Steel bridges thermal expansion

[dina82]

Hi guys,

Would you please help me with this question:
steel bridge girders are set in place on their bearings when the ambient temperature is 65°F. if the temperature of the steel is expected of 15°F and 95°F . what is most nearly the expansion gap that must be provided at the bearings?
select one:
A.1/8 in
B. 1/4 in
C. 1/2 in
D. 3/4 in
The coefficient of the thermal expansion for steel a= 7.3 *10^-6 /F
Note that girder length=90 ft
Many thanks in advance

 

[BAretired]

That is obviously a homework question, so we can't just hand you the answer. It seems to me that the 65^oF. setting temperature is not relevant to the size of the gap, but is relevant to the location of the gap.

BA

 

[dina82]

The question is for engineering exam, the location of the gap is at support, if we consider the temperature change is between the two extremes, we will get a value doesn’t match with any of the available choices

 

[zeusfaber]

For what it's worth, I think the setting temperature is relevant, and I get a figure very close to one of the answers on offer.

Next step is probably for you to share the value you get, what assumptions you made along the way and what you did to get your value.

A.

 

[dina82]

Thanks for ur reply,

ΔL = α*L* ΔT
ΔL = 7.3 * 10^-6 * 90* 12 *(95-15) = 0.63 inch

Here I considered temperature change between expected extremes

 

[BAretired]

I realize that the gap is at the support, but I was meaning something a little more precise than that. Most nearly does not mean exact. I get an answer which is slightly more than half way between two of the values given. From that, I would conclude that the larger of these values is most nearly the total temperature gap required.

If, by expansion gap, the examiner is referring only to expansion, and not to contraction, my answer would be wrong, in which case the 15^oF. would not be relevant. Moreover, I would consider the question badly phrased and having nothing to do with engineering principles.

EDIT: I got the same answer you did, but I'm not sure that was what the examiner meant.

 

[Eric C.]

The temperature at setting is relevant. Assuming all of the expansion is to be allowed at one end only I get "most nearly" one of the answers. If, somehow, expansion is allowed at both ends I get "most nearly" one of the other answers.

 

[BAretired]

dina82 obviously understands the principle involved. I believe he came up with the correct answer which depends on the complete range of temperatures expected, namely (95-15) or 80 degrees F. The installation temperature makes a difference to where the gap is located relative to the end of the beam, but it does not affect the length of gap. Those who believe otherwise should clarify their reasoning.

In real life, no one works with that kind of precision because the temperature extremes are not known with certainty. Sensible design practice would provide additional movement to accommodate more extreme temperatures.

BA

 

[zeusfaber]

I'm in the same place as Eric. If forced to choose, I would pick an answer (for an exam) based on the assumption that there's a whole series of beams in a row, and calculate each gap based on 1x the expansion of a single beam - but I'd prefer the question to be clearer.

In the real world, you can't afford to sit around waiting for the coldest day imaginable before you place your beams - nor to refrigerate the beams to the minimum design temperature. Instead, you have to set the gap based on the temperature you measure on the day. Bear that in mind, and you start to get answers that match the options on offer.

BA, I think I (and probably the examiner) are using a much more simplistic definition of "gap" than you are.

A.

 

[BAretired]

I believe the examiner is doing what has become commonplace at universities today in order to reduce time required for marking, namely multiple choice questions.

I don't know how the examiner defines "gap". If the connection consists of bolts in a slotted hole, the length of slot is the gap and should include the bolt diameter. If the girder bears on a low friction plate, the only concern would be expansion, in which case, the gap would be for a (95-65) or 30^oF. difference. If it's a neoprene bearing pad, the gap would be the total range of movement, or 80^oF.

And if he considers the possibility of the sun beating down on the beams in the summer, he would likely bump the upper limit up considerably.

Poorly worded question in my opinion.

BA

 

[Eric C.]

My reasoning is that the beam is 90' long at 65 degrees. No gap is needed to provide for shrinkage. A gap is required to provide room for the expansion that would take place when the temperature rises from 65 degrees to 95 degrees.

Bear in mind that my reasoning is based only on the context of the question which appears to be an exercise in thermal expansion and contraction in a Mechanics of Materials class as opposed to a Bridge Design class.

 

[BAretired]

My reasoning is that the beam is 90' long at 65 degrees.

We don't know that. The girder could have been
fabricated at a different temperature. It was nominally 90' long. It was set in place when the temperature was 65 degrees. The beam could be a little longer or shorter when it was installed.

No gap is needed to provide for shrinkage.

We don't know that, but if so, why provide the 15^oF temperature? It depends on the detail used to hold the girder down. If the girder was held down using bolts in slotted holes, or is supported on flexible bridge pads, provision is needed to accommodate contraction as well as expansion.

Bear in mind that my reasoning is based only on the context of the question which appears to be an exercise in thermal expansion and contraction in a Mechanics of Materials class as opposed to a Bridge Design class.

But then why not simply ask the student how much a 90'-0" beam would change length with a particular change in temperature? Of course, an elementary school student could answer that question.


BA

 

[jhardy1]

Let's not over-think this and confuse the OP even further. This is clearly an "Engineering 101" question, and as others have pointed out, if you do the obvious, basic calculations, you arrive very closely at one of the four supplied answers.

If this is a basic multiple-choice test, you often don't even get an opportunity to explain your thinking or working. If the assignment allows for calculations and explanations, the OP could list their assumptions and any simplifications etc.


The problem has obviously been set for first-year engineering students (or equivalent), and the question is phrased to make sure they have a bit more understanding than an elementary student with a calculator. E.g. to work out what information is relevant to the problem, and what might be considered to be a "red herring", or may be relevant in a supplementary question, such as "How much contraction allowance should be provided on the sliding (non-fixed) bearing?"

If this was a real-world problem, these would all be part of the defining parameter set, as would be specification of the applicable bridge codes, solar insolation and shielding effects, composite behavior of the bridge deck, whether bearings of multiple spans are arranged in simple Fixed / Sliding / Fixed / Sliding repeating series (one fixed and one sliding bearing on each pier), or whether they are Fixed / Sliding / Sliding / Fixed / Fixed etc (two fixed bearings on one pier, and two sliding bearings on the next pier).

http://julianh72.blogspot.com

 

[Eric C.]

Sure, the girder COULD have been fabricated at a different temperature but that information wasn't given in the problem statement. The beam COULD have been a little longer or shorter when it was installed, however that information was not given in the problem statement. The problem stated that the beams were 90' long and it was 65 degrees.

Sure, some consideration for shrinkage should be allowed for in the slotting of the holes, however, no information was given on the details of the connection. Maybe the beam was just sitting on a roller in which case I'm not sure a contraction gap would be needed. At least not in the context of this problem.

As to why the question was not simply how much would a beam shrink I think maybe the professor was attempting to equate the issue of thermal expansion to an engineering application. Certainly appropriate for an early class in engineering.