General loading, shear and moment relationships

emRage

Hi everyone,

I'm struggling to get my head around the convention of internal moments and shear forces of a loaded beam.

I just can't seem to make any sense of why F is facing upwards and F+dF is facing downwards. It's driving me absolutely insane. Surely both of them will be facing upwards to cancel out wdx?

Please help =/

Thank you.

tiny-tim

Hi emRage!
No, the F upward shown on the left of the section matches the F downward (not shown) on the right of the next section to the left (Newton's third law!).

And the next section to the right will similarly have an F + dF upward on its left (not shown), and that matches the F + dF downward shown.

To look at it another way …

the wdx is a very small amount, and tends to zero as dx tends to zero.

It must therefore be "cancelled" by an equally very small amount …

and that isn't going to be the rather large F + F + dF, is it?

emRage

Thank you tiny-tim,

Now my next question is:

The arrows for F and F+dF are facing that way to cancel out the hidden F and F+dF. Why do the (visible) arrows have to face that particular direction? Because if I were to change the direction they are facing, that would change the shear force and bending moment equilibrium eqtns am I correct?

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tiny-tim

They don't have to.

If you put the arrows that way round, and then solve the equations, you'll find that F will come out negative.

In some problems, it isn't at all obvious which way up they should be, so you just have to make a guess, and if the guess turns out wrong it doesn't matter … you'll have, say, -3N up instead of 3N down … same thing.

emRage

Thanks for ur help, Ok so here's the next question,

C-section beam of 300mm , Sy = 1000N
Finding bending stresses 100mm from the point of load...The force causes compression on top and tension on the bottom hence bottom stresses should be +ve and top stresses -ve.

100mm from the point of load would mean a bending moment of 1000x100 = 100000Nmm in the positive sense about x-axis.

The bending moment caused by Sy in this case is +ve Mx (moment in the x-axis). Am I correct?

I'm getting positive values at the top corners and negative at the bottom corners for bending stress which is clearly wrong!

Regards.

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tiny-tim

uh-uh, can you please start a new thread?

(and can you make it clear where the point of application of the force is?)

Then other members will come in and help …

all this stress and moment is getting a bit out of my depth.