# Solid Hollow Shaft Torsion Resistance: How Will It Change?

• praveenpandiyan
In summary, the conversation is about the effect of melting a hollow shaft and creating a new solid shaft on its resistance to torsion. It is determined that the torsional resistance of the solid shaft will decrease compared to the hollow shaft, as it is proportional to the polar moment of inertia. However, there is some confusion about whether the cross sectional area or the polar moment of inertia should be considered. After further discussion, it is concluded that the polar moment of inertia is the key factor in determining the torsional resistance.

## 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]

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".

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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?.

Yes, torsional resistance decreases.

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

Chet

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 :(

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 :(

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

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
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

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

yeah thanks Nas.