Question 3:The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadingsshown. Determine the absolute maximum and minimun shear stresses on the outer surface of theshaft and specify their locations, measured from the fixed end A.Take :AA=1.6BB =0.9CC =1200AN/ m2 kN-m/mAA mCC NmBвB mSolution := CC N-mTABCC N-m2o0ox N.mCC N.m The internal torque for segment BC is Constant T = CC Nm However,the internal for segment AB varies with x,T-2000 x+ A4 = 0; T = (2000x- CC) NmThe minimum shear stress occurs when the internal torque is zero in segment AB.By setting T = 00= (2000x- CC); x=AnsAndd= AA-x =AnsAnsThe maximum shear stress occurs when the internal torque is the greatest. Thisoccurs at fixed support A whered =AnsAt this location,(Ts) = 2000.44 –CC=The polar moment of inertia of the rod is J=(0.03*) = 0.405(10“ )r.Thus,(T) (0.03)T)0.405(10-T.MPaAnsJ

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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 = 1.6 m BB = 0.9 m CC - 1200 kV/m 2 kN-m/m AA m CC Nm B вB m

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 = 1.6 m BB = 0.9 m CC - 1200 kV/m 2 kN-m/m AA m CC Nm B вB m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

The internal torque for segment BC is Constant T = CC Nm However,
the internal for segment AB varies with x,
T-2000 x+ A4 = 0; T = (2000x- CC) Nm
The minimum shear stress occurs when the internal torque is zero in segment AB.
By setting T = 0
0= (2000x- CC); x=
Ans
And
d= AA-x =
Ans
Ans
The maximum shear stress occurs when the internal torque is the greatest. This
occurs at fixed support A where
d =
Ans
At this location,
(Ts) = 2000.44 –CC=
The polar moment of inertia of the rod is J=(0.03*) = 0.405(10“ )r.
Thus,
(T) (0.03)T)
0.405(10-
T.
MPa
Ans
J

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