Reference no: EM132505967
MIME 3130 Mechanics of Materials Assignment - IBRA College of Technology, Oman
Answer all the questions.
Q1. i) A hollow cylinder has an outside diameter of 25 cm carrying an axial load of 2.2 x 103 kN. Calculate the internal diameter of the cylinder, if stress is 120 MN/m2.
ii) A compound bar 1 m length consists of a circular rod of steel of 3 cm diameter rigidly fused into a copper tube of internal diameter 3 cm and external diameter 4.2 cm. If the compound bar is subjected to a bad of 0.1 MN, estimate the load and stresses developed in the two materials and total extension of the bar. Take Es = 2 x 105 N/mm2 and Ec = 1.2 x 105 N/mm2.
Q2. i) A steel bar which is 6 m long, 5 cm wide and 3 cm thick is subjected to an axial pull of 40 kN in the direction of its length. Take E = 2 x 105 N/mm2 and Poisson's ratio = 0.3. Calculate the different types of strains developed in the steel bar.
ii) A circular rod of diameter 3 cm and 25 cm long is subjected to a tensile force of 80 kN. If the change in length is 0.15 mm and change in diameter is 0.005 mm, compute Poisson's ratio and Young's modulus of the rod.
Q3. i) A Cantilever beam of length 3 m carries point loads of 300 N, 400 N and 800 N at 0.5 m, 2 m and 3 m respectively from the fixed end. Another point load 500 N acts at 2 m from the free end. Construct the shear force and bending moment diagrams for the Cantilever beam and also identify the point at which the maximum shear force and bending moment is acting on the beam.
ii) The principal tensile stress at a point across two mutually perpendicular planes is 80 N/mm2 and 40 N/mm2. If the tangential stresses on the oblique plane are 25 N/mm2, estimate the angle made by the oblique plane with the axis of minor principal stress using analytical method.
Q4. i) A fixed beam of rectangular cross section AB, 8 m long is carrying a point load 60 kN at its center and maximum deflection is found to be 1 cm. If the breadth of the beam is 0.2 m, calculate the depth of the beam and end moments of the beam. Take E = 2.2 x 105 N/mm2.
ii) Give a real time example of continuous beam and explain it with a simple sketch.
iii) Compute the external diameter of the 10 m length hollow steel column, if the external diameter is two times the internal diameter. The safe load on steel column with both the ends hinged is 100 kN with factor of safety 3. Use Euler's formula and take E = 120 kN/mm2.
Q5. i) A wooden beam 5 m long, simply supported at its ends, is carrying a point load of 8 kN at its centre. The cross-section of the beam is 160 mm wide and 270 mm deep. If E for the beam is 70 x 109 N/m2, calculate the deflection at the center.
ii) A timber beam with a span of 4 m and 175 mm deep induces maximum bending stress 100 N/mm2. The beam is carrying a uniformly distributed load of 3.2 kN/m runs over the entire length. Compute the width of the beam.