Punjab Engineering College (Deemed to be University)

Assignment No.- 1
Strength of Materials (ES2306)
Semester - 2024-25-01

1. A tensile test was conducted on a molested rod. The following data was obtained from the test:
diameter of bar is 16 mm, gauge length of bar is 50mm, load at proportionality limit is 48.5 kN,
Extension at the proportionality limit is 0.05 mm, load at yield point is 50.3 KN, ultimate load is 90KN,
final length between gauge points is 64 mm, diameter of the neck at fracture is 13.7 mm. Determine
the Young’s modulus at elastic limit, yield stress, ultimate stress, % elongation and % reduction in
area.

2. A bar of 20mm diameter is tested in tension. It is observed that when a load of 40 KN is applied the
extension measured over a gauge length of 200 mm is 0.12 mm & contraction in diameter is 0.0036
mm. Find Poisson’s ratio, young’s modulus, bulk modulus and rigidity modulus.

3. A circular brass bar of 12 mm diameter is tested under tension. If the increase in the gauge length of
100 mm is 0.12 mm, determine the stress developed in the bar. What is the change in the diameter?

4. A metallic bar 300 mm×100 mm × 40 mm is subjected to a force of 5KN, 6KN, 4 KN, 4 KN along x,y,
z direction respectively. Determine the change in volume if the young’s modulus is 2×10 5 MPa. Take
Poisson ratio as 0.25.

5. A vertical circular bar150 cm high is subjected to a uniform stress of 26kg/cm2 throughout its length.
The diameter at the bottom edge is 6 cm, determine the diameter at the top edge if it is fixed in the
ceiling. Given the weight density =0.0078 kg/cm3.

6. A metallic structure consists of steel and aluminium as shown in figure 1. Determine the compressive
load P when the steel bar having length 30cm and aluminium bar having 38 cm length. Take Young’s
modulus value for steel 2.1x105 N/mm2 & foraluminium7x104N/mm2.Also area of cross section of
steel is 5 cm x 5 cm and area of aluminium is 10 cm x 10 cm. Change in length is 0.25 mm.

Fig 1
 7. A solid circular shaft of diameter 120 mm has a collar of 20 mm thickness as shown in Fig. 2 below.
The shaft is subjected to a compressive force of 250kN. Determine (i) Compressive stress developed
in the shaft. (ii) Shear stress developed in collar section.

8. A steel rod of 3cm diameter risen closed in a hollow copper tube of external diameter 5cm and
internal diameter 4cm.The composite bar is then subjected to axial pull of 45000 N. If the length of
each bar is equal to 15 cm determine (i) the stresses in the rod and load carried by each bar. Take
Young’s modulus value for steel 2.1 x 105 N/mm2 & for copper 1.1x 105 N/mm2.

9. A stepped circular bar having diameters 20 mm, 15 mm and 10 mm over axial lengths of 100 mm,
80mm and 60mm is subjected to an axial tensile force of 5KN. If E=100x103 N/mm2 and 1/m=0.32 for
the material of bar, determine total change in length and change in each diameter.

10. Compare the strain energy absorbed by the bars A and B as shown in Fig3. Bar A of length L having
diameter d at one end and uniformly increasing to the other end is subjected to compressive force P.
Bar B of the same material, but as tepped bar of diameter d for half of its length and diameter D of
the remaining half of its length is subjected to the same compressive force P. Given d=0.6 D.

11. A specimen of an aluminium alloy 1·2 cm in diameter was tested under tension. The linear strains
parallel to the application of the force P and the lateral strains measured with the help of strain
gauge, were as follows:
P( kg) 400 800 1200 1600 2000 2400 2800 3200 3400 3600 3700 3800 3900 3950
Linear
strain
0.343 0.692 1.03 1.39 1.72 2.07 2.40 2.734 3.53 4.30 4.90 5.65 6.95 8.40
ϵ1 (1x
10-3)
Lateral
strain
0.108 0.217 0.322 0.435 0.541 0.650 0.754 0.857 - - - - - -
ϵ2 (1x
10-3)
Plot the graphs:
(i) P Vs ϵ1 (ii) ϵ1 Vs ϵ2

and determine (a) Young's modulus of elasticity,(b) Poisson's ratio, and (c) 0·1%Proof stress.

12. A flat steel bar 20mm x 8mm is placed between two aluminium alloy bars 20mm x 6mm each, so as
to form a composite bar of section 20mm x 20mm. The three bars are fastened together at their ends
when the temperature of each is 75°F. Find the stress in each when the temperature of the whole
assembly is raised to125°F. Determine the temperature stresses developed in the steel and aluminium
alloy bars.

13. A 10 mm diameter-steel rod passes centrally through a copper tube 25mm external diameter and 15
mm internal diameter and 2·5m long. The tube is closed at each end by thick steel plates secured by
nuts. The nuts are tightened until the copper tube is reduced in length by 0.6mm.The whole
assembly is then raised in temperature by 20°C. Calculate the stresses in the steel rod and copper
tube before and after the rise in temperature. The thickness of the end plates remains unchanged.
Esteel=208000 N/mm2 , E copper= 104000 N/mm2, αs= 12 X 10-6/°C, αc= 17.5 X 10-6/°C.

14. A rigid bar EF 3m long is supported by two wires AB and CD as shown in the Fig 4.Wire AB is of steel,
2m long and 6mm in diameter. Wire CD is of brass,1·4m long and 5mm in diameter. The bar carries a
vertical load of 1·6kN at the end F and end E is hinged. Determine the stresses in steel and brass
wires. ES= 2EB=210 x 1000 N/mm2.

Fig4
15. Two aluminium bars and a brass bar support a load of 50 kN as shown in Figure 5.Due to an
error in fabrication, the brass bar is 0.2 mm shorter than required. Find the stresses in the
bars when a load of 50 kN is applied. Eal, = 70 GPa and Eb = 105 GPa.
 Fig5

16. A steel tie rod 20 mm diameter is encased in a copper tube of external diameter 36 mm and internal
diameter 24mm with the help of washers and nuts. The nut on the tie rod is tightened so as to
produce a tensile stress of 400kg/cm2 in steel rod. This combination is subjected to a tensile load of 2
tonnes.
Determine the resultant stresses in steel rod and the copper tube, if
a. Es= 2Ec= 2100 tonnes/cm2.
b. Now if the temperature of the assembly is raised by 80°C, determine the resultant
-6 -6
stressesdeveloped in the rod and the tube. Take αs= 12 X 10 /°C, αc= 17.5 X 10 /°C.
17. A steel rod15m long is at a temperature of15oC.Find the free expansion of the length when the
temperature is raised to 65oC.Find the temperature stress produced when:
a) The expansion of the rod is prevented
b) The rod is permitted to expand by 6mm.
α=12*10 -6 per oC and E = 200 GN/mm 2