Strength of Materials
Assignment 2
1- The beam, ABC, show in Figure 1, is 2 m long and is simply supported at either ends and carries a
uniformly distributed load of 8 kN/m over the span, BC. The flexural rigidity of the beam EI, is 4 x
104 Nm2. Using Castigliano’s theorem determine:
(a) The deflexion at position B
(b) The slope at position B
8 kN/m
A B C
1.2 m
2m
Figure 1
2- For the structure shown in Figure 2, each member has a modulus of elasticity E and area A, the
length of the member BC and CD is L.
(a) Determine the total strain energy in the structure.
(b) Using the work energy approach, determine the vertical deflection of point C.
(c) Using any energy approach, determine the deflection of point D.
L L
45o 45o
B L D
L√2
Figure 2
3- A composite consists of 40 % continuous E-glass fibres aligned in an epoxy matrix. If the elastic
moduli of the glass and epoxy are 76 and 2.7 GPa, calculate the composite modulus:
(a) Parallel to the fibre axis.
(b) Perpendicular to the fibre axis.
4- Determine the nodal displacements, support reactions and element stresses for the loaded bar
shown below.
E= 200 GPa A1= 350 mm2
A2= 700 mm2 P= 500 kN
T= f= 0
A2
A1
1 2 P 4
3 5
150 mm 150 mm 150 mm 150 mm
5- An alloy Steel bar 1500 long and 2500 mm 2 in cross-sectional area is subjected to an axial tensile
load of 8.9 kN at an operating temperature of 600 oC. Determine the value of the creep
elongation in 10 years using the relationship ε =β σ n if, for 600 oC, β = 26 x 10-12 hr-1 (N/mm)-6,
and n= 6.0
6- When subjected to fatigue under a Δ σ=140 MPa , and alloyed showed a following fatigue
crack propagation relationship
da
(m
dN cycle )
=0.66 ×10−8 ( ∆ K )2.25,where ∆ K is in MPa m ½.
Estimate the number of cycles required for the crack to grow from 2 mm to 8.8 mm. assume
K ic =1.12 σ √ πa
