A torsional moment T = 5,382 Nm and a load P = 55,253 N are applied at the same time to a circular hollow shaft of unknown length L, as shown in Figure Q5. The load P is offset from the centre of the circular cross-section by a distance e = 6 mm. The shaft has an inner diameter d = 43 mm and an outer diameter D = 97 mm. Point A in Figure Q5 is on the outer surface of the shaft.      Figure 5   Calculate the direct (or normal) stress in the x-direction σx at point A (the 'x-direction' is along the longitudinal axis of the shaft, along its length L). Use π = 3.14159 if needed. Calculate your answer in the unit: mega-Pascal (MPa).

The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 101 GPa] with a cross-sectional area of A₁ = 230 mm². Bar (2) is an aluminum alloy [E = 71 GPa] with a cross-sectional area of A₂ = 740 mm². All bars are unstressed before the load P is applied; however, there is a 4-mm clearance in the pin connection at A. Assume L₁ = 2040 mm, a = 1020 mm, b = 630 mm, c = 460 mm, and L₂ = 1470 mm. If a load of P = 155 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar. (1) L₁ a b B Answers: (a) σ₁ = 02= (b) VA= i i i C MPa MPa mm (2) L2

A steel bar with a circular cross section, AC, is built in at both ends (A and C) and is subjected to a 300N point load at B, 300mm from point A, as shown in the figure below. The bar has a diameter of 8 mm and the material has a Young's modulus of 200GPa. Determine the magnitude of the reaction force at A? O O O O 380 N 150 N Don't Know 210 N 300 N 300mm B 300 N 700mm

A torsional moment T = 8,019 Nm and a load P = 39,980 N are applied at the same time to a circular hollow shaft of unknown length L, as shown in Figure Q8. The load P is applied in the centre of the shaft's circular cross-sectional area. The shaft has an inner diameter d = 38 mm and an outer diameter D = 90 mm. Point A in Figure Q8 is on the outer surface of the shaft.        Figure 8   Calculate the maximum principal stress at point A. Use π = 3.14159 if needed. Calculate your answer in the unit: mega-Pascal (MPa). Report you answer to 3 decimal places.