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1. Axial Loading 01
Practice Session
Strength OF Material
Lamiya Naseem

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13. Q1. Find the ratio of loads shared by parts ‘AB’ and ‘BC’ of the bar
shown below.
A B C
2L/3 L/3

14. Q2. ABC is a rigid bar. It is hinged at ‘A’ and supported at ‘B’ and ‘C’
by two wires ‘BD’ and ‘CE’ made of copper and steel respectively. The
bar carries a load of 1 t at ‘F’ midway between ‘B’ and ‘C’.
Given:
𝐀𝐜 = 𝟒 𝐜𝐦𝟐; 𝐀𝐬 = 𝟐 𝐜𝐦𝟐 𝐄𝐜 = 𝟏 × 𝟏𝟎𝟓 𝐍/𝐦𝐦𝟐; 𝐄𝐬 = 𝟏 × 𝟏𝟎𝟓 𝐍/𝐦𝐦𝟐
Determine the ratio of forces in copper and steel wires.
A B C
1 m 1 m
1 t
E
F
D

15. Q3. A steel rod of cross sectional area 2000 mm2 and two brass rods
each of 1000 mm2 together support a load 10 kN. Es = 2 x 105 MPa; Eb =
1 x 105 MPa. Find the stresses developed due to 10 kN in steel and
brass in MPa are respectively.
600 mm
Steel Brass
300 mm
10 kN

16. Q4. A mild steel rod of 20 mm diameter and 300 mm long is
centrally enclosed inside a copper tube of same length and having
external diameter 30 mm and internal diameter 25 mm. The ends
are brazed together. The composite bar is subjected to an external
tensile force of 40 kN. Es = 200 GPa; Ec = 100 GPa
Determine:
(i) The stresses developed in steel and copper respectively in
MPa.
(ii) The extension of composite bar in mm.

17. Q5. Two vertical wires are supported at a distance of 50 cm apart
as shown in figure below. Their upper ends are firmly secured and
their lower ends support a rigid horizontal bar which carries a load
W. The left hand wire has a diameter of 1.5 mm and is made of
copper and the right hand wire has a diameter of 1.0 mm and is
made of steel. Both wires initially are 4.5 m long. Determine
(a) The position of line of action of W if, due to W, both wires extend
by the same amount and
(b) The slope of the rigid bar if a load of 200 N is hung at the center
of the bar.
Copper 1.5 mm f
W
x
50 cm
4.5 m
Steel 1 mm f
Rigid beam

18. Q6. In the arrangement as shown in the figure, the stepped steel
bar ABC is loaded by a load P. The material has Young’s modulus E
= 200 GPa and the two portions AB and BC have area of cross
section 1 cm2 and 2 cm2 respectively. The magnitude of load P
required to fill up the gap of 0.75 mm is :
(a) 10 kN
(b) 15 kN
(c) 20 kN
(d) 25 kN
A
B
C
1 m
Gap 0.75 mm
1 m
P

19. Q7. A rod of length L, area of cross section A, density r and
modulus of elasticity E hangs vertically from a roof. The maximum
longitudinal strain in the rod is
(a) 0
(b) rgL/2E
(c) rgL/E
(d) 2rgL/E

20. Q8. A sphere of 80 mm diameter lies at a depth of 500 m in sea
water. The bulk modulus of sphere is 200 GPa. The specific weight
of sea water is 10.3 kN/m3. Find the decrease in the volume of the
sphere.
(a) 4.2 mm3
(b) 5.6 mm3
(c) 6.2 mm3
(d) 6.9 mm3

21. Q9. A steel tie bar of section area 125 mm2 supporting a timber
beam. The moment of inertia of the beam section is 1.95 x 108 mm4.
Find the axial force in the bar. Total weight of the section is 45 kN.
Modulus of elasticity for steel = 2 x 105 N/mm2 and modulus of
elasticity for timber 13750 N/mm2.
(a) 25.92 kN
(b) 28.43 kN
(c) 34.99 kN
(d) 36.63 kN

22. Q10. A flat steel plate is of trapezoidal form. The thickness of the
plate is 15 mm and it tapers uniformly form a width of 60 mm to a
width of 10 mm in a length of 300 mm. Determine the elongation of
the plate under an axial force of 120 kN. Take E = 2.04 x 105 N/mm2.
(a) 0.422 mm
(b) 0.453 mm
(c) 0.478 mm
(d) 0.493 mm

23. Q11. A sphere of 100 mm diameter is immersed to a depth of 1000
m in sea water. The unit weight of sea water is 1.025 g/cc. The
modulus of elasticity is 2 x 105 N/mm2 and modulus of rigidity is 0.8
x 105 N/mm2. The change in volume of sphere is
(a) 20.42 mm3
(b) 40.25 mm3
(c) 58.32 mm3
(d) 62.83 mm3

24. Q12. The following stress strain diagram is obtained for a material.
It indicates
(a) rigid body behavior
(b) perfectly plastic behavior
(c) elastic-linear strain hardening behavior
(d) elastic-plastic behavior
sy
s
e

26. Thank You!