Q1 (a) (b) (c) IVIZU Using Hooke's equation derive an equation for shear modulus (G), and bulk modulus (K) expressed in terms of Young modulus and Poisson's ratio. The equation for shear modulus and bulk modulus set the limit for physically possible values Poisson's ratio, what is that limit? Justify your answer. [6] A thin-walled hollow circular tube is subjected to an axial tensile force, which produces normal stress 10 MPa on any cross-section (see Figure Q1). It is also subjected to a torque, which produces shear stress of 20 MPa, as shown. Sketch the Mohr's circle for any element of the tube, and hence calculate the magnitudes of the principal stress and the maximum shear stress. Calculate axial force, assuming that the inner radius of the circular hollow section is 20 cm and outer radius is 21 cm. [10] A second material plate is subjected to a two-dimensional stress state, and a strain gauge rosette with gauges at 0, 45 and 90 is attached to the surface of the plate. The strain gauges register the following direct strains: E=120 microstrains 45=-60 mictostrains = -120 microstrains, x' where 45 is measured 45 anticlockwise from E. Sketch the Mohr's circle of strain and hence calculate the magnitude of the principal strain and the direction of the major principal strain relative to x. [17] = 10MPa T = 20MPa Figure Q1 Continued overleaf Page 2 of 6