Problem 1: Axial Stress & Deformation

An assembly consists of 2014-T6 aluminum C rods AB and CD, and a rigid plate BD, each  with the given dimensions. If the assembly is subjected to the external loads as shown, determine the displacement, δ_E. Also determine the new diameter, d_AB, after loading.

You may assume that points B, D, and E all move only in the vertical direction.

Use the following parameters:
d_AB = 10 mm, d_CD =12 mm, L₁ = 300 mm, L₂ 400 mm, L₃ = l00 mm, P = 5 kN, w = 30N/mm

Problem 2: Stress Concentration Factors & Factors of Safety

The plate shown has the geometry listed below, and a thickness, t. If it is machined from A-36 structural steel determine the magnitude of the maximum safe load P if we are designing for a factor of safety of 2 against yielding.

Let:
t = 5 mm, h₁ = 50 mm, h₂ = 25 mm, d_h, = 10 mm, r_f= 20 nun, L₁ = 100 mm, L₂= 150 min

Problem 3: Average Shear Stress

A lap joint is constructed as shown above with 2 rivets holding together the 5 plates shown. Determine the required diameter, d_req, to the nearest 1/8", of each rivet if the stack of plates is in equilibrium. Take P = 1.5Q= 1000 lb and assume that the rivets are manufactured from 2014-16 aluminum. Also take the thickness of each plate to be 1/2". Make sure and draw a free body diagram of the entire bolt, as well as the section free body diagram you use to determine the average shear stress in the bolt.

Problem 4: Mechanical Properties

For the stress-strain diagram shown, determine approximately the following parameters (show your work where applicable):
a) Elastic Modulus
b) Ultimate Tensile Strength
c) Yield Strength
d) Strain at Failure
e) Proportional Limit

Bonus Determine the permanent strain for a material with the stress-strain response shown below loaded to 10.8x10³ ksi and then unloaded.

Take: σ₁ = 10x10³ ksi, σ₂ = 11x10³ ksi, ε₁ = .0015 in/in, ε₂ = .25 in/in.