CIVL2001 Mechanics of Materials
1st Semester 2025/26
Assignment 4
Name:______________________
Student No.:_________________
Date: 16th October, 2025
1. Using an allowable stress of 155 MPa, determine the largest bending moment M that can
be applied to the wide-flange beam shown. Neglect the effect of fillets.
Figure 1
Figure 3
2. Two vertical forces are applied to a beam of the cross section shown. Determine the
maximum tensile and compressive stresses in portion BC of the beam.
Figure 2
3. A couple M will be applied to a beam of rectangular cross section which is to be sawed
from a log of circular cross section. Determine the ratio d/b, for which (a) the maximum
stress 𝜎𝑚 will be as small as possible, (b) the radius of curvature of the beam will be
maximum.
4. A copper strip (𝐸𝑐 =105GPa) and an aluminum strip (𝐸𝑎 =75GPa) are bonded together to
form the composite beam shown. Knowing that the beam is bent about a horizontal axis by
a couple of moment M=35 𝑁 ∙ 𝑚, determine the maximum stress in (a) the aluminum strip,
(b) the copper strip.
5. A steel bar (𝐸𝑠 =210 GPa) and an aluminum bar (𝐸𝑎 =105GPa) are bonded together to form
the composite bar shown. Determine the maximum stress in (a) the aluminum, (b) the steel,
when the bar is bent about a horizontal axis, with M=60 𝑁 ∙ 𝑚.
Figure 4
Figure 5
6. The reinforced concrete beam shown is subjected to a positive bending moment of 175 𝑘𝑁 ∙
𝑚. Knowing that the modulus of elasticity is 25 GPa for the concrete and 200 GPa for the
steel, determine (a) the stress in the steel, (b) the maximum stress in the concrete.
125 mm
750 mm
25 mm
600 mm
60 mm
300 mm
Figure 6
Figure 7
7. Knowing that the bending moment in the reinforced concrete beam is +200 k𝑁 ∙ 𝑚 and that
the modulus of elasticity is 25 GPa for the concrete and 200 GPa for the steel, determine
(a) the stress in the steel, (b) the maximum stress in the concrete.
8. The four forces shown are applied to a rigid plate supported by a solid steel post of radius
a. Knowing that P=100 kN and a=40mm, determine the maximum stress in the post when
(a) the force at D is removed, (b) the forces at C and D are removed.
100 mm
100 mm
Figure 8
Figure 9
9. In order to provide access to the interior of a hollow square tube of 6-mm wall thickness,
the portion CD of the side of the tube has been removed. Knowing that the loading of the
tube is equivalent to two equal and opposite 60-kN forces acting at the geometric centers
A and E of the ends of the tube, determine (a) the maximum stress in section a-a, (b) the
stress at point F. Given: the centroid of the cross section is at C and 𝐼𝑧 = 2 × 106 𝑚𝑚4 .
10. A beam having the cross section shown is subjected to a couple 𝑀0 that acts in a vertical
plane. Determine the largest permissible value of the moment 𝑀0 of the couple if the
maximum stress in the beam is not to exceed 84 MPa. Given: 𝐼𝑦 = 𝐼𝑧 = 4.7 × 106 𝑚𝑚4,
𝐴 = 3064 𝑚𝑚2 , 𝑘𝑚𝑖𝑛 = 25 𝑚𝑚. (Hint: By reason of symmetry, the principal axes form
2
an angle of 45° with the coordinate axes. Use the relations 𝐼𝑚𝑖𝑛 = 𝐴 𝑘𝑚𝑖𝑛
and 𝐼𝑚𝑖𝑛 +
𝐼𝑚𝑎𝑥 = 𝐼𝑦 + 𝐼𝑧 ).
Figure 10