Strength of Materials and Structural Analysis — Practice

Question 1

A steel bar of length 2 m and area 500 mm2 carries 100 kN with E = 200 GPa. Find its elongation.

Accepted Answer

delta = PL/AE = (100e3 x 2)/(500e-6 x 200e9) = 2 mm.

Question 2

State the maximum deflection of a cantilever with a point load P at the free end.

Accepted Answer

PL^3 / 3EI.

Question 3

A column with both ends fixed has length 4 m. Find its effective length and compare its buckling load with the same column hinged at both ends.

Accepted Answer

Le = L/2 = 2 m. The load varies as 1/Le^2, so the fixed column carries (4/2)^2 = 4 times the load of the hinged one.

Question 4

A simply supported beam of span 6 m has a central load of 20 kN. Section modulus is 400 cm3. Find the maximum bending stress.

Accepted Answer

M = PL/4 = 20 x 6/4 = 30 kN m. sigma = M/Z = 30e6 N mm / 400e3 mm3 = 75 N/mm2.

Question 5

A plane stress state has sigma x = 80 MPa, sigma y = 20 MPa and tau xy = 40 MPa. Find the principal stresses and maximum shear stress.

Accepted Answer

Centre 50 MPa, radius sqrt(30^2 + 40^2) = 50. sigma1 = 100 MPa, sigma2 = 0, and maximum shear = 50 MPa.

Question 6

State the fixed-end moments for a fixed beam of span L with a UDL w and with a central point load P.

Accepted Answer

UDL: wL^2/12 at each end. Central point load: PL/8 at each end.

Question 7

A plane truss has 10 members, 3 reaction components and 6 joints. Is it determinate?

Accepted Answer

m + r = 13 and 2j = 12, so it is indeterminate to the first degree.

Question 8

Why is a hollow shaft more efficient than a solid one of the same weight?

Accepted Answer

Material near the axis is lightly stressed, so moving it outwards raises the polar moment for the same mass.

Practice — Strength of Materials and Structural Analysis