Why is the Maximum Bending Stress in a Hogging Beam Compressive at the Bottom?

[MathsRetard09]

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.

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

... \sigma


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.

 

[PhanthomJay]

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.