Indian institute of technology ,Jammu
Mechanics of solids
Tutorial 1
1. A vertical rod tapers uniformly from a diameter of 65 mm at the top to 35 mm at the bottom. It is
rigidly fixed at the upper end and is subjected to an axial load of 25 kN. If its length is 2.5 m determine
the total extension in the bar.
Take density of material = 2 × 105 kg/m3 and Young’s modulus = 210 GN/m2.
2. A concrete cylinder of diameter 150 mm and length 300 mm when subjected to an axial compressive
load of 240 kN resulted in an increase of diameter by 0.127 mm and a decrease in length of 0.28 mm.
Compute the value of Poisson’s ratio μ and modulus of elasticity E.
3. A straight uniform bar AD is clamped at both ends and loaded as shown in Fig. Initially the bar is
stress free. Determine the stresses in all the three parts (AB, BC, CD) of the bar if the cross-sectional
area of bar is 1000 mm2
4. A brass bar having cross-sectional area of 1000 mm2 is subjected to axial forces shown in the Fig.
Find the total elongation of the bar. Modulus of elasticity of brass = 100 GN/m2.
5. A rigid bar is supported by three rods in the same vertical plane and equidistant. The outer rods are
of brass and of length 600 mm and diameter 30 mm. The central rod is of steel of 900 mm length and
of 37.5 mm diameter. Calculate the forces in the bars due to an applied force P, if the bar remains
horizontal after the load has been applied. Take E s/ Eb=2.
6. A cylindrical bar has a length L = 5 m and cross section area S = 10 m² The bar is made of a linear
elastic material with a density p = 2700 kg/m³ and Young's modulus E = 70 GPa. The bar is suspended
as shown in the figure and is in a state of uniaxial tension due to its self-weight. Calculate the elastic
strain energy stored in the bar. Take g=9.8m/s2 .
7. A steel bar is placed between two copper bars each having the same area and length as the steel bar at
15°C. At this stage, they are rigidly connected together at both the ends. When the temperature is raised
to 315°C, the length of the bars increases by 1.5 mm. Determine the original length and final stresses
in the bar. Take E, = 210 GN/m². E = 110 GN/m²: as=0.000012 per °C: ac=0.0000175 per °C.
8. A steel tie rod 50 mm in diameter and 2.5 m long is subjected to a pull of 100 kN. To what length the
rod should be bored centrally so that the total extension will increase by 15 percent under the same
pull, the bore being 25 mm diameter? Take E = 200 GN / m2.
9. Two parallel steel wires 6 m long, 10 mm diameter are hung vertically 70 mm apart and support a
horizontal bar at their lower ends. When a load of 9 kN is attached to one of the wires, it is observed
that the bar is 2.4° to the horizontal. Find ‘E’ for wire.
10. If a tension test bar is found to taper uniformly from (D – a) to (D + a), prove that the error involved
in using the mean diameter to calculate Young’s modulus is (10a/D)2 per cent.
