Solid Hollow Shaft Torsion Resistance: How Will It Change?

[praveenpandiyan]

Homework Statement

internal diameter of a hollow shaft is two third of its external diameter .if it is melted and new solid shaft is made.what would happen to the shaft resistance of torsion. in percentage?

Homework Equations

as i know T/j=G*angle of twist/length.
torsional resistance=G*teta(twist)

The Attempt at a Solution

i have no idea . any help would be appeciable .thanks[/B]

 

[NascentOxygen]

The first step is to determine the relative diameter of the solid shaft. It comprises the same volume of material as for the hollow shaft, so (assuming shafts of identical lengths), how to determine the dimensions of the solid shaft?

Perhaps start by saying: let the outer diameter of the hollow shaft be "D".

 

[praveenpandiyan]

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?.

 

[NascentOxygen]

Yes, torsional resistance decreases.

 

[Chestermiller]

The torsional resistance is proportional to the cross sectional area, not the polar moment of inertia.

Chet

 

[praveenpandiyan]

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 :(

 

[Chestermiller]

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 :(

What does your textbook say?

 

[praveenpandiyan]

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

 

[Chestermiller]

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

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.

Chet

 

[NascentOxygen]

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?.

It seems well covered here: http://www.engineeringtoolbox.com/torsion-shafts-d_947.html

 

[praveenpandiyan]

yeah thanks Nas.