Topic 8.7b - Special Topics - Problem Assignment 2
1. A structural element with given axial and shear stresses is shown in Diagram 1.
Determine principal planes, the principal stresses, and the maximum shear stress.
[16.8o, 106.8o, axial max 6,606 psi.,axial min -606 psi., shear = 3606 psi.]
Also determine the axial and shear stresses on a plane which makes an angle of 37 degrees counterclockwise from the negative vertical axis in the given element.
[axial 5750 psi., shear -2235 psi.]
2. A structural element with given axial and shear stresses is shown in Diagram 2.
Determine principal planes, the principal stresses, and the maximum shear stress.
[41.4o, 131.4o, axial max 9,530 psi.,axial min -1,470 psi., shear = 4030 psi.]
Also determine the axial and shear stresses on a plane which makes an angle of 60 degrees counterclockwise from the negative vertical axis in the given element.[axial 8714 psi., shear -2433 psi.]
3. In Diagram 3 we have shown a shaft attached to a wall at end A with a torque of 1800 ft-lb. and a horizontal axial force of 24,000 lb. acting at end B.
Determine the principal planes, principal stresses and the maximum shear stress for a structural element on the outer edge of the shaft. (We will assume that the normal axial stress is uniform across the area of the shaft.)
[56.3o, 146.3o, axial max 6,112 psi.,axial min -2,716 psi., shear = 4,414 psi.]
4. A loaded cantilever beam is shown in Diagram 4. The beam cross section is a 2" by 2" square.
Determine the principal planes, principal stresses, and maximum shear stress on a structural element 1/2 foot from the wall, and at point P in the cross sectional area, as shown in Diagram 4.
[2.4o, 92.4o, axial max 20,285 psi.,axial min -35 psi., shear = 10,160 psi.]
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