Question

Question 3 (continued) Determine by suitable calculations: a) the torsion constant (K) of the cross-section; b) the maximum value of torsional shear stress (in N/mm2) present at any point within c) (6 marks) (6 marks) the beam, and state clearly where this occurs; the vertical deflection (in mm) of the centroid of the cross-section at the free end of the beam; (6 marks) d) the total vertical deflection (in mm) of the point A located at the outside edge of the comer of the cross-section at the free end of the beam, including both elastic bending and torsional effects. (7 marks) (25 marks) Question 4 A cantilever beam spans 1200 mm and supports a concentrated vertical load of magnitude W at its free end (see Figure Q4a). a) 160 12 200 1200 mm Figure Q4a 23 ALL DIMENSIONS IN MILLIMETRES 10 Figure 04b The beam is made from two steel plates of different thicknesses to form the unequal angle cross-section shown in Figure 04b At the free end of the cantilever, the concentrated vertical load W acts at a distance of 23 mm from the inside face of the vertical leg of the cross-section (see Figure Q4b) The self-weight of the beam can be ignored Determine by suitable calculations i) the magnitude of W (in KN) when the maximum value of torsional (8 marks) shear stress anywhere in the beam is 150 N/mm2 i) the angle of twist (in degrees) at the free end of the beam when the value of W is that calculated in Q4(a)i above. The value of the shear (4 marks) modulus of steel can be assumed to be 77 GPa

Answer 1

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