A body is subjected to stresses as shown in the figure given below. 90 MPa 35 MPa 145 MPa The FOS as per maximum principle strain theory if the yield stress of the material is 230 MPa and Poisson ratio of material is 0.38. (assume plane stress condition)
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- 3. An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in the figure. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 13.05 ksi, or in bronze of 100 MPа. Aluminum A = 400 mm? Bronze A = 200 mm Steel A = 500 mm? 2P 4D 2.5 m 2.0 m 1.5 mTime len A material has the stress-strain behavior shown in the Figure below. Calculate the toughness (T) of this material. given that S1=195 Mpa; S2=243.75 Mpa; El=0.19; E2=0.38 E1 Strain E2 Stress - Strain diagram of a metal alloy OA.T= 18.52 Mpa O B.T= 92.62 Mpa O C.T= 37.05 Mpa O D.T= 60.21 Mpa Stress (Mpa) 3The stresses shown in the figure act at a point on the free surface of a machine component. If o= 45 MPa in the direction shown, determine the normal stress oy at the point. Ox 27 MPa 30° 50 MPa O-16.3 MPa O-19.5 MPa O-22.8 MPa O-17.2 MPa O -20.5 MPa
- 2. For the state of stress shown, determine the range of value of for which the normal is equal to or less than 100 MPa and 50 MPa. stress x' + 90 MPa 60 MPa =The stress concentration occurs whenever there is an abrupt change in the cross-section of a component or there is any discontinuity in the material. The figure given below shows a flat plate with a hole of diameter d. The plate is fixed at one end and the other end is subjected to a tensile load of P = 44 kN due to which there is a change in length of 0.4 mm. The thickness of the plate is 11.5 mm. The maximum stress developed in the flat plate is 228 MPa. Take Young's modulus(E) = 210 GPa and theoretical stress concentration factor =2, Calculate the following values: i) Width of the plate (W2) in mm ( ii) Nominal Stress in MPa ( iii) Diameter of the hole (d) in mmThe stress concentration occurs whenever there is an abrupt change in the cross-section of a component or there is any discontinuity in the material. The figure given below shows a flat plate with a hole of diameter d. The plate is fixed at one end and the other end is subjected to a tensile load of P = 41 kN due to which there is a change in length of 0.4 mm. The thickness of the plate is 11 mm. The maximum stress developed in the flat plate is 235 MPa. Take Young's modulus(E) = 210 GPa and theoretical stress concentration factor =2, Calculate the following values: i) Width of the plate (W2) in mm ii) Nominal Stress in MPa iii) Diameter of the hole (d) in mm Hole with stress concentration factor 2 35 mm W2 35 mm P 300 mm 350 mm- 250 mm
- M A cylinder of outer radius R2=100 mm is fitted on another cylinder of outside radius R₁=85 mm with thickness t=30 mm, as depicted below. If the (tensile) maximum hoop stress at the interface between the two cylinder is 90 MPa, solve the following questions (E=105 MPa and v=0.15). === R₁ What is the radial stress between the cylinders? What is the shrinkage allowance at the interface? ( M R₂ )The state of stress at a certain point in a stressed body is shown in figure. The magnitudes of normal stresses in x & y directions are 100 MPa& 100 MPa respectively. Determine the radius of Mohr's circle representing this state of stress (in MPa). Ox Oy CySolid shaft made of cast iron shown in the figure, T = 400 lb. It is subject to flick torque. Determine the smallest radius that will not generate strength loss according to the theory of greatest normal stress? The cast iron sample tested in tensile has a stress of 20 µm axim um.
- A brass wire of diameter d = 2.33 mm is stretched tightly between rigid supports so that the tensile force is T = 93 N (see figure). T The coefficient of thermal expansion for the wire is 19.5 x 106/°c, and the modulus of elasticity is E = 110 GPa. (a) What is the maximum permissible temperature drop (in °C) if the allowable shear stress in the wire is 60 MPa? (Enter the magnitude.) °C (b) At what temperature change (in °C) does the wire go slack? °CAn element has a tensile stress of 600 N/mm2 and a compressive stress of 400 N/mm2 acting on two mutually perpendicular planes and two equal shear stresses of 100 N/mm2 on these planes as shown in figure. (by Mohr's circle аpproach) 400N/mm 100N/mm 600N/mm 600N/mm? 100N/mm 400N/mm (a) Find the principal stresses and maximum shear stress.30. An aluminum alloy rod has a circular cross section with a diameter of 8mm. The rod is subjected to a tensile load of 5kN. Assume that the material is in the elastic region and E = 69 GPa. If Poisson's Ratio is 0.33, what will be the lateral strain? E= 6/8 v = -E(lateral)/(axial)