Mechanics Of Material (ASE 1004) Assignment-1 PDF

Mechanics of Material (ASE 1004) Assignment-1 1. A member LMNP is subjected to point loads as shown in Figure-1. Calculate (i) Force P necessary for equilibrium. (ii) Total elongation of the bar. Take E = 210 GN/m2. 2. A straight uniform bar AD is clamp...

Mechanics of Material (ASE 1004) Assignment-1 1. A member LMNP is subjected to point loads as shown in Figure-1. Calculate (i) Force P necessary for equilibrium. (ii) Total elongation of the bar. Take E = 210 GN/m2. 2. A straight uniform bar AD is clamped at both ends and loaded as shown in Figure-2. 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 the bar is 1000 mm2. 3. A 700 mm length of aluminium alloy bar is suspended from the ceiling so as to provide a clearance of 0.3 mm between it and a 250 mm length of steel bar as shown in Figure-3. Aal = 1250 mm2, Eal = 70 GN/m2, As= 2500 mm2, Es = 210 GN/m2. Determine the stress in the aluminium and in the steel due to 300 kN load applied 500 mm from the ceiling. 4. A solid steel cylinder 500 mm long and 70 mm diameter is placed inside an aluminium cylinder having 75 mm inside diameter and 100 mm outside diameter. The aluminium cylinder is 0.16 mm longer than the steel cylinder. An axial load of 500 kN is applied to the bar and cylinder through rigid cover plates as shown in Figure-4. Find the stresses developed in the steel cylinder and aluminium tube. Assume for steel E = 220 GN/m2 and for aluminium, E = 70 GN/m2. 5. Refer figure given below for the tapering bar of circular cross-section which is subjected to point loads as shown. The section AB has a uniform diameter of 60 mm and for the section CD, the uniform diameter is 30 mm. Determine load P3 for equilibrium and net change in length of bar. Take modulus of elasticity of the bar material as E = 200 GPa. P1 = 150 kN P2 = 275 kN P3 P4 = 100 kN C D A B 200 mm 300 mm 150 mm 6. Figure shows a circular steel rod supported in a recess and surrounded by coaxial brass tubes. The upper end of the rod is 0.1 mm below that that of the tube and an axial load is applied to a rigid plate resting on the top of the tube. Calculate the following: I. The magnitude of the permissible load if the compressive stress in the rod is not to exceed 110 MN/m2 and that in tube is not to exceed 80 MN/m2. II. The amount by which the tube will be shortened by the load if the compressive stress in the tube is same as the rod. Take Esteel= 200 GN/m2 & Ebrass= 100 GN/m2. 7. A copper bar 250 mm long and 50 mmx 50mm in cross-section is subjected to an axial pull in the direction of its length. If the increase in volume of the bar is 37.5 mm3, find the magnitude of the pull. Take poisons ratio = 0.25 and E = 100 GPa. 8. Two wires, one of steel and the other of copper are of the same length and are subjected to the same tension. If the diameter of the copper wire is 2mm, find the diameter of the steel wire, if they are elongated by the same amount. Take Es = 200 GPa and EC = 100 GPa. 9. The modulus of rigidity of a material is 0.8 x 106 kg/cm2. When a 6mm x 6 mm rod of this material was subjected to an axial pull of 350 kg, it was found that the material dimensions of the rod changed to 5.9991 mm x 5.9991 mm. Find the poisons ratio and the modulus of elasticity. 10. A steel bar 50 mm in diameter and 2 m long is surrounded by a shell of a cast iron 5 mm thick. Compute the load that will compress the combined bar a total of 0/8 mm in the length of 2 m. Take Es = 200 GPa and ECI = 100 GPa. 11. The rigid bar AB and CD as shown are supported by pins at A and C and the two rods. Determine the maximum force P that can be applied as shown if its vertical movement is limited to 5 mm. neglect the weighs of all members.