3.For a body under three dimensional stress state, describe the procedure for obtaining the absolute maximum shearing stress at a given point. What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s circle for strain.
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3.For a body under three dimensional stress state, describe the procedure for obtaining the absolute maximum shearing stress at a given point. What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s circle for strain.
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- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positive
- 2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain = 0.15 strain. For the sample in the x-direction, the width strain was measured to be ew= -0.0923 at that instant. For the sample in the y-direction, the width strain was measured to be gw=-0.1000 at that instant. The yield strength of the x-direction specimen was 50 kpsi and the yield strength of the y-direction specimen was 52 kpsi. Determine the strain ratio for the x direction tensile test specimen. Determine the strain ratio for the y-direction tensile test specimen. Determine the expected yield strength in the z-direction. Give your answer in units of kpsi (just the number). If the sheet is plastically deformed in equal biaxial tension (a, = 0, to the point where & = 0.15, calculate the strain, 6, that would be expected.Question-1: The strain rosette shown in the figure was used to obtain normal strain data at a point on the free surface of a machine part. (a) Determine the strain components &, S, and %, at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point. (c) Draw a sketch showing the angle 6, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. 45 45 &- 50 με, 8--730 με , ε375 με, ν-0.30
- Project 2: 40-mm sides glass polymer fibers composite cube is shown in Figure.1. The Glass polymer fibers aligned in the x direction. The cube is constrained against deformations in the y and z directions and is subjected to a compression load of 65 kN in the x direction. Estimate the strain, change in length and stresses in x,y, and z directions as well as determine the volumetric strain. Illustrate the effect of two and three-dimensions by constructing appropriate sketches. If the cube is only constrained against deformations in the y direction, describe the changes in two and three-dimensions by constructing appropriate sketches. E,= 50 GPa E, = 15.2 GPa v = 0.254 15.2 GPa =0.254 %3D 0.42SFor the following data, using Mohr's circle of stress and trigonometry, (a) Find the principle stresses and show their sense in properly oriented element and (b) find the maximum (principle) shear stresses with the associated normal stresses and show the results on a properly oriented element.Derive the expression for the strain transformation.
- Part 1 A thin square plate PQRS is symmetrically deformed into the shape shown by the dashed lines in the figure. Assume d = 255 mm, d₁ = 256.1 mm, and d₂ = 253.6 mm. For the deformed plate, determine (a) the normal strain of diagonal QS. (b) the shear strain Yxy at corner P. d₂ Answer: dos d = i d₁ Undeformed Calculate the deformation of diagonal QS. R Deformed X mmUse the principle of Strain energy due to direct stresses strength of materials 2A brittle material made of ASTM grade 30 cast iron has ultimate strength in tension of 31 kpsi and ultimate strength in compression of 109 kpsi and undergoes the following plane of stress state: o, = 20 kpsi and Tyy = 10 kpsi (CW). a) using the 3D Mohr's circle, find all three principal normal stresses. b) using the Brittle-Coulomb-Mohr theory and Modified-Mohr theory, find the factors of safety for the given plane of stress state.