Problems for Practice

PROBLEMS FOR PRACTICE

Theory of simple bending

1. A beam is freely supported at a distance of 16m apart carries a uniformly distributed load of 25 kN/m and also carries a point load of 15 kN at 6m from the left support. Calculate the maximum bending moment, if the permissible stress in timber is 60 Mpa, design a suitable rectangular section by making the depth twice the width.

2. A beam of symmetrical section has a depth of 55 mm and a moment of inertia of 8000 cm4 about its axis of bending. Calculate the length of the beam if, simply supported at the ends, it has to carry a UDL of 8 kN/m without exceeding a bending stress of 120 N/mm2.

3. A mild steel cantilever 35 mm wide and 20 mm deep is fixed at one end in a wall. The overhanging length is 4m. At the free end is applied a clockwise moment of 65 × 106 N-mm. Determine the radius to which the cantilever will bend. Find also the vertical displacement of the free end. Assume E = 2 × 105 N/mm2.

4. A beam 42 mm × 60 mm of symmetrical section simply supported over a span of 6m. Calculate (a) the uniformly supported load it may carry, (b) the concentrated load it may carry at the centre, if the maximum bending stress is not exceed 25 N/mm2.

5. A 150 mm × 100 mm rolled steel joist of I-section has flanges 15mm and web 10 mm thick. It is simply supported over a length of 5m. Determine the total load uniformly distributed on the entire span that the beam could carry in addition to a concentrated load of 8 kN at its centre in order that the extreme fibre stress is limited to 19.5 N/mm2.

6. A boiler shell has a MS pipe of 200 mm diameter and 4 mm thickness simply supported freely at two points 8m apart. Find the maximum stress in the pipe when it is running full. Take unit weight of MS as 92 kN/m3 and that of water 10 kN/m2.

7. A steel tube 175 mm outer diameter and 140 mm inside diameter is used as a simply supported beam on a span of 7.5m, and it is found that the maximum safe load it can carry at mid span is 80 N/mm2. Four of these tubes are placed parallel to one another and firmly fixed together to form in effect a single beam, the centers of the tubes forming a square of 175 mm side with one pair of centers vertically over the other pair. Find the maximum central load which this beam can carry if the maximum stress is not to exceed is not to exceed twice that of single tube.

8. A cast iron T section of length 5m is used as a cantilever. The top horizontal flange of the T is 60 mm × 10 mm and the vertical leg is 8 mm × 50 mm. If the tensile stress is not to exceed 30 Mpa and the compressive stress is not to exceed 50 Mpa, determine UDL at the cantilever can carry.

9. A composite beam consists of a timber joist 100 mm deep × 75 mm wide with a steel plate 75 mm × 10 mm bolted on each side, the steel plates being symmetric about the axis of bending. If the stresses in the timber and steel are not to exceed 12 Mpa and 90 Mpa respectively, find the maximum bending moment the beam will carry and the maximum stresses in the two materials when carrying this moment. Compare the value of this moment with that of the timber joist alone. Esteel = 210 Gpa and Etimber = 15 Gpa.

10. A flitched timber beam consists of two joists 90 mm deep and 60 mm wide with a steel plate 80 mm deep and 15 mm thick placed symmetrically between and clamped to them. It is freely supported over a span of 4m and carries a point load of 2500 N. Calculate the maximum stress induced in the joist and the steel plate. E for steel is 16 times that of wood.