Can I convert multiple point loads into a single uniform distributed load?

I have a beam that has a given limit of 1690 lbs uniform load for a 24" span. I will be subjecting this beam to multiple point loads at different locations on the beam. In order to determine if the loads will exceed the beam allowable limit (1690 lbs) I was wondering if I could add up all these point loads into a single uniform load to compare to the load allowable. Is this possible?

An easy way is to back-calculate the S, section modulus of the beam, and its bending strength then you can verify if it will support your set of loads or any other load.

$$M = S*\sigma_{b .max} = wL^2/8=1960*2^2/8 = 980lbs.ft$$

Therefore you calculate the combined moment of say n point loads P1, P2, P3...Pn separately and add their moments to check if it adds up to less than 980lbsft.

For each individual load, F, the moment is

$$M_{n \max} = F_{n}ab / L$$

Where a and b are the distance of force Fn from the supports.

And sum of all these moments must be less than your beam's max allowed bending moment.

$$\sigma M= M1 +M2+ ..+Mn <980$$

• Thanks for the response. So here's what I did. The beam is a 24 in cantilever. I used the max moment equation for a cantilever with distributed load: (wL^2)/2 to find the limiting value. I obtained 486720 lbs-in. I then added up individual max moments using the formula: wL. The moments sum up to 1533.88 lbs-in. The process above makes sense but the moment I get seems so far below the allowable, its odd. Additionally the max moment is given by the manufacturer as 5070 lbs-in. What do you think might be the discrepancy? – Ryan C Feb 9 at 13:17
• @Ryan C, my be they based the bending strength of the beam on other criteria such as connection limit. how is it connected. or my by it is suppoeted by a post or some plate. can you draw a sketch? – kamran Feb 9 at 16:53

Your design is governed by the moment, the equivalent uniformly distributed load, $$W = \frac{2*M}{L^2} = 17.6 lb/in$$

If you want to place multiple point loads on the beam, you should sum all moments due to the point loads, then compare it with the limit given by the manufacturer.