Evaluate maximum shear stress, Mechanical Engineering

Evaluate maximum shear stress:

Derive equation subjected to combined bending and torsion for finding out maximum shear stress and its equivalent twisting moment.                                                                                                

Sol.: In general we assume that shaft is subjected to torsion only but in actual practice because of weight of the pulley, couplings, pull in belts or ropes etc, shaft is subjected to bending. Therefore actually in shaft, both the shear stress because of torsion and direct stress because of bending are induced.
From the bending equation,
1248_Evaluate maximum shear stress.png 
From torsion equation,
1366_Evaluate maximum shear stress1.png 
(i) The maximum principal stress at section
1926_Evaluate maximum shear stress2.png 
The bending moment corresponding to maximum principal stress is termed as equivalent bending moment, Me . Therefore;
626_Evaluate maximum shear stress3.png 
Where;

Me = Equivalent bending Moment

M = Maximum Bending Moment from bending moment diagram

T = Torque transmitted

(ii) The maximum shear stress developed at section
439_Evaluate maximum shear stress4.png 
The twisting moment corresponding to maximum shear stress on surface of shaft is called as equivalent twisting moment, Te

. Therefore;
2382_Evaluate maximum shear stress5.png 
Where Te = Equivalent Twisting moment
Finally;

Equivalent Bending moment
1133_Evaluate maximum shear stress6.png 
Equivalent Twisting moment
437_Evaluate maximum shear stress7.png 
Maximum principal stress σmax
1947_Evaluate maximum shear stress8.png 
Minimum Principal stress σmin
1047_Evaluate maximum shear stress9.png 
Maximum shear stress ιmax
816_Evaluate maximum shear stress10.png 
862_Evaluate maximum shear stress11.png

 

Posted Date: 10/27/2012 1:32:08 AM | Location : United States







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