I need to build a set of ramps for my dump trailer. The ramps will be
6' long. I have and want to use 1" x 3" 11 gauge rectangular steel. If
I were to take one 6' piece of this material, stand it on its'
narrowest edge, support it at both ends and place a load at its'
center how much weight will it suppurt before failing. A little
deflection is allright just so it does not permanently bend.

Hello usajohnson, I think I can help you. I searched for properties of
1" x 3" 11 gauge rectangular steel tubing, but that is an odd size. We
will have to calculate the section modulus (excluding corner radius):

S = bd^3 - b1d1^3/6d

b = 1"
d = 3"
b1 = 1 - 2x0.091 = 0.818
d1 = 3 - 2x0.091 = 2.818

S = [(1 x 3^3) - (0.818 x 2.818^3)] / (6 x 3) = 0.483 in^3

M (maximum bending moment) = [P (point load) x l (length)] / 4

Solving for P:

P = 4M/l

M = s x S
Where:
s (allowable bending stress) = .55 x yield strength of steel
To be conservative we will assume that the steel you have is 30,000 psi

M = .55 x 30,000 x 0.483 = 7,969 in-lb

P = 4 x 7,969 / 72 in = 442#

So, you can say that the tubing will safely support at least 442#. The
tubing you have may actually be as high as 50,000 psi yield strength,
but we don't really know.

Please ask for a clarification if there is any of this that you don't understand.

Good luck with your project, Redhoss

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Request for Answer Clarification by usajohnson-ga on 06 May 2006 22:20 PDT

Thank You for your response to my question. According to my suppliers'
catalog this 1" x 3" tubing is "mechanical astm a513". Thanks again.

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Clarification of Answer by redhoss-ga on 07 May 2006 05:58 PDT

Unfortunately ASTM A513 only refers to the method of manufacturing. It
means that your tube was produced by electric resistance welding
(ERW). There are several types available and the yield strength can
vary over a wide range. I think that the 30,000 psi number I used is
probably close to what you have. We would rather be safe than sorry.

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Request for Answer Clarification by usajohnson-ga on 07 May 2006 08:09 PDT

I will call my supplier in the morning to find out the grade. Does the
strength of the steel go up proportionaly with the yeild strength,
that is to say if I were to find that the yeild strength of my
material is 45,000 psi would it mean it cwould support 50% more
weight. Thanks again for answering my question this has been very
helpful.

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Clarification of Answer by redhoss-ga on 07 May 2006 13:49 PDT

Yes, the higher the yield strength, the higher the bending strength.
Give me a new number and I will modify my answer.

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Request for Answer Clarification by usajohnson-ga on 08 May 2006 10:45 PDT

You were right on the mark. The yeild strength is 30,000 psi. Thank
you very much for the help.

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Clarification of Answer by redhoss-ga on 08 May 2006 13:32 PDT

You are most welcome.

This was just the information Iwas looking for. Thia is a very usefull forum.