Problem 8-11 The staves or vertical members of the wooden tank are held together
ID: 1857112 • Letter: P
Question
Problem 8-11
The staves or vertical members of the wooden tank are held together using semicircular hoops having a thickness of 0.5 in. and a width of 2 in. Determine the normal stress in hoop AB if the tank is subjected to an internal gauge pressure of 2 psi and this loading is transmitted directly to the hoops. Also, if 0.25-in.-diameter bolts are used to connect each hoop together, determine the tensile stress in each bolt at A and B. Assume hoop AB supports the pressure loading within a 12-in. length of the tank as shown.
I have the solutions manual. so I know the answer for normal stress in the hoop is 432 psi and the tensile stress in the bolts is 8800.63 psi. I understand why the answers are these. What I don't understand is the forces in the cross-section represent.
What is the Fr force and the F force? Is Fr the froce from the pressure on the wall? Is F the force of the hoop/bolts? I'm just a little confused.
Explanation / Answer
Fr is the resulant force from the pressure of the gas. Which is equal to the cross section x pressure, (12*36) * 2 = 864 lbs. F is the force of the bolts/hoops holding the barrel together. F = Fr/2 since there are two F's. So F = 432 lbs which is the axial stress in the bolts/hoops. HOpe this helps.