Mechanics of Solids
Tutorial-I
(Problems On Unit-I)
Problems on Uniform cross-section of Bar:
1. A circular rod of diameter 20 mm and 500 mm long is subjected to a tensile force of 45 KN.
the modulus of elasticity for the material is 2.1x105 N/mm2. Find the stress, strain & the
elongation (change in length) and the change in volume of circular rod. µ = 0.25
2. A tensile test is performed on a brass specimen 10mm in diameter using a gauge length of
50mm when applying axial tensile load of 25KN it is observed that the distance between the
gauge mark increased by 0.152mm. calculate modulus of elasticity of brass.
3. A tensile test was conducted on a mild steel bar. The following data was obtained from the
test: (i) Diameter of the steel bar = 4 cm (ii) Gauge length of the bar = 22 cm (iii) Load at
elastic limit = 250 kN (iv) Extension at a load of 160 kN = 0.235 mm (v) Maximum load = 390
kN (vi) Total extension = 70 mm (vii) Diameter of rod at failure = 2.35 cm
Determine the Young’s modulus, the stress at elastic limit, the percentage of elongation &
the percentage decrease in area.
Problems on Tapered cross-section of Bar:
4. A circular alloy bar 2m long uniformly tapers from 30mm diameter to 20mm diameter.
Calculate the elongation of the rod under the axial force of 50kN. Take E=140GPa
Problems on Varying cross-section/varying Loads of Bar:
5. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown in figure. If
the Young’s modulus is taken as 2.1x105 N/mm2, Determine: (i) Stresses in each section and
(ii) Total extension of the bar.
6. A brass bar, having cross-sectional area of 1000 mm2, is subjected to axial forces as shown in
figure. Find the total elongation of the bar. Take E=1.05x105 N/mm2
7. A member ABCD is subjected to point loads P1, P2, P3 and P4 as shown. Find P2 required for
necessary equilibrium, if P1 = 45kN, P3 = 450kN and P4=130kN. Determine the total
elongation of the member.
Problems on relation between Elastic constants:
8. Determine the Poisson’s ratio and bulk modulus of a material for which young’s modulus is
1.2 x 105 N/mm2 and modulus of rigidity is 4.8 x 104 N/mm2.
9. A bar of 30mm dia.is subjected to a pull of 60KN.The measured extension is 0.09mm and
gauge length of 200mm and change in diameter is 0. 0039mm. calculate a) Poisson’s ratio b)
Young’s modulus c) Bulk Modulus d) Rigidity Modulus
10. The Young’s modulus for a given material is 100Kn/mm^2 and its modulus of rigidity is 40
KN/mm2. Determine its bulk modulus and its lateral contraction if the diameter is 50mm and
length is 2m and extension is 2mm.
Problems on Thermal Stresses of Bar:
11. A brass rod 2m long is fixed at both its ends. If the thermal stress is not to exceed 76.5
N/mm2. Calculate the temperature through which the rod should be heated. Take the values
of α= 17x10-6 /°K and E =90Gpa
12. A steel rod of 3 cm diameter and 5 m long is connected to two grips and the rod is
maintained at temperature of 95°C. Determine the stress and pull exerted when the
temperature falls to 30°C, if (i) The ends do not yield, and (ii) The ends yield by 0.12 cm.
Take E=2x105 N/mm2 and α=12x10-6/°C.
Problems on Composite/Compound Bars:
13. A steel rod of 3 cm diameter is enclosed centrally in a hollow copper tube of external
diameter 5cm and internal diameter of 4cm. the composite bar is then subjected to an axial
pull of 45000N.if the length of each bar is equal to 15 cm, determine: i) The stresses in the
rod and tube, and (ii) Load carried by each bar.
14. Three bars made of copper, zinc and aluminium are of equal length and have cross section
555, 705, and 1020 sq.mm respectively. They are rigidly connected at their ends. If this
compound member is subjected to a longitudinal pull of 255kN, estimate the proportional
of the load carried on each rod and the induced stresses. Take the value of E for copper =
1.3×10 5 N/mm2, for zinc = 1×105 N/mm2 and for aluminium = 0.8×105 N/mm2.
15. A steel tube of 30mm external diameter and 20mm internal diameter encloses a copper rod
of 15.5mm diameter to which it is rigidly joined at each end. If, at a temperature of 10°C
there is no longitudinal stress, calculate the stresses in the rod and the tube when the
temperature is raised to 200°C. Take Es = 2.1x105 N/mm2 and Ec = 1x105 N/mm2 Co-efficient
of linear expansion 11x10-6/°C and 18x10-6/°C
Problems on Principle stresses and Principal Planes using Analytical
Method:
16. The tensile stresses at a point across two mutually perpendicular planes are 120 N/mm2 and
60 N/mm2. determine the normal, tangential and resultant stresses on a plane incline at 30°
to the axis of the minor stress.
17. The stresses at a point in a bar are 200 N/mm2 (tensile) and 100 N/mm2 (compressive).
determine the resultant stress in magnitude and direction on a plane inclined at 60° to the
axis of the major stress. Also determine the maximum intensity of shear stress in the
material at the point.
18. An elemental cube is subjected to tensile stresses of 30 N/mm2 and 10 N/mm2 acting on
two mutually perpendicular planes and a shear stress of 10 N/mm2 on these planes.
determine the magnitudes and directions of principal stresses and the greatest shear stress.
19. Direct stresses of 120 N/mm2 tensile and 90 N/mm2 compressive exist on two perpendicular
planes at a certain point in a body. They are also accompanied by shear stress on the planes.
The greatest principal stress at a point due to these is 150 N/mm2. i) What must be the
magnitude of shearing stresses on the two planes? ii) What will be the maximum shearing
stress at the point?
Problems on Principle stresses and Principal Planes using Graphical
Method (Mohr’s Circle):
20. The tensile stresses at a point across two mutually perpendicular planes are 120 N/mm2 and
60 N/mm2. Using Mohr’s circle method determine the normal, tangential and resultant
stresses on a plane incline at 30° to the axis of the minor stress.
21. The stresses at a point in a bar are 200 N/mm2 (tensile) and 100 N/mm2 (compressive). Use
Mohr’s Circle; determine the resultant stress in magnitude and direction on a plane inclined
at 60° to the axis of the major stress. Also determine the maximum intensity of shear stress
in the material at the point.
22. An elemental cube is subjected to tensile stresses of 30 N/mm2 and 10 N/mm2 acting on
two mutually perpendicular planes and a shear stress of 10 N/mm2 on these planes. Draw
the Mohr’s circle of stresses and determine the magnitudes and directions of principal
stresses and the greatest shear stress.
