## Bending moment, Shear force for a beam on a simply supported beam.

## Bending moment, Shear force for a beam on a simply supported beam.

(OP)

Hi,

From the problem in the image, how do we express P in terms of F? Does the couple generated by the I-beam on top of simply supported beam translate as-is into the bottom section and we can draw this as just another beam with 3 point loads? I am trying to refresh my Strength of Materials knowledge but don't know how to approach this.

Thank you, in advance.

From the problem in the image, how do we express P in terms of F? Does the couple generated by the I-beam on top of simply supported beam translate as-is into the bottom section and we can draw this as just another beam with 3 point loads? I am trying to refresh my Strength of Materials knowledge but don't know how to approach this.

Thank you, in advance.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

A simply supported beam loaded by a moment ... reactions are a couple P*L = F*L2 ... yes? the BM diagram starts at zero at the LH end, increases linearly to the load point, drops by F*L2, then increases linearly to zero at the RH end

"Hoffen wir mal, dass alles gut geht !"

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

_{total}P = (F x L2)/L

_{total}www.PeirceEngineering.com

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

Sign of shear and moment shown below is the usual convention.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

+ve shear. +ve force on a +ve face, and a -ve force on a -ve face at the other end...

I use the international convention for signs... You often encounter SFD and BMD drawn using the opposite signage.

-----*****-----

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

~~I don't think that shear diagram is correct.~~The reaction at the left side and right side will be different, and there will be a step in the diagram "a" away from the left support.

I think the shear diagram is correct. When I typed my previous response I missed the upward force "F"

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

There is no concentrated shear in the span of the beam, so there is no jump in the SFD.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

-----*****-----

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

-----*****-----

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

A simple beam supporting gravity load has tension on the bottom and compression on the top. I consider that to be positive moment. For length 'a', this beam has compression on the bottom and tension on top, which I consider negative moment. The short section 'b' has positive moment.

If there is some international convention which says otherwise, I am not aware of it. Common practice is as I have indicated above.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

"Shear diagram is correct... I'd use the opposite signs... +ve shear. +ve force on a +ve face,"-----*****-----

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

I am not sure where you found this convention, dik, but it is not intuitive. The sketch below indicates positive shear on the left end and negative shear on the right side of a beam loaded with gravity load F. When the reaction at A is upward, shear is positive, but in our case, the left reaction is downward, so shear is negative all the way across the beam.

Bending moment at any point 'x' in the span is the integral of the SF Diagram over length 'x', so it makes sense to call the shear negative for consistency, because we choose to call the moment negative for length 'a'.

Perhaps it's not worth debating, because if we view the beam from the opposite side, the sign of the shear is reversed. As Luceid suggested, if you know what you're doing, use whatever convention you like.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

Again, whatever works for us!

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

It was the international convention 55 years back when I first got into stress analysis. I no longer have a source and it may have changed. It is intuitive. With a right hand coord system, the forces could have any of the three axis directions. The face of the surface under consideration would take that axis. For example a force on the x face, acting in the x direction and the stress would be σ

_{xx}and a force acting in the opposite direction would be -σ_{xx}(compression), in the same way, a force acting in the positive x face in the y direction would be -σ_{xy}or (tau)xy. Moments were taken the same way M_{xy}would be a moment on the x face with the vector in the y direction. M_{xx}would be a moment on the x face in the x direction (this would be torsion).I dunno... seems pretty straightforward.

-----*****-----So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

positive is the direction of the right hand orthogonal axis system, generally. +ve x is in the direction of the +ve x-axis. It could be up, down, sideways, or whatever.

-Dik

## RE: Bending moment, Shear force for a beam on a simply supported beam.

## RE: Bending moment, Shear force for a beam on a simply supported beam.

P = 5k

a = 16 ft

b = 4 ft

L = 6 ft (I changed symbol for L2 to simply "L")

HT = 10 ft (even though HT does not matter to the beam solution)

R1 = -1.5k

P = R2 = 1.5k

V = -1.5k throughout beam

M1 = 0.

M4L = -288. k-in [left side of Joint 4]

M4R = 72. k-in (right side of Joing 4)

M5 = 0.

It's a little difficult to do by hand because we are so practiced to draw shear and moment diagrams for the typical beam loads of concentrated forces and uniform loads. Adding the moment from the frame just makes our brains work a little harder.

To solve for P

Sum(M) = 0 = F(L/2)*2 - P(a+b)

P(a+b) = F*L2

P = F*L/(a+b) =5k*6'/(16'+4') = 30/20 = 1.5 k

## RE: Bending moment, Shear force for a beam on a simply supported beam.