Any enginers in? calculation question...
 

1. A steel tape 40m long has cross section of 12mm x 1mm.
Find the stress if the entire tape is stretched and held taught by a force of 50N.
What will be the increase in length? (Assume E= 206 GN/m sq)

2. A hollow cast iron cylinder has external dia 250mm and internal dia 200mm. It is 3m long.
What is the stress and by how much will it shorten under a compressive load of600kN/ (Assume E= 55GN/m sq).

Thanks for any help......

In both cases the quality of the material will determine the answer.

With the pipe is the load being applied internally, externally or longitudinally?

I agree ...... It's basics :rolleyes:

For the first question I will assume the load is applied to the cross section. Therefore stress = force/area and use the cross sectional area. Strain = stress/E. Change in length = strain x original length

Second question is exactly the same method as to shorten the cylinder significantly it will have to be loaded axially. Therefore calculate the CSA (outer area - inner area which is why you have been given 2 diameters) then follow the same method as above. This time your stress and strain will both be negative (compressive force), therefore showing the cylinder will "shorten"

Note - you will have to use SI units for all these calculations ie N, m and Pa which will give you a final change in length in metres

E is the modulus of elasticity, which defines how the material deforms under a given force.

For Q1, assuming gravity isn't a factor, the stress is 50N on a cross-sectional area of 12mm^2, so 4.1667x10^6 N/m^2. E is the theoretical stress required to double the length of the tape (theoretical because it only applies to elastic deformation, and doubling the length would not be elastic). So the increase in length is 40m x 4.1667x10^6 / 206x10^9 = ~0.81 mm.

I'll leave you to do Q2 - you need to work out the cross-sectional area of the solid part of the pipe, then follow the same process as Q1.

Jef,

Why do you need to know?

Chip

Basic strength of materials.. :luxhello:

================================================== ==========

stress=force/area (N/m^2)

strain=observed change in length/original length (unitless ratio)

Elastic modulus=stress/strain (N/m^2)

================================================== ==========

You can solve your questions with the above. :thumb:

It's more stuff the lad is revising for his exams after Christmas.

didnt he listen in class then???

:lol1::lol1::lol1:

Does he have an engineers pocket book?. They are invaluable.

Yes, he listened and hasn't missed a lecture yet, but they are doing stuff he's never touched before, whereas the others have got "A" levels etc so have the underpinning. Also the lecturers go at top speed to cover large amounts of work, aqnd it's up to the student to make sense of it...which is where I'm coming in;)
He doesn't have a pocket book, what is one and can you recommend one please?

Quick search for structural engineering - others available for mechies etc... http://www.google.co.uk/products/cat...ed=0CHEQ8wIwAw

Jef,

There are lots of different pocket books to suit all kinds of engineering. Best to go along to a good bookshop and take a look. I got mine in Waterstones years ago, I assume they still sell them. Cost less than a tenner I seem to recall. It's been invaluable over the years.

Chip

Check out ebay as well.

University bookshop probably a good idea, I'll tell him to ask his tutor.
He's already bought a good book on Mechanics, on the tutor's recommendation.

Although these days, they tend to recommend NOT buying, with books at £50- £100, and only used for part of the content, or for part of a year, the internet is preferred.

What about 2nd hand books, Jeff? Is there a market for them with new costing so much? Or are the prices on them inflated too.

Was the link I posted of any use :)