Tutorial 5 PDF

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2019 S1 MEC2402 Tutorial 5...

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Tutorial 5: Stress Analysis 5.1 (i) For the given state of stress, determine (a) the principal planes, (b) the principal stresses. [26.5° CW, 190 MPa, -10 MPa] (ii) For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the co-existing normal stress. [18.5° CCW, 100 MPa, 90 MPa]

5.2 (i) For the given state of stress, determine (a) the principal planes, (b) the principal stresses. [23.5° CCW, -46 MPa, 117 MPa] (ii) For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the co-existing normal stress. [21.5° CW, 81 mPa, 35 MPa]

5.3 The steel plate has a thickness of 10 mm and is subjected to the edge loading as shown. Determine the maximum in-plane shear stress and the co-acting normal stress developed in the steel for the maximum in-plane shear stress orientation. [1.5 MPa, 2.5 MPa]

5.4 Determine the state of stress if the element is rotated: (a) 30º clockwise, and (b) 30º counterclockwise. In both cases, represent these states of stress on an element in the correct orientation. [4 MPa, 26 MPa, 69 MPa; -39 MPa, 69 MPa, 44 MPa]

5.5 For the state of stress shown, determine the maximum shearing stress when (a) σz = 0, (b) σz = +60 MPa, (c) σz = –60 MPa. [91.0 MPa, 91.0 MPa, 108.0 MPa]

Additional Questions 5.6 At a point on the surface of a generator shaft the stresses are x = -50MPa, y = 10 MPa, and xy = -40 MPa. Determine the following: (a) the stresses acting on an element inclined at an angle of 40º counter-clockwise [-64.5 MPa; 24.6 MPa; 22.6 MPa]; (b) the principal stresses [30MPa; -70 MPa; 26.5º CCW]; (c) the maximum shear stresses. [50MPa]. (Consider only the in-plane stresses, and show all results on sketches of properly oriented elements.) 5.7 A propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear stress of 70 MPa (-ve on the x-face of the element) and a compressive stress of 100 MPa. Determine: (a) the principal stresses and show them on a sketch of a properly oriented element, [-136 MPa, 36 MPa 27°]; (b) the maximum in-plane shear stress and associated average normal stresses and show them on a sketch of a properly oriented element. [86 MPa; -50 MPa; 18º CW]

5.8 For a state of plane stress it is known that for each of two given orientations of the coordinate axes, the normal and shearing stresses are directed as shown and the magnitudes of the normal stresses σx, σy, and σx′ are, respectively, 80 MPa, 30 MPa, and 75 MPa. Determine (a) the principal planes and principal stresses, (b) the maximum in-plane shearing stress. [9.55° CCW, 81.5 MPa, 28.5 MPa; 26.5 MPa]

5.9 For the state of plane stress shown, determine the maximum shearing stress when (a) τxy = 42 MPa, (b) τxy = 96 MPa. (Hint: Consider both in-plane and outof-plane shearing stresses.) [69.0 MPa; 104 MPa]...