Calculate the axial stress sigma psi on a 10 bolt under an a

Calculate the axial stress sigma [psi] on a #10 bolt under an axial load of 500 # tension for the following. a. Coarse thread b. Fine thread Calculate the shear stress tau [psi] on a 1.375\" bolt under a transverse shear load of 16 kips for the following. a. Coarse thread b. Fine thread Consider the following 2D state of stress: sigma_x = -9 ksi, sigma_y = 26 ksi and tau_xy = 16 ksi. a. Draw the original 2D stress clement. b. Calculate the principal stresses sigma_max and sigma_min, angle of rotation theta_p and draw the new stress clement using Mohr\'s Circle. c. Repeat part b using the eigenvalue/eigenvector method.

Solution

For #10 Bolt: (d=0.19\")

Axial stress for coarse thread = tensile force/weakest cross section area

Tensile force = 500 lb

Weekest cross section= 0.84d=0.84*0.19 =0.1596\"

Axial stress =500/(pi/4 X 0.1596^2) = 24,992.96 psi.

For Fine thread, weakest cross section =0.88d =0.88*0.19 =0.1672\"

Axial stress = 22772.33 psi.

2. For bolt of 1.375\" with shear load of 16 kips,

for coarse thread d_c=0.84d= 1.155\"

Shear stress = load/cross-section area = 16/(pi/4 x 1.155^2) = 15.27 kpsi (Assuming single shear)

for fine thread d_c=0.88d = 1.21\"

Shear stress = 16/(pi/4 x 1.21^2) = 13.91 kpsi