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
MathsRetard09
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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.
 
  • #5


Dear student,

Thank you for reaching out for help with your homework question. Based on the information provided, it seems like you are on the right track in terms of finding the suitable size for the gantry girder beam. Let me provide some clarification and guidance to help you proceed with your solution.

Firstly, M represents the bending moment in the equation sigma max = M / Z. This moment is the product of the applied load and the distance from the point of support to the point where the bending stress is being calculated. In this case, the maximum bending stress in the girder is given (32MN/m^2) and the modulus of elasticity (E) is known. Therefore, you can rearrange the equation E/R = sigma/y = M/I to solve for the moment, M.

Once you have the moment, you can use it to calculate the section modulus, Z, which is a measure of the resistance of the beam to bending. This can be done using the equation Z = M / sigma max. With the section modulus known, you can then look up the appropriate beam size in the standard section table for gantry girders.

In terms of the other questions, to determine the radius of curvature, you can use the equation R = E / sigma max, where E is the modulus of elasticity and sigma max is the maximum bending stress. To determine the actual maximum stress value in the chosen beam, you can use the equation sigma max = M / Z, where M is the bending moment and Z is the section modulus.

I hope this helps guide you in the right direction. Remember to always check your units and make sure they are consistent throughout your calculations. Best of luck with your homework!
 

What is a simply supported beam?

A simply supported beam is a type of structural element that is supported at both ends and carries a load along its length. It is one of the most commonly used structural elements in buildings and bridges.

How do you determine the reactions at the supports of a simply supported beam?

To determine the reactions at the supports of a simply supported beam, you can use the equations of equilibrium. The sum of forces in the vertical direction must equal zero, and the sum of moments about any point must also equal zero. By solving these equations, you can determine the reactions at the supports.

What are the different types of loads that can act on a simply supported beam?

The different types of loads that can act on a simply supported beam include point loads, distributed loads, and moments. Point loads are concentrated forces acting at a specific point on the beam, while distributed loads are spread out along the length of the beam. Moments are rotational forces that can cause bending in the beam.

How do you calculate the deflection of a simply supported beam?

The deflection of a simply supported beam can be calculated using the equation: δ = (WL^3)/(48EI), where δ is the deflection, W is the load applied to the beam, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. This equation assumes that the beam is made of a homogenous material and has a constant cross-section.

What are the limitations of a simply supported beam?

A simply supported beam has some limitations, including its ability to resist lateral or torsional forces. It is also not suitable for long spans or heavy loads. Additionally, the assumptions made in the calculations for a simply supported beam may not always accurately reflect the real-world behavior of the beam. Therefore, it is important to consider these limitations when designing a structure using simply supported beams.

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