Simply Supported Beam Question

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In summary: This is a compressive stress since the top fibers are being squeezed together. Overall, the maximum bending stress is compressive for this particular example. In summary, for a beam that is 'hogging', the maximum bending stress is compressive. This is because the top fibers are being squeezed together, causing compressive stress, while the bottom fibers are being stretched, causing tensile stress. In a symmetric beam, these stresses would be equal, but for an asymmetric beam, the maximum stress will occur at the outmost fibers of the flange furthest from the neutral axis, resulting in a compressive stress.
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MathsRetard09
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Homework Statement



Question: Sketch the cross section of the gantry girder and indicate on it the position of the maximum bending stress. State if this stress is tensile or compressive for this particular example, explain how you decided

Homework Equations



There aren't any required

Relevant information however: The Beam is Hogging and the Maximum Bending Stress is positive

The Attempt at a Solution



I've sketched the cross-section and previously indicated the maximum bending stress on the top to indicate the tensile factor.

However this is wrong and instead is Compressive.

What i struggle with is explaining why this is the case.

___________
|.....|
...|...|
...|...|
...|...|
...|...|
____|...|____
|.....|

... [itex]\sigma[/itex]


This is the cross section with the sigma sign beneath to indicate the max bending stress is compressive.

Just to show visually what I've done.

I just need help explaining why it would be compressive / how i decided. Just to clarify, i didn't decide this, i was told by my tutor but i have to figure out why and there's nothing out there on the internet that discusses this.
 
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  • #2
If a beam is 'hogging', it is deflecting upward, that is, it has upward curvature. This tends to expand (stretch) the topmost fibers and to compress (squeeze) the bottom fibers, as you can see by drawing a quick sketch. The top fibers would be in tension and the bottom fibers would be in compression. For a symmetric beam, these 2 stresses would be equal. If the beam is not symmetrical, which apparently is your case, the max stress occurs at the outmost fibers of the flange furthest from the neutral axis.
 

1. What is a simply supported beam?

A simply supported beam is a structural element that is supported at two points, typically at its ends or near its ends. These supports allow the beam to freely rotate and move vertically, but not horizontally.

2. How do I determine the reactions at the supports of a simply supported beam?

The reactions at the supports of a simply supported beam can be determined using the equations of static equilibrium. The sum of all vertical forces must equal zero, and the sum of all moments about any point must also equal zero.

3. What are the key assumptions made in the analysis of a simply supported beam?

The key assumptions in the analysis of a simply supported beam include: the beam is straight and the cross-section remains constant, the material is homogenous and isotropic, the beam is loaded in its plane of symmetry, and the beam deflects only in its vertical direction.

4. How do I calculate the maximum bending moment in a simply supported beam?

The maximum bending moment in a simply supported beam occurs at the midpoint of the beam, and can be calculated using the formula Mmax = WL/4, where W is the applied load and L is the length of the beam.

5. Can a simply supported beam support a varying load along its length?

Yes, a simply supported beam can support a varying load along its length. The bending moment at any point on the beam can be calculated using the equation M = WLx/2, where x is the distance from the support to the point of interest.

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