A rectangular block has dimensions of 3 in, 4 in, and 5 in along the X-, y-, and z- axes, respectively. The block is subjected to triaxial loading of three uniformly distributed loadings of 30 kips (C), 45 kips (T), and 60 kips (C) along the x-, y-, and z- axes, respectively. If the strain along the X- axis and the z-axis are 0.00021 (C) and 0.00042 (T), respectively, determine the Poisson's ratio and the modulus of elasticity of the material. Also, what is the change in volume of the material?

A rectangular block has dimensions of 3 in, 4 in, and 5 in along the X-, y-, and z- axes, respectively. The block is subjected to triaxial loading of three uniformly distributed loadings of 30 kips (C), 45 kips (T), and 60 kips (C) along the x-, y-, and z- axes, respectively. If the strain along the X- axis and the z-axis are 0.00021 (C) and 0.00042 (T), respectively, determine the Poisson's ratio and the modulus of elasticity of the material. Also, what is the change in volume of the material?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.4P: An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy =...

See similar textbooks

Similar questions

- 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 spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Calculate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is O.h Assume E = 4 MPa and v = 0,45.
A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.
If the Young's modulus and Poisson's ratio of the container material are 100 GPa and 0.3 respectively, What is the axial strain in the cylinder wall at mid-depth?
A Mild steel rod of 15mm diameter that is 1.5 cm in length is elongated by 0.15mm along its longitudinal direction by a load of 15 kN. Hence, the strain of the material is …………….. mm/mm.
Two fully loaded tractor trailers travel over the bridge putting substantial loading on the structure. As they pass over the middle of the bridge, one of the vertical supporting pillars, which is fixed at its bottom, deforms as shown below. The weight of the trucks causes point T to move to point T'—a distance of 2.5 cm along the x-axis. If the pillar has an original height of 27 m , find the shear strain at point T.
Rigid bar ABCD is supported by two bars as shown. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in bar (2) is measured as −3,300 μm/m. Use the dimensions L1 = 1,600 mm, L2 = 1,200 mm, a = 240 mm, b = 420 mm, and c = 180 mm. Determine (a) the normal strain in bar (1). (b) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin C before the load is applied. (c) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin B before the load is applied.
2.Show that volumetric strain in a bar is equal to the sum of strains in three mutually perpendicular directions. 3. Explain the terms: (i) Modulus of elasticity (ii) Modulus of rigidity and (ii) Bulk modulus. 4. Derive the relationship between (i) Modulus of elasticity and modulus of rigidity (ii) Modulus of elasticity and bulk modulus
A rectangular steel block is 4 inches long in the x-direction, 6 inches long in the y-direction, and 3 inches long in the z-direction. The block is subjected to a tri-axial loading of three uniform distributed forces as follows: 55 kips compression in the x direction, 62 kips tension in the y direction, and 24 kips tension in the z direction. If the Poisson’s ration is 0.26 and E = 29 x 106 psi, determine the single uniform distributed load in the y direction that would produce the same deformation in the x direction as the original loading.
A thin rectangular plate having the dimensions of a =20 mm and b=12 mm is acted upon by a stress distribution resulting in the uniform strains Subscript[\[CurlyEpsilon], x]=300 \[Mu], Subscript[\[CurlyEpsilon], y]=500 \[Mu], and Subscript[\[Gamma], xy ]= 200 \[Mu]. Compute the changes in length of diagonals QB and AC based on small deformation theory.
Please include a free body diagram Solve for: a) Normal strain in the x- direction −4.0 × 10^−34.0 × 10^−310 × 10^−3-10 × 10^−3 b) Normal strain in the y- direction −4.0 × 10^−34.0 × 10^−310 × 10^−3-10 × 10^−3 c) Total shear strain 0.6 deg.0.7 deg.0.8 deg.0.9 deg.