# Radius of Curvature in a simply supported beam

1. Nov 20, 2007

### spggodd

Hey, hopefully this is a suitable forum to put this in! I've been having a bit of trouble trying to find an example to learn from about finding the raidus of curvature in a simply supported beam.

I've got a point loads and a UDL to take into account and seem to find it near impossible to find any examples where the two are combined.

If it helps the question is as follows:

1. A simply supported beam of length 6m supports a vertical point load of 45kN a distance of 4m from one end. If the maximum allowable bending stress is 120MPa:

If the beam has a young's modulus of 200GPa calculate the radius of curvature.

Any information you might need just ask!

Thanks!!

Edit: Read a sticky and you want my own attempt?

Well I would show you what I've done but im that stuck that i dont have anything!!
I'm just trying to get hold of some useful info to get started!

Last edited: Nov 20, 2007
2. Nov 20, 2007

### TVP45

What class is this from? What text do you use?
Have you Googled this? With what results?

3. Nov 21, 2007

### spggodd

This from an Mechanical Engineering HNC course, in the engineering science unit on Static engineering systems assignment.

The text books i have are Higher Engineering science by W. Bolton and also Higher Engineering Maths by J. Bird + various handouts which i cant seem to find the information needed.
I've also had a look through the general Higher engineering book by M Tooley i think?

I've googled it but it just comes up with results about calculating laser curvature radius and when i go more specific in my query it doesnt bring back hardly any results.

4. Nov 21, 2007

### PhanthomJay

I don't often see problems asking for curvature raddii based on the deflected the shape of the beam under load, , but in any case, it can't be calculated without knowing the moment of inertia of the beam's cross section...is it given?

5. Nov 22, 2007

### spggodd

i have a sheet tha tcame with my assiugnment based on BS 5950-1:2000 which guives me some universal beams, dimensions and properties but i catn see the moment of inertia on it?

But.. seein as the beam is supported at both ends i wouldn't have thought it would be spinning therefore not having a angular momentum? (moment of inertia)

6. Nov 22, 2007

### spggodd

I have just read about about moments of interia and they say that sometimes its called the 2nd moment of area.. which i DO have!

in the X-X axis it is 10087cm^4 and in the Y-Y axis it is 357cm^4

7. Nov 22, 2007

### PhanthomJay

Well fine, then the radius of curvature is simply EI/M , where E is Youngs modulus and the value you use for I depends upon whether the beam is bending about the strong axis (X-X) or weak axis (Y-Y). Now you just need to calculate M as a function of x, the length along the beam. The radius varies along the deflected shape of the beam. Can you calculate the bending moment M?

8. Dec 2, 2010

### spggodd

It appears I am stuck on the same kind of question, yet a little harder.
I googled for an answer and I got linked to this site.. which was a question of mine almost 3 years ago haha!

I was looking for the Engineering Bending Equation to calculate the Raidus of curvature, but the above post has already helped.

Shows how far I've come over the past few years....!