Problem 1: find out the bending (σ_{x}) and shear stress (τT_{xy}) at the surface element shown on the solid circular shaft below. Use Mohr's circle to find out the principle stresses, σ_{1}, σ_{2} the maximum shear stress on the element, τ_{max} and the angle, θ, between the plane shown and the plane of principle stresses. Use the following data:
F = 20 kips
d = 16 in
L = 6 ft
c = 3 in
E = 29000 ksi
G = 11200 ksi
Problem 2: find out the minimum critical Euler axial compression force, σ_{cr} and the minimum critical Euler axial compression stress, σ_{cr}, for the column below which is pinned at the top and bottom ends and braced as shown. Use the following properties....
A = 12 in^{2}
l xx = 300 in^{4}
I ri = 50 in^{4 }
L = 20 ft
E = 29,000 ksi
Problem 3: Derive the equations of the elastic curve and use them to find out the deflection and rotation at point B in terms of E, I, F and L.
Problem 4: find out the maximum bending stress in the wood AND steel of the composite section shown below, knowing:
E_{w} = 1875 ksi
E_{s} = 29000 ksi
M = 400 in-kip
Problem 5: The round tensile specimen shown below has a diameter of 0.5 in. A load, F, is applied and the deflection, δ, is measured. Given the following:
d = 0.5 in
L_{o} = 10 in
F = 5 kip
g = 0.022 in
find out E (elastic modulus) for the material of the specimen. Also, find out the axial tension, σ_{u}, in the specimen and the engineering axial strain, ε. Assume that stresses and strains are in the elastic range of the stress-strain diagram.