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)=R01+x2L.
A concentrated torque of magnitude Q is applied at the midsection of the bar C (x=L/2) 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[N·m], and R0[m] (enter this as R_0).
1) Obtain a symbolic expression for the redundant reaction TxD in terms of any of the known quantities listed above.
TxD=
3) Obtain a symbolic expression for the maximum magnitude of shear stress in the shaft τmax in terms of any of the known quantities listed above.
τmax=
unanswered
At what value of x does this maximum shear stress occur?
Exactly at x=0
At a position in the range 0<x<L/3
Immediately to the left of L/2 (x=L/2−)
Immediately to the right of L/2 (x=L/2+)
At a position in the range 2L/3<x<L
Exactly at x=L
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