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!

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?

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?

 

[tiny-tim]

Why do the (visible) arrows have to face that particular direction?

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.

 

[tiny-tim]

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

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.