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posted by  makoy on 7/18/2008 2:45:37 AM  |  status: Live  

Torsion Stress

Course Textbook Chapter Problem
Fluid Mechanics Fundamentals of Fluid Mechanics (4th) by Munson, Young, Okiishi N/A N/A
Question Details:
The compound shaft consist of bronze and steel segments both having 120 mm diameter. If the torque T causes a maximum shear stress of 80 MPa in the bronze segment, determine the angle of rotation of the free ent. Use G = 83 GPa for Steel and G = 35 GPa for bronze.
Bronze = 4.5 meter
Steel    = 3.5 meter

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posted by rooya on 7/26/2008 7:30:55 AM  |  status: Live
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d=dAB=dBC=120mm=0.12m
fAB=80MPa = 80*10^6 N/m2
GBC=83*10^9 N/m2
GAB= 35*10^9 N/m2
JAB=JBC= πd4/32 = π*0.124/32 =2.036*10-5
Torque in AB
TAB=π/16 *f*(dAB)3 = π/16*80*106 *(0.12)3
TAB =27143.36N.m
we know that  T/J = Gθ/L
θ= TL/JG
θB=TAB*LAB/ (JAB*GAB) =  TAB*LBC/(JBC*GBC)
TBC =TAB * (JBC/JAB)*(GBC/GAB)*(LAB/LBC)
TBC = 27143.36 * (83*10^9/35*10^9)*(4.5/3.5)
TBC = 82759.55
At free end
θC= (TBC*LBC)/(JBC*GBC) =82759.55*3.5/(2.036*10^-5 * 83*10^9)
θC= 0.17 rad
 
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posted by mousey on 7/26/2008 11:13:26 AM  |  status: Live
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