Question

Question 1 An end capped cylindrical pressure vessel with internal pressure p = fully supported at one end, is also subjected to a force F= 10 kN in the y direction at the other end as shown. The internal diameter of the pressure vessel is d= 160 mm and its thickness is t= 10 mm 3 MPa, assumed to be Determine the magnitudes of the stress components in x, y and z coordinates at points H and K and sketch the state of stress elements representing these points (include coordinate axes Note: you do NOT have to determine the principal 0.2 on for reference) 0.8 m stresses 0.2 m (Centroidal moment of inertia for a circle, = d/64 Polar moment of inertia for a circle, J = /d*/32 Centroid of semi-circle = 4r/3n) F= 10 kN Question 2 The state of stress on the surface of a machine component is as shown in the diagram. If the yield stress for the material is S, =320 MPa, determine the factor of safety (based condition) for the state of stress at this point (assuming this is the location of maximum stress) using both the von-Mises and Tresca yield criteria. 150 MPа yield as the limiting on 15 MPa 50 MPa Question 3 Use energy methods to determine the vertical displacement and angle of the cantilever beam at end D when loaded with an end load F as shown. Clearly state any assumptions or simplifications EI 2EI Question 4 It is estimated that a particular aluminium component has been exposed to the following levels of service each year for 5 years An alternating stress range of 150 MPa about a mean stress of 50 MPa for 500,000 cycles and an alternating stress range of 180 MPa about a mean stress of 60 MPa for 200,000 cycles. The aluminium has an ultimate tensile strength Crs = 240MP2. The material follows Basquin's Law for high-cycle fatigue, i.e Δσν,-C where a 0.125, C\ = 1600MP2 and Aois the cyclic stress range. Using this information and assuming that future loading will be the same as in the past, predict the remaining life (in years) of this component Question 5 Strain measurements taken with a 45° strain gauge rosette on the surface of a machine component are as shown below. Young's Modulus E = 200 GPa and Poisson's ratio v = 0.27 for the component material. Determine the principal stresses and maximum shear stress in the component at where the strain measurements were taken the point 150 uE &2 800 HE 600 uE & =

Answer 1

3 600 200 G Pa E VSO.27 (e,-2(-3) + t LISO+8 o o) t (tS0-8 6) 2-+ (600 -600 2 - dos staaims nipl ste ss с, - 1-(0.27) 2 a37 22 3 Joo-dos o27(155) - д2 - (o. 2 72 237 223 - 23-0S max" shoay sre ss may o 08 max