Roll №: _____________________
Amrita Vishwa Vidyapeetham
Amrita School of Engineering, Coimbatore Campus
Department of Mechanical Engineering
23ARE202 – Mechanics of Materials
S3 ARE Tutorial 1: Simple Stress and Strain 15.07.2025
1. A hollow circular post ABC (see figure) supports a load P1 = 1700 lb acting at the top. A second load P2 is uniformly
distributed around the cap plate at B. The diameters and thicknesses of the upper and lower parts of the post are d AB
=1.25 in., tAB = 0.5 in., dBC = 2.25 in., and tBC = 0.375 in., respectively.
(a) Calculate the normal stress sAB in the upper part of the post.
(b) If it is desired that the lower part of the post have the same compressive stress as the upper part, what should be
the magnitude of the load P2?
(c) If P1 remains at 1700 lb and P2 is now set at 2260 lb, what new thickness of BC will result in the same compressive
stress in both parts?
2. A high-strength steel bar used in a large crane has diameter d = 2.00 in. (see figure). The steel has modulus of elasticity
E = 29 x106 psi and Poisson’s ratio v = 0.29. Because of clearance requirements, the diameter of the bar is limited to
2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmax that is permitted?
3. A solid bar of circular cross section (diameter d) has a hole of diameter d/5 drilled laterally through the center of the
bar (see figure). The allowable average tensile stress on the net cross section of the bar is σallow.
(a) Obtain a formula for the allowable load Pallow that the bar can carry in tension.
(b) Calculate the value of Pallow if the bar is made of brass with diameter d = 1.75 in. and σallow =12 ksi.
Page 1 of 2
Mrs. Sivaselvi K
4. Truss members supporting a roof are connected to a 26-mm-thick gusset plate by a 22-mm diameter pin as shown in
the figure and photo. The two end plates on the truss members are each 14 mm thick.
(a) If the load P = 80 kN, what is the largest bearing stress acting on the pin?
(b) If the ultimate shear stress for the pin is 190 MPa, what force Pult is required to cause the pin to fail in shear?
5. A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Eb = 14,000 ksi) and weight W = 2 kips, as
shown. The outside diameter of the pipe is dc = 6 in. (a) If the allowable compressive stress in the pipe is 5000 psi
and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness tc,min? (Include the
weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod dr due to both load
W and its own weight? (c) What is the minimum required clearance h? Given: 𝛾𝑠 = 2.836 × 10−4 𝑘/𝑖𝑛3
𝛾𝑏 = 3.009 × 10−4 𝑘/𝑖𝑛3
6. A cast-iron tube is used to support a compressive load. Knowing that E = 10 x 106 psi and that the maximum
allowable change in length is 0.025%, determine (a) the maximum normal stress in the tube, (b) the minimum
wall thickness for a load of 1600 lb if the outside diameter of the tube is 2.0 in.
Page 2 of 2
Mrs. Sivaselvi K
7. The rod ABC is made of an aluminum for which E = 70 GPa. Knowing that P = 6 kN and Q = 42 kN, determine the
deflection of (a) point A, (b) point B.
8. A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of steel ( Es =
200 GPa, s = 11.7 x 10-6 °C) and portion BC is made of brass (Eb = 200 GPa, b = 11.7 x 10-6 °C). Knowing that
the rod is initially unstressed, determine the compressive force induced in ABC when there is a temperature rise of
50°C.
9. A steel rod of 30 mm diameter is enclosed in a brass tube of 42 mm external diameter and 32 mm internal diametr.
Each is 360 mm long and the assembly is rigidly held between two stops 360 mm apart. The temperature of the
assembly is then raised by 50°C. Determine:
(a) stresses in the tube abd the rod
(b) stresses in the tube abd the rod if the stops yields by 0.15 mm
(c) yield of the stops if the force at the force at the stops is limiyed to 60 kN.
Es = 205 GPa, s = 11 x 10-6 °/C, Eb = 90 GPa, b = 19 x 10-6 /°C
Page 3 of 2
Mrs. Sivaselvi K
10. A bar, 12 mm in diameter, is acted upon by an axial load of 20 kN. The change in diameter is measured as 0.003 mm.
Determine (a) Poisson’s ratio and (b) the modulus of elastic and the bulk modulus. Take E = 80 GPa..
11. The bar shown, is tested in universal testing machine. It is observed that at a load of 40 kN the total extension of the
bar is 0.280 mm. Determine the Young’s modulus of the material.
12. An 18-m-long steel wire of 5 mm diameter is to be used in the manufacture of a prestressed concrete beam. It is
observed that the wire stretches 45 mm when a tensile force P is applied. Knowing that E = 200 GPa, determine (a)
the magnitude of the force P, (b) the corresponding normal stress in the wire.
Page 4 of 2
Mrs. Sivaselvi K
