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PROBLEM 3 (20 PTS) l=4 in, a=20 in, t=0.5 in, h=1 in, F=50 lbf, od=1 in, id=0.75 in a) Draw the Free Body Diagram for the tube. For point A (top of tube near wall) show Shear and Moment Diagrams for the tube. Determine the bending torque T, moment M, and shear V at point A. b) Determine the torsional shear stress at A: $\tau_{xy} = \frac{Tr}{J}$, where $J = \frac{\pi(d^4 - d^4)}{32}$ c) Determine the bending stress, at A: $\sigma_x = \frac{Mc}{I}$, where $I = \frac{\pi(d^4 - d^4)}{64}$ d) Determine the transverse shear stress at A: $\tau_x = \frac{VQ}{It}$, where $r = \frac{2V}{A}$ for a tubular cross section. e) This is a plane stress case, so draw the incremental element at A with stresses acting it and determine the principal stresses at A, where $\sigma_1 = \frac{\sigma_x + \sigma_y}{2} + \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}$ and $\sigma_2 = 0$ (Note: sum the $\tau_{xy}$ components) Double-sided printing Mid term Exam - Spring-Summer Intercession 2016 10/12

          PROBLEM 3 (20 PTS)

l=4 in, a=20 in, t=0.5 in, h=1 in, F=50 lbf, od=1 in, id=0.75 in
a) Draw the Free Body Diagram for the tube. For point A (top of tube near wall) show Shear and Moment
Diagrams for the tube. Determine the bending torque T, moment M, and shear V at point A.
b) Determine the torsional shear stress at A: $\tau_{xy} = \frac{Tr}{J}$, where $J = \frac{\pi(d^4 - d^4)}{32}$
c) Determine the bending stress, at A: $\sigma_x = \frac{Mc}{I}$, where $I = \frac{\pi(d^4 - d^4)}{64}$
d) Determine the transverse shear stress at A: $\tau_x = \frac{VQ}{It}$, where $r = \frac{2V}{A}$ for a tubular cross section.
e) This is a plane stress case, so draw the incremental element at A with stresses acting it and determine the
principal stresses at A, where $\sigma_1 = \frac{\sigma_x + \sigma_y}{2} + \sqrt{(\frac{\sigma_x - \sigma_y}{2})^2 + \tau_{xy}^2}$ and $\sigma_2 = 0$ (Note: sum the $\tau_{xy}$ components)
Double-sided printing
Mid term Exam - Spring-Summer Intercession 2016
10/12

PROBLEM 3 (20 PTS)

l=4 in, a=20 in, t=0.5 in, h=1 in, F=50 lbf, od=1 in, id=0.75 in
a) Draw the Free Body Diagram for the tube. For point A (top of tube near wall) show Shear and Moment
Diagrams for the tube. Determine the bending torque T, moment M, and shear V at point A.
b) Determine the torsional shear stress at A: τxy = (Tr)/(J), where J = (π(d^4 - d^4))/(32)
c) Determine the bending stress, at A: = (Mc)/(I), where I = (π(d^4 - d^4))/(64)
d) Determine the transverse shear stress at A: = (VQ)/(It), where r = (2V)/(A) for a tubular cross section.
e) This is a plane stress case, so draw the incremental element at A with stresses acting it and determine the
principal stresses at A, where σ1 = ( + )/(2) + √((( - )/(2))^2 + τxy^2) and σ2 = 0 (Note: sum the τxy components)
Double-sided printing
Mid term Exam - Spring-Summer Intercession 2016
10/12

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