How do I calculate the bending moment in a beam for my ramp design?

[sockless]

So for school I'm designing a ramp. The problem is that I need to calculate various things in it, none of which I've ever been taught, since I'm pretty sure it's all uni level. I've asked multiple teachers, including my physics teacher and my technology teacher, and they haven't been any help.

Basically, my ramp is a 50.8 mm square aluminium tube with 3.25mm walls, which is 2m long. I want it to be able to hold at least 200kg, which I guess can be modeled as a point force in the middle (i.e. 1m). However, I don't have a clue how to calculate the bending moment, so that I can calculate the strength of the beam (via it's section modulus, which I have figured out). The ramp is supported at both ends and can be modeled as being horizontal. I've looked on the internet, but nothing makes any real sense.

I don't want the solution as much as I want an explanation on how to calculate the bending moment.

 

[huntoon]

Basically, my ramp is a 50.8 mm square aluminium tube with 3.25mm walls, which is 2m long. I want it to be able to hold at least 200kg, which I guess can be modeled as a point force in the middle (i.e. 1m). However, I don't have a clue how to calculate the bending moment, so that I can calculate the strength of the beam (via it's section modulus, which I have figured out). The ramp is supported at both ends and can be modeled as being horizontal. I've looked on the internet, but nothing makes any real sense.

I don't want the solution as much as I want an explanation on how to calculate the bending moment.

let's calculate beam deflection first. as if it were horizontal.

you have to look up the young's modulous for aluminum. Wikipedia says 69 gigapascals.

okay here's the most basic equation:

(length of beam * force) / (young's modulus * cross section area)

result is in meters.


length of beam = 2m
force= 200kgs*9.81= 1962N
young's mod=69Gpa (1pa =1 N/m²)
cross section= 50.8²-(50.8-3.25)²= 319.6375mm² =0.0003196375 m²

plug and chug:

2 meters * 1962 Newtons / 69x10⁹Newtons/meter² * 0.0003196375 m²


=0.00000017791894 meters

That probably didn't help. sorry.

 

[Mech_Engineer]

Well Huntoon wasn't much help, fortunately its a pretty easy calculation. Everything you need can be found here:

http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=simple_centerload

The specific equation you're looking for is:

Note that beam calculator I linked to will also calculate the max stress.