In uniaxial loading the poisson's ratio is 0.30 and the strain in the x-direction is 250 x 10^-6. What is the strain in the z- direction? * A -8.5 x 10^-5 B -7.5 x 10^-5 C 7.5 x 10^-5 9.5 x 10^-5 D
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- 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 300A 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?A joint between two glass plates A and B is filled with a flexible epoxy that bonds securely to the glass. The height of the joint is/p = 0.5 in, its length is L = 30 in, and its thickness is/ = 0.5 in. Shear force of I' = 25 kips is applied to the joint. Calculate the displacement of the joint if the shear modulus of elasticity G of the epoxy is 100 ksi. Calculate the average shear strain in the epoxy.
- An element of material in plain strain has the following strains: x = 0.001 and y = 0.0015. (a) Determine the strains for an element oriented at an angle = 250. (b) Find the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.In uniaxial loading the poisson's ratio is 0.30 and the strain in the x- direction is 250 x 10^-6 . What is the strain in the z- direction?If an isotropic material has a shear modulus of 125 Gpa and a Poisson's ratio of 0.2, calculate its Young's modulus. Select one: O E= 80 Gpa O E= 450 Gpa O E= 60 Gpa %3D O E= 30 Gpa %3D O E= 300 Gpa %3D If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal BD.
- On the free surface of a component, a strain rosette was used to obtain the following normal strain data: €a = 300µɛ, ɛp = 400µs, and Ec = 200µe. Calculate the normal and shear strains in the x-y plane.The tensorial strain at a particular point in a loaded medium is found to be as follows: 1 -2 07 [6]=-2 6 0 x10* 0 1 (a) Calculate the normal strain at this point in the direction of the vector A=e, + 2e, -2e, (Hint: The direction cosines in this direction are the components of unit vector along vector A) (b) Considering a CCW rotation of 90° about the x,- axis, construct the transformation matrix.O 0.6% 19% If an isotropic material has a Young's modulus of 85 Gpa and a Poisson's ratio of 0.25, calculate its shear modulus. Select one: O G = 29 Gpa O G = 34 Gpa G = 25 Gpa O G= 77 Gpa O G= 46 Gpa If a rubber material is deformed as shown in the following figure, determine the normal strain along diagonal BD. C 2 mm 4 mm EN DO O
- Calculate the moment and axial load capacity of the circular column corresponding to the given strain distributions. Use the formulas given below for the area and the centroid of circle segment. Column diameter D=2r= 500 mm 60 fek= 40 MPa Eco= 0.0021 mm/mm 140 E= 40000 MPa fy= 420 MPa 140 E= 200000 MPa 8-030 Area of one o30 bar= 707 mm2 60 a) Ec top= 0.003 mm/mm c= 200 mm b) Ecsop= 0.003 mm/mm c= 400 mmAn initially rectangular element of a material is deformed into the shape shown in the figure. Deformed Undeformed 16.6 0.1992 mm 15.7 0.2 mm Normal strain in the x- direction * -4.0 x 10^-3 4.0 x 10^-3 10 x 10^-3 -10 x 10^-3 Normal strain in the y- direction O -4.0 x 10^-3 4.0 x 10^-3 O 10 x 10^-3 O -10 x 10^-3 0.1515 mm 0.15 mmThe state of plane strain on an element has components €z = -340(10 6), Ey = 0, and Yzy = 130(10 ®). (Figure 1)