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1. A stepped cylindrical bar of cross sectional areas AAB. Agc and Ace carries five axial forces as illustrated in Figure Q1. What is the maximum value of P for the stresses not to exceed 100 MPa in tension and 140 MPa in compression. c A / B + C C T E c P. 6P. 4P. P. 2P D =225 mm² Asc = 900.mm² Ace = 400 mm² Figure Q1. A B C D E 7.5 kN 15.5 kN 20.5 kN 4.5 kN 22.5 kN 2. Two plates are joined by four bolts of d = 20 mm diameter as shown in Figure Q2. Determine the maximum load P given that the shearing, tensile and bearing stresses are limited to 80, 100 and 140 MPa, respectively. 15 mm 20mm Shoar 10 mm 100 rom + 80 mm 120mm * P Figure Q2 A B C 129.4 MPa D 158.9 MPa F 90.0 kN 283.1 MPa 141.5 3. An aluminium alley pipe of internal diameter d' and outter diametter 0 is filled with concrete and a compressive load P is applied to the migid cap as illustrated in Figure Q3. What is the maximum allowable azad Par Giwem de 300 mm. o = 340 mm. E, = 70 GPa, Es = 15 GPa, (wh = so = 20 MPa. Rigd cap Concrete di a Figure Q3. A B C o e 25.41 kN 1.14 kN 5.42 kN 1.02 kN 5. A steel rod of diameter 15 mm is held snugly (but without any initial stress) between rigid walls by the arrangement shown in Figure Q5. Calculate the temperature drop AT (degrees Celsius) at which the average shear stress in the 12 mm diameter bolt becomes 55 MPa. (For steel use as = 12 x 10°PC and Es = 200 GPa.) 15 mm 12 mm diameter bolt Figure Q5 A B C D E 19.5° 10.7° mm 29.3° 15.2° 31.4° 6. A 9m long steel pipe (E = 200 GPa) has an outside diameter of 220 mm and a wall thickness of 8mm. The column is supported only at its ends and may buckle in any direction. Calculate the critical load where the column is pinned at both ends. A B C D E 442 kN 729 kN 215 kN 969 kN 114 kN 7. A solid constant-diameter shaft is subjected to the torques shown in Figure Q7. The bearings shown allow the shaft to turn freely. If the allowable shear stress in the shaft is 80 MPa, determine the minimum acceptable diameter for the shaft. 110 N-m y 330 N-m 380N-m (1) 160N-m (2) (3) T-TY B D J= TD 37 Figure Q7 A B C D 15.2 mm E 35.6 mm 45.3 mm 22.4 mm 24.1 mm 8. An element in plane stress is subjected to stresses Ox = 110 MPa, a = 40 MPa and Txy = 30 MPa as shown in Figure Q8. Determine the stresses acting on an element oriented at 0 = 30° from the x axis, where the angle is positive counterclockwise. 40 MPa 30 MPa 110 MPa Figure Q8 A B C D E Ox1 = 118.5 MPa Ox1 = 110.0 MPa Oxt = 58.0 MPa Oxt = -125.1 MPa Okt =-22.8 MPa Txty1" -15.3 MPa Txty1E 30.0 MPa -13.4MPa Tx1y1=-76.2 MPa Tx1y13 = -21.3 MPa Ov1 =31,5 MPa Oyl = 40.0 MPa - 22.0 MPa On = 39.1 MPa Oy1 - 58.8 MPa 9. Determine the moment of inertia 1xx of the "Z" section about the x axis which passes through the centroid C in Figure Q9. y 200 mm 20 mey x C 20 that 600 mm 200 mm 20 mm Figure Q9 A B C D E 1.21 X 109 mm" 124 x 106 mm 62 x 106 mm4 112 x 106 mm4 82 x 109 mm4 10. The beam-column in Figure Q10 is fixed to the floor and supports the load shown. Determine the shear force at point B due to this loading. 5kN - 25AN 0.5m 04m 4 0.2m 2m Figure Q10 A B C D E 5.0 kN 0.0 kN 7.5 kN 2.5 kN 1.5 kN 11. Determine the maximum value of moment in the simple beam shown in Figure Q11. 12 NN/m 30kN m 5 to 5m Figure Q11 A B C D E 60 kNm 104 kNm 90 kNm 96 kNm 125 kNm 12. Determine the distance "a" between the supports in Figure Q12 in terms of the shafts length "L" so that the bending moment in the symmetric shaft is zero at the shaft's centre. The intensity of the distributed load at the centre of the shaft is Wo. a L Figure Q12 A B C D E L/5 L/4 L/3 L/2 13. Determine the shear force and bending moment at point C for the beam illustrated in Figure Q13. 4 kN/m A C B 3 m 6m Figure Q13 A B C D E 12 kN 24 kN 36 kN, 12 kN 10 KN -24.0 kNm -12. 0 kNm -81.0 kNm 20.0 kNm -18,0 kNm 14. During construction of a highway bridge, the main girders are cantilevered outwards from one pier to the next as shown in Fighure Q14. Each girder has a cantilever length of 48m and an I-shaped cross section with dimensions as shown in the figure. The load on each girder (during construction) is assumed to be 9.5 kN/m, which includes the weight of the girder. Determine the maximum bending stress in a girder due to this load. 16 A wood beam ABC with simple supports at A and B and an overhang BC is subject to loads 3P and P acting as shown in Figure Q16. The beam has actual dimensions 90 mm x 286 mm. Determine the maximum permissible load P based upon an allowable shear stress in the wood of 0.7 MPa. (Disregard the weight of the beam.) 3P P. Bedia 286 mm 90 mm 2 m 2 m 1.2m- Figure Q16 A B C D E 6.67 KN 4.09 kN 5.21 KN 8.56 kN 9.93 kN

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