A tapered thin$-$wall circular shaft has constant wall thickness $t,$ length $L,$ and diameters linearly varying

between $d_A$ at support $A(x=0)$ and $d_B$ at the shaft's free end, $B(x=L).$ The shaft is homogeneous with

shear modulus $G.$

HW$6\_1\_1$

Obtain a symbolic expression for the torsional stiffness $K_T=\frac{Q}{}$ of the shaft in terms of $t,L,G,$ and $d_A.($You

will have factors of $$ in your answers: enter $$ as pi $.)$

$K_T=$

You have used $0$ of $6$ attempts

HW$6\_1\_2$

Obtain a symbolic expression for the maximum shear strain on the generic $x-$section along the shaft, ${}_{\text{m}\text{a}\text{x}}(x)$

$,$ in terms of $t,L,G,Q,x,$ and $d_A.($You will have factors of $$ in your answers: enter $$ as pi $.)$

${}_{\text{m}\text{a}\text{x}}(x)=$