Simply Supported Beams - Stuck On A Question

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In summary, to determine a suitable size for a gantry girder beam, you need to find the appropriate Z value from your properties table that will result in a maximum bending stress of less than 32 MPa when given a maximum bending moment of 120 kNm. This will help you choose the correct girder from the standard section tables.
  • #1

Homework Statement

This is the question i am asked:

Determine a suitable size for the (gantry girder) beam selected from standard section tables.

Prior to that is some information:

The cross-section of the beam shows that of a Gantry Girder. The maximum bending stress in the girder musn't exceed 32MN/m^2 and the modulus of elasticity can be assumed to be 280GN/m^2

Homework Equations

What has been looked at in class before being given the homework follows:

Section Modulus: Sigma max = M / Z

Theory of Simple Bending: E/R = sigma/y = M/I

The Attempt at a Solution

I believe I need to find Z to help locate in the standard section table the chosen girder.

Looking at the information, i have the following values known:

sigma max = 32MN/m^2 = 32 x 10^6 N/m^2
Modulus of E = 280GN/m^2 = 280 x 10^9 N/m^2

Thats all i have, i know it's a gantry girder so in the section tables i look in the table for gantry girders only.

I remember doing something in class to find the Z value, which when known you look into the Zxx column of the table and find the nearest values to yours and then read the row to find the breadth and depth.

What does M represent in this equation: sigma max = M / Z? I know it isn't the modulus of E.

Thats why I'm looking at this other equation: E/R = sigma/y = M/I - because both values known are in this equation, but how to i find M from this if this is how i do it?

I have questions following this one such as:

Determine radius of curvature and Determine the actual maximum stress value in the chosen beam.

I don't want help with these, i just need reminded of how to find the right girder or am i mis-reading the question and i should just chose one instead?

The sooner you reply the sooner i can thank you :)
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  • #2
There's probably some stuff that you haven't told us about your problem.
Steel tables don't have a section titled 'gantry beams'. Beams are listed by size and/or weight.
You are given maximum bending stress for the material. Perhaps M is the bending moment?
If you want more help remembering what it is you want to do with this problem, supply us with more information.
  • #3
I have a sheet titled 'Tables of Properties'

On it are Universal Beams, Structural Tees and Gantry Girders.

Before this question i drew a simply supported beam with two UDL's, a SFD and a BMD, But that is irrelevant to this erm...

My maximum bending moment was 120kNm however on my BMD analysis. If that could be my M value then I'm sorted, but before i dive in, could you confirm if ths sounds right?

Thanks for replying and for pointing out the lack of info, i tried my best.
  • #4
Select Z from your properties sheet so that the max. bending stress of your gantry beam is less than 32 MPa, given the max, BM of 120 kNm. You might have two Z values for each girder, so choose the one which is correct for the way the bending moment is applied.

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