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# Thermal expansion effects on inside diameter of hole2

## Thermal expansion effects on inside diameter of hole

(OP)
If a steel plate containing a hole were heated, would the inside diameter increase?
Replies continue below

### RE: Thermal expansion effects on inside diameter of hole

Depends on the shape of the steel plate. Is it the steel plate flat or cylindrical--go figure it out.

### RE: Thermal expansion effects on inside diameter of hole

Yes. We fabricate large centrifugal fan inpellers that qualify as "a plate with a hole in it". We heat the hub of the fanwheel. The bore of the hub (hole) enlarges. We then install this on a cold shaft to achieve a "shrink fit".

lesgutzy

### RE: Thermal expansion effects on inside diameter of hole

Every dimension will increase by the same percentage, even the diameter of the hole.

### RE: Thermal expansion effects on inside diameter of hole

So... my professor who said "holes shrink, rings grow" was incorrect?

### RE: Thermal expansion effects on inside diameter of hole

TCM,

No, your professor was correct.  The previous answers are ambiguous, mainly because this phenomenon is dependent highly upon the specific geometry of a component.

### RE: Thermal expansion effects on inside diameter of hole

2

Read attentively the given condition: “a steel plate containing a hole were heated”

The answer is as simple as that:  if the whole plate is heated – INCREASE; if the local heating (around the hole) is applied – DECREASE.

The same is valid for a RING or ANY OTHER SHAPE

### RE: Thermal expansion effects on inside diameter of hole

Let's assume a square hole: each side (metall) will
expand -- so will the hole, too.

### RE: Thermal expansion effects on inside diameter of hole

Viktor,
No no no for local heating.  It also depends on how much material is around the hole.  If there is minimal material around the hole, the thermal expansion of the heated volume can strain the unheated perifery so that even though the net effect is increase in hole size.

### RE: Thermal expansion effects on inside diameter of hole

Metman

I agree with that. There is alway a transition zone where you can have even no effect of local heating - you heat but the diameter does not change.  However, this is relatively small "gray" area.  In reality you may have both INCREASE and DECREASE depending upon the force balance, which, in turn, depends on how much material you have around the hole.

### RE: Thermal expansion effects on inside diameter of hole

Every metal expands when heated, unless restrained, thus the material around the hole expands and the diameter increases, providing of course you haven't heated your steel ruler up at the same time.

### RE: Thermal expansion effects on inside diameter of hole

Corus

You contradict to your statement about restriction.  If you try heat material around the hole and other part of the plate is not heated thus preventing expansion – where this material goes?  The material expands to the direction of the least resistance - is it clear?  If not, select u unit volume of the material and construct a free-body diagram – see for example Section 8.10 Problems Involving Temperature Changes in Beer F.P. and Johnson E.R “Mechanics of Materials” 5ed. McGraw-Hill and try to solve problem 2.45 (p. 61)  - it might help to understand.

### RE: Thermal expansion effects on inside diameter of hole

There is going to be a lot of resistance to making that hole smaller due to thermal expansion.  There's not really "room" for the material to expand inward.

I'll have to see if I can find a copy of the 5th edition.  I have my 2nd edition from when I took the class, and, from reviewing the "Problems Involving Temperature Changes" in that edition, I don't see how that's going to make the hole get smaller.

Edward L. Klein
Pipe Stress Engineer
Houston, Texas

All opinions expressed here are my own and not my company's.

### RE: Thermal expansion effects on inside diameter of hole

Viktor,
If something is heated and restrained from expansion then the material is compressed to remain in the same space. It basically doesn't go anywhere and is subject to compressive stresses. If you locally heat a hole in a plate then the region around the hole will be in compression and material away from the hole will be in tension. There will however still be some increase in the hole diameter as the material away from the hole is not infinitely stiff to resist the thermal expansion presumably.

### RE: Thermal expansion effects on inside diameter of hole

The hole diameter in any geometry will expand. Think about what is happening on the atomic scale! The vibratory ation increases so the RMS distance of the individual molecules increases therefore the hole expand!

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