10.75 in. wide, and the upper
plate has the same width. The load imposed on the column by the timber beam is 80
kips. Determine:
a. The average bearing stress at the surfaces between the pipe column and the
upper and lower steel bearing plates.
b. The length L of the rectangular upper bearing plate if its width is 10.75 in. and
the average bearing stress between the steel plate and the wood beam is not to
exceed 500 psi.
c. The dimension a of the square lower bearing plate if the average bearing stress
between the lower bearing plate and the concrete slab is not to exceed 900 psi.
3. A rigid bar ABCD is supported by two bars as shown in Figure below. There is no strain in
the vertical bars before load P is applied. After load P is applied, the normal strain in bar
(1) is 570 μm/m. Determine:
a. The normal strain in bar (2).
b. The normal strain in bar (2) if there is a 1 mm gap in the connection at pin C
before the load is applied.
c. The normal strain in bar (2) if there is a 1 mm gap in the connection at pin B
before the load is applied.
4. A rigid steel bar is supported by three rods as shown in Figure below. There is no strain
in the rods before the load P is applied. After load P is applied, the normal strain in rod
(2) is 1,080 μin./in. Assume initial rod lengths of L1 = 130 in. and L2 = 75 in. Determine:
a. The normal strain in rods (1).
b. The normal strain in rods (1) if there is 1/32 in. gap in the connections between
the rigid bar and rods (1) at joints A and C before the load is applied.
c. The normal strain in rods (1) if there is a 1/32 in. gap in the connection between
the rigid bar and rod (2) at joint B before the load is applied.