Q1. A shell is fired with a velocity of 420 m/sec at 40° above the horizontal from a point at the foot of a slope inclined at 12° above the horizontal. Calculate the range of the shell, as measured along the slope.
Q2. A load of 3 tonne resting on tapered block A is to be raised using two identical wedges B and C as shown in Fig Q4. The coefficient of friction between the wedges and block A is 0.3 and between the wedges and the ground is 0.4. The load on each wedge can be assumed to remain equal.
Calculate the horizontal force ‘P’ required at each wedge.
Q3. A propeller shaft is designed to be solid with a diameter of 280 mm. It is then decided to replace this shaft with a hollow shaft of 350 mm outside diameter of the same material and length. Neither the maximum shear stress nor the angular twist per unit length of the original shaft is to be exceeded.
Calculate EACH of the following:
(a) The maximum permissible inside diameter of the hollow shaft;
(b) The percentage reduction in weight.
Q1. A horizontal cantilever beam is 2.8 m long. It carries a concentrated load of 2400 N at its free end and a uniformly distributed load of 360 N/m over its entire length. The beam has a hollow rectangular cross-section with outside dimensions of 100 mm wide by 150 mm deep and a constant thickness of 14 mm. Calculate EACH of the following:
(a) The maximum bending stress in the beam;
(b) The total deflection at the free end of the beam.
Note: d = WL3/ 3EI for a concentrated load where W = concentrated load (N)
d = wL4 / 8EI for a distributed load where w = distributed load (N/m)
Modulus of Elasticity for beam material = 210 GN/m2
Q3. A steel bar is 0.9 m long and 50 mm diameter. An axial hole 30 mm diameter is to be drilled from one end to such a depth that the extension of the drilled part is twice the extension of the solid part when an axial tensile load is applied. Calculate EACH of the following:
(a) The required depth of the drilled hole;
(b) The strain energy in the bar when an axial tensile load of 24 kN is applied.
Note: Modulus of Elasticity for steel is 210 GN/m2.
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