Checking the moment diagram shape for fixed/fixed beam with 2 point loads 2

[kjoiner]

Hello,

This should be a basic question but I want to double check my moments so I can size a frame member and I haven't done this in a while.

I have a beam, fixed on both ends, 87" long with 2 point loads at 29" and 58". Each point load is 543 lb downward. In reality, my point loads are about 1" further outboard, but this approach seems simpler and more conservative.

I arrived at the end moments using M=Pab^2/l^2. This formula should work for beams where the point loads are at l/3. The end moments calculate to 6998 in-lb.

I'm interested in the maximum bending moment so I cut the beam at 29". The moment calculates to 29(543) - 6998 = 8749 in lb.

On my moment diagram, the moment starts at -6998, then jumps vertically to 8749 at 29". Then the moment curve slopes down, crosses 0 at 43.5" and then reaches max negative moment of -8749 in-lb at 58".

Am I correct that the moment line with rise vertically where the shear is 0 (at 29") since the ends have negative moments?

Thanks,

Kyle

 

[IDS]

It would be worth doing a refresher on beam bending basics.

[ol 1]
[li]The formula you used gives the end moment for one load. You have to add in the second load, which for loads at 1/3 span will generate exactly half the moment at end 1.[/li]
[li]Starting from the left hand end you have a constant shear (543 lbf) from the support to the first load, then zero shear to the second load, then -543 to the right hand end.[/li]
[li]The change in bending moment is equal to the area under the shear force diagram, so taking the end moments as negative the bending moment is linear to a positive value at the first load, then constant, then linear to an equal negative moment at the other end.[/li]
[li]Finite applied shear forces can't create a step in the bending moment diagram.[/li]
[li]The maximum absolute moment occurs at the ends. The constant moment between the applied loads at the 1/3 points is exactly half the end moments (and opposite sign).[/li]
[/ol]

I'd suggest sketching out the shear force and bending moment diagrams, and the deflected shape (based on the moment diagram) to get a feel for how they all interact.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[kjoiner]

Hi Doug,

Thank you for responding. I realize I'm rusty on this and I'm trying to arrive at a solution quickly since I need to change my frame drawings in a timely manner to get them into future production runs. My main goal is to determine the maximum bending moment so I can select the correct section properties from available frame members (8020 frame extrusion) to keep the stress at an acceptable level.

I've looked at Rourk's etc. and other sources that show fixed/fixed beams with single point loads.

Your comment #4 does confirm my thoughts about the moment curve. The step in my moment diagram is where I'm wrong and I believe it now makes sense.

I'll re-draw the moment diagram correctly.

Can you confirm that since both end moments are negative, I need to add them together to obtain the maximum bending moment on the beam?

Thank you,

Kyle

 

[kjoiner]

Hi Doug,

Nevermind, I finally got my process straight and the loads are in an acceptable range.

Kyle

 

[robyengIT]

I hope it can help (even if You don't understand italian)