(a) the strains in these directions, (b) the changes in dimensions, (c) the volumetric strain and (d) the change in volume. Take E = 214 GPA and Poisson’s ratio = 0.33.
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A cube has sides that are initially 80 mm and is subjected to stresses of 40 MPa (tensile), 30 MPa (compressive) and 70 MPa (tensile) in the x, y and z -directions, respectively. Calculate (a) the strains in these directions, (b) the changes in dimensions, (c) the volumetric strain and (d) the change in volume.
Take E = 214 GPA and Poisson’s ratio = 0.33.
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- - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?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?Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300
- The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.A rectangular steel block is 300mm in the x direction, 200mm in the y direction and 150mm in the z direction. The block is subjected to a triaxial loading consisting of three uniformly distributed forces as follows: 250kN tension in the x direction, 320kN compression in the y direction and 180kN tension in the z direction. For steel, v=0.30 and E=200,000MPa. Determine the total strain in the x direction due to the forces applied in the three directions.A rectangular block is 7 cm long in the x-direction, 5 cm in the y-direction, and 9 cm long in the z-direction. The block is subjected to a triaxial loading of three uniformly distributed forces as follows: 15 kN in the x- direction, 21 kN in the y-direction, and 18 kN in the z-direction. Calculate the strain in the direction y if Poisson's ratio v = 0.30 and having a modulus of elasticity of E = 150 GPa. y 7 cm 9 cm 21 kN 15 kN 5 cm 18 kN
- 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 0.42SA thin metal alloy plate is loaded by biaxial stress (2 directions) given by 8000 psi in the x direction and 5000 psi in the y direction. The measured strains due to this stress are 950 x 10* in thex and 335 x 10* in the y direction. Evaluate the Poisson ratio and Young's modulus for this material and the strain in the z direction.5. A rectangular piece of steel (E = 200 GPa, ν = 0.30) has dimensions of 100 mm, 200 mm, and 40mm in the x, y, and z directions. Forces of 40 kN and 80 kN are uniformly distributed on the xand y faces, respectively.(a) Calculate the stresses in the x, y, and z directions.(b) Calculate the strain in the x-direction.(c) Calculate the strain in the y-direction.(d) Calculate the change in thickness in the z-direction
- The longitudinal strain in a cylindrical bar of diameter 20mm and length 2.5m during the tensile stress is 3 times the lateral strain. Calculate the modulus of rigidity, bulk modulus and also find the change in volume when the bar is subjected to hydrostatic pressure of 150MPA. Take E = 150GPA.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 mmTensile 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.