Question

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SI SHAFT WITH VARIABLE SECTION

The shaft BCD in the figure has length L and is composed of a homogeneous material with shear modulus
G. The bar is fixed between walls at B (x = 0) and D (x = L). The shaft has a round cross section, with outer radius changing along the length of the bar as defined by the function:

R(x) = R0/SQUARE R {[1 + (x/2L)]}

A concentrated torque of magnitude Q is applied at the midsection of the bar C (x = /L2) as indicated. Use the Force Method for SI structures taking D as the redundant support to solve this problem.

The given KNOWN quantities are L[m], G[Pa], Q[Nám], and R0[m] (enter this as R_0).


#1:
Obtain a symbolic expression for the redundant reaction Tx(D) in terms of any of the known quantities listed above.
Tx(D) = ?


#2
Obtain a symbolic expression for the maximum magnitude of shear stress in the shaft τ max in terms of any of the known quantities listed above.

T max = ?