Mid Level Statics Problem

I need someone to help me with the first problem on the attachment. Its asking me to find all the forces at each point. I'm a bit confused with how to set up first, and the member connected to the pully is thowing me off.

Elastic plastic beam problem

See attachment. Review1 is similiar to a design I am doing but will be in the plastic regime and curvilinear. Please show me where I am going wrong. thank you.

Elastic plastic rotating shaft problem

(See attached file for full problem description) I think I am going wrong on the doublet function. I have solved this with finite elelments but would like to learn the analytical solution. thank you

Elastic, perfectly plastic infinite thin plate with a hole

The problem I need to solve is this: I have a thin infinitely large plate with a circular hole of radius Ri. A uniform radial pressure, p, is applied at the surface of the hole at R=Ri. 1) i need to figure out how the solution for the stress fields work. If the pressure is less than the pressure to cause yielding the stress tensor is: Trr= -p(Ri/R)^2= - (stress in theta theta direction) (polar cordinates used). HOW DID IT REDUCE TO THIS? HOW IS IT DERIVED? Py is the limiting pressure for complete elastic behavior. 2) If i use the Tresca yield criterion, i need to find Pressure at yield (Py) in terms of the yield stress Y. 3) When p>Py, i need to determine the str... click for more

Find surface area and volume of object through 180 degrees of rotation

I need to calculate the volume and total surface area of a shape that has been rotated through 180 degrees. Please see the attached file.