The discussion revolves around the torsional resistance of a hollow shaft compared to a solid shaft, specifically focusing on how the change in geometry affects torsional resistance. Participants explore the implications of melting a hollow shaft to create a solid shaft, examining the relationships between cross-sectional area, polar moment of inertia, and torsional resistance.
Participants express differing views on the relationship between torsional resistance, cross-sectional area, and polar moment of inertia. There is no consensus on the implications of switching from a hollow to a solid shaft regarding torsional resistance.
Participants have not fully resolved the mathematical relationships involved, and there are assumptions regarding the uniformity of material properties and shaft lengths that remain unexamined.
What does your textbook say?praveenpandiyan said:sorry. J represent torsional constant. its the resistance to torsion. I am i correct ? ..or how can i use area here to calculate variation in resistance. bit confued :(
Don't thank me so soon. I was wrong about it. The shear strain in the shaft is rdθ/dz. If you use this to determine the shear stress, and then the torsional moment, you find that it's the polar moment of inertia that is the thing that comes into play (as you said), not the cross sectional area (as I had said). So your were right in the first place. Senior Moment. Sorry about that.praveenpandiyan said:well .torsion for solid shaft , i have torsion eqn T/J=G*tete/L=shear stess/R
but i found finally its torsional stiffness k=T/twist that provide solution. if not i need to do some ground work myself .thanks chester
It seems well covered here: http://www.engineeringtoolbox.com/torsion-shafts-d_947.htmlpraveenpandiyan said:ok. i get that . so my area of solid shaft = .55*A(hollow ).. but resistance depends on polar moment of inertia right? .
j(solid)=pi/32(D)4 .if I am not wrong .. then does my shaft resistance decreasce?.