Yes you have a linear structure so you can use superposition. So work out the moment along the beam for each individual load, and then add them together. Or, construct a shear force diagram and integrate it to get bending moment.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
Is there a quick way to determine which one has highest moment? Or perhaps we can extrapolate from say comparing the denominator (one point load: M=PL/4, but I don't know what are the formulas for 2 or 3 point loads)? Thanks!
Do you know the formula for finding the moment in the beam due to a single point load in the middle?
Do you know the formula for finding the moment in the beam due to a distributed load along the length of the beam?
Which one of these formulas results in a larger moment (assuming total vertical load resisted is equal)?
As you keep dividing your point load up and distributing it along the length of the beam, it becomes more and more like a distributed load. So, we can say multiple point loads evenly distributed will result in a moment somewhere between a single point load in the middle and a fully distributed load.
> I don't know what are the formulas for 2 or 3 point loads)
You don't need a formula. My approach looking at the problem (since I didn't initially recognize thru intuition where along the beam the highest moment would lie) was to sketch out a shear and bending moment diagram:
[li]First sketch out your force distribution. It will consist of dirac delta impulse function for each point load (include your reaction forces as point loads).[/li]
[li]Then sketch out shear distribution as the integral of force with respect to distance along the beam. For your case no distributed load, the shear is constant between each point load and step-changes at the point loads.[/li]
[li]Then sketch out moment distribution - it is proportional to the integral of shear with respect to distance along the beam (proportionality constant depends on the beam... the same in all 3 cases)[/li]
Edit - there are a lot of ways to solve this. If you want to just look up formulas (assuming you know where highest moment is) then that can answer your homework problem but no-one here is going to look up those formulas for you, and we will encourage you to not just look for an answer but more to look for something that helps you understand. Shear and bending moment diagram is a powerful and fundamental tool for beam analysis (under Euler Bernoulli assumption) that is well worth understanding imo (and will save you from having to memorize a bunch of other beam results because you can derive many of them yourself). And apparently for Greg too... I hadn't noticed he already suggested that before me.
Got it. I should have thought about it before: distributed load is essentially the same as having multiple point loads acting on the beam. Thanks, guys!
be careful if the image in your original post is accurate then stated another way the problem is:
Which has the peak moment:
- All of the load applied at the center of the beam
- 1/2 the load applied at the 1/4 and 3/4 points
- 1/3 the load applied at the 1/4, 1/2, and 3/4 points
Intuitively moving some load towards the support will reduce the bending demand on the beam, so option 1 will have the largest moment as it places all of the load at the furthest distance (moment arm) from both supports.
Calculate the reactions for each of the three beam cases and then draw the shear and moment diagrams for each. If you do not understand this, you better ask the professor for some help before it is too late. What you asked about is as simple as structural design can be. It only gets harder from here on. Don't wait.
I found with beam problems that finding the reaction forces, drawing the shear force diagram, and then sketching the bending moment diagram, was so powerful that I almost always did it unless I was given a cookbook problem.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
