A 165.1 times 3.0 CHS manufactured by Smorgon Steel Tube Mills is built-in at th

Question

A 165.1 times 3.0 CHS manufactured by Smorgon Steel Tube Mills is built-in at the base and is experiencing a variety of loads. It experiences 2 applied twisting moments and an unknown axial tension. The torques are applied at mid-height and at the end, while the tension is applied at the free end. At the support, there is a point on the outer surface of the CHS which is under consideration. The Smorgon Steel Tube Mills product catalogue gives the following geometric properties for this section A = 1530 mm^2, I = 5.02 times 10^6 mm^4, Z = 60.8 times 10^3 mm^3, J = 10.0 times 10^6 mm^4. Draw the BMD, TMD and AFD and determine the internal actions that apply at the cross-section at the support. At the point under consideration, determine the stress due to the torsion. Is this a normal stress or a shear stress? Use von Mises' yield criterion and given that f_y = 400 MPa, determine the maximum value of P that will cause yielding due to the combined stresses caused by P and the applied torques. Draw a diagram that shows the stresses acting at this point, draw the Mohr's circle, and establish the principal stresses for this point based on the value of P calculated in (c). How would the answers to (b) and (c) above change if the point under consideration was on the inside surface of the CHS? Explain the answer.

Explanation / Answer

Using index notation prove the following identities among vectors A,B,C,D a- (AXB)X(CXD)=[A.(CXD)]B-[B.(CXD]A

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