A material has a height of 50mm (y), a width of 50mm (x) and a depth of 50mm (z) and is stressed by 2MPa in the x direction and 5MPa in the y direction and 7MPa in the z direction. Given the elastic constants of E=205GPa and v=0.27, calculate the strain and dimension change in all three directions
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A material has a height of 50mm (y), a width of 50mm (x) and a depth of 50mm (z) and is stressed by 2MPa in the x direction and 5MPa in the y direction and 7MPa in the z direction. Given the elastic constants of E=205GPa and v=0.27, calculate the strain and dimension change in all three directions
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- A material has dimensions 50mm x 40mm (2 dimensional). It is stressed 2MPa in the x direction and 5MPa in the y direction. Given the elastic constants of E=205GPa and v=0.27, calculate the strain in both directions.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.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.
- 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 kNFind the value of strain stress 30 MPa Modulus of elasticity=65 MPaA bar of aluminum alloy of rectangular section75 mm x 20 mm and 800 mm long is stretched by an axial force of 150 kN. Find the volumetric strain, the actual change in volume and the percentage reduction in cross – sectional area of the bar. Take E = 70 GN/m2 and v = 0.34
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- The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression vy/3E where y = 2.4 lb/in.³ is the specific weight of the material, y = 3.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 19 in. is the length of the bar, and E= 24000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Part 1 Calculate the change in length of the bar due to its own weight. Answer: d = i x10-6 in.A bar of a uniform cross section is subjected to uniaxial tension and develops a strain in the direction of the force of 1/800. Calculate the change of volume per unit volume. assume v= 1/3You must perform mechanical tests with a linear elastic material (the material follows Hooke's law) applying forces (tension) in the range 0 to Fmax/2 for Sample A and between 0 to Fmax for Sample B. The samples are made of same material but have different geometries (see illustration). (a) Which of the two samples receives the maximum stress (σmax)? (b) Which of the two samples will have the larger length change (ΔLmax)? (c) Plot the expected curves for the two samples in the force-length and stress-strain planes. (d) Clearly indicate the values that the variables force, length, stress, and strain take at the beginning and end of each curve.