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Question 3: The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimun shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A. Take : AA = 1.57 m BB = 0.87 m CC = 1207 kN/m Solution : The internal torque for segment BC is Constant T_{BC} = CC Nm. However, the internal for segment AB varies with x, T_{AB} - 2000x + AA = 0; T_{AB} = (2000x - CC) Nm The minimum shear stress occurs when the internal torque is zero in segment AB. By setting T_{AB} = 0 0 = (2000x - CC); x = [] m Ans And d = AA - x = [] m Ans au_{min} = [] Ans The maximum shear stress occurs when the internal torque is the greatest. This occurs at fixed support A where d = [] m Ans At this location, (T_{AB})_{max} = 2000 AA - CC = [] The polar moment of inertia of the rod is J = frac{pi}{2} (0.03^4) = 0.405(10^{-6})pi. Thus, au_{max} = frac{(T_{AB})_{max} c}{J} = frac{(0.03)(T_{AB})_{max}}{0.405(10^{-6})pi} = [] MPa Ans

          Question 3:
The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings
shown. Determine the absolute maximum and minimun shear stresses on the outer surface of the
shaft and specify their locations, measured from the fixed end A.
Take :
AA = 1.57 m
BB = 0.87 m
CC = 1207 kN/m

Solution :
The internal torque for segment BC is Constant T_{BC} = CC Nm. However,
the internal for segment AB varies with x,
T_{AB} - 2000x + AA = 0; T_{AB} = (2000x - CC) Nm
The minimum shear stress occurs when the internal torque is zero in segment AB.
By setting T_{AB} = 0
0 = (2000x - CC); x = [] m Ans
And
d = AA - x = [] m Ans
	au_{min} = [] Ans
The maximum shear stress occurs when the internal torque is the greatest. This
occurs at fixed support A where
d = [] m Ans
At this location,
(T_{AB})_{max} = 2000 AA - CC = []
The polar moment of inertia of the rod is J = frac{pi}{2} (0.03^4) = 0.405(10^{-6})pi.
Thus,
	au_{max} = frac{(T_{AB})_{max} c}{J} = frac{(0.03)(T_{AB})_{max}}{0.405(10^{-6})pi} = [] MPa Ans

$Question 3: The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimun shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A. Take : AA = 1.57 m BB = 0.87 m CC = 1207 kN/m Solution : The internal torque for segment BC is Constant TBC = CC Nm. However, the internal for segment AB varies with x, TAB - 2000x + AA = 0; TAB = (2000x - CC) Nm The minimum shear stress occurs when the internal torque is zero in segment AB. By setting TAB = 0 0 = (2000x - CC); x = [] m Ans And d = AA - x = [] m Ans aumin = [] Ans The maximum shear stress occurs when the internal torque is the greatest. This occurs at fixed support A where d = [] m Ans At this location, (TAB)max = 2000 AA - CC = [] The polar moment of inertia of the rod is J = fracpi2 (0.03^4) = 0.405(10^-6)pi. Thus, aumax = frac(TAB)max cJ = frac(0.03)(TAB)max0.405(10^-6)pi = [] MPa Ans$

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