Advice on working out the thickness of a U beam.

[andy5]

Advice on working out the thickness of a "U" beam.

First off hello all, seems a great forum and I look forward to posting up on here!

I have an problem that needs some advice, I'm trying to work out the thickness of a U-beam. I have a few restriction on the dimensions of the U-beam, here are my specs:

Beam dimensions, Width, Height and Thickness, where H=2W, and T=W/20

The tensile yield strength, factor of safety, length of the U-beam and maximum bending moment have been provided. Knowing these factors, can someone inform me of the formula/method to obtain the width, height and thickness of the U-beam using the information already provided?

Cheers for any replies.

Andy.

 

[edgepflow]

First establish the allowable stress in your beam: allowable stress = yield stress / safety factor.

Then based on the beam bending moments, you can calculate the required section modulus (see Machinery's Handbook or any other source of beam formulas).

Then use a formula for the section modulus of your U-beam cross section to solve for the required thickness.

 

[engtobe]

anymore help for this please?

 

[Studiot]

anymore help for this please?

Help in what way?

 

[engtobe]

an example of how to calculate a channel sections dimensions when

length, yeild stress, max bending moment, load, youngs modulus, strain and max SF.

are all known

 

[Studiot]

The answer has already been given, but in case you found it a bit brief:

The max allowable stress (S_max) is found by dividing the yield stress by the factor of safety.

The Moment of Resistance obviously equals the applied moment (M) and the formula edgepflow was referring to relates this to the max stress and is called the flexure formula.

Max stress = Applied moment divided by section modulus

$${S_{\max }} = \frac{M}{Z}$$

The section modulus is the section moment of inertia (I) divided by the distance (c) from the centroid to the extreme edge.

$$Z = \frac{I}{c}$$

You can find I and c either in standard tables or by calculation using a knowledge of the dimensions.
In the original problem the dimensions were given in terms of the thickeness (T) so an expression to could be written in terms of T and solved to obtain T.

Since the U section is not symmetrical the distance to the extreme compression edge and tension edges will be different so both will need to be checked and the smaller value adopted.

 

[engtobe]

Thanks
we are lucky to have folks like yourself helping us out.

I was under the illusion that it could be done without looking up a table. That is obviously where i was going wrong.

guess that's my only option seeing as i don't know the dimensions.

thanks again :)

 

[Studiot]

You don't need a table, you just have to work out the moment of inertia from first principles, same as with any other shape. Amd a channel is fairly easy since it is only three rectangles.

It's just that since manufacturers publish tables of this data for standard shapes (that they manufacture) such as I beams, angles and channels you might as well use them.

 

[engtobe]

thanks again for your help

I found out i can't use the tables i have to calculate everything without any dimensions just the ratios that andy posted.

the penny finally dropped and I've managed to get it started.

 

[Studiot]

the penny finally dropped and I've managed to get it started.

Excellent.



Come back when you need more help.