A solid piece of metal of volume 10,000 mm3 is compressed by a pressure of 70 MPa. Determine the bulk modulus given that the Young’s modulus E is 214 Gpa and the Poisson’s ratio is 0.33. Also determine the change in the volume. 2. Starting from the first principles derive the relation between Young’s modulus (E), shear modulus (G) and Poisson’s ratio (υ)

Determine the change in the volume of a 10 cm diameter copper sphere that is subjected to a hydrostatic pressure of 120 MPa assuming linear elastic behavior up to this stress level. (V =4/3 n 13) (E: 125 GPa, v = 0.34, SY = 200 MPa)

Determine the bulk modulus for each of the following materials: (a) rubber, Er = 0.4 ksi, nr = 0.48, and (b) glass, Eg = 8(103) ksi, ng = 0.24.

When a mass of m = 22 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12° with the horizontal as shown in. The elastic 12° Part A m 12° modulus for aluminum is 7.0 × 10¹0 N/m². Determine the radius of the wire. Express your answer to two significant figures and include the appropriate units.

A silicon carbide ball with 5 mm in diameter has volume based CLTE (a,) of 8.1 x106/°C. If the ball is heated from 100 to 1750°F, calculate the increase in diameter. Convert first the temperature to °C. Note: (AV/V) = (V-V.)/Vo= av AT

Show with tensors and in three-dimensional space that all directions are principal axes for the stress state at a point where τ1=τ2=τ3

The following stress condition is applied to a cubic material.Normal stress in the x direction is 15 Mpa, normal stress in the z direction is -7 Mpa and the shear stress in the x-z plane is 59 Mpa.(a) Write the stress tensor(b) Find the maximum normal stress(c) Find the angle with respect to the x- axis at which the maximum normal stress is applied(d) Find the maximum shear stress(e) Determine the angle with respect to the x-axis at which the maximum shear stress is experienced

A heavy crate rests on an inclined surface. Find the smallest force P required to keep the crate from sliding back down the inclined surface, given:Mcrate = 170 kg, μ = 0.2 θ = 20 °

A spherical tank of diameter 1.2 m and wall thickness 50 mm contains compressed air at a pressure of 17 MPa. What is the value of tensile stress? (Assume E = 210 GPa, v = 0.29)