Moment, Torque and Shear Calculations

[sethro5hc]

I'm designing a bike rack from square and round tubing, and need the tubing to be as thin as possible. I have none of my books with me and could use help with which equations I'll need to calculate if the thing will be strong enough or not. The car from front to back will be the X axis and the road to the roof of the car is the Y axis. The load acts straight down towards the ground from a point X out and Y up on the hitch pin, which calulations will I need? I assume a moment, shearing, and possibly torque calculation. Also, which properties will I compare these values with to ensure that it won't yield?

 

[rb1957]

load will act in any direction that you can pull on the rack; consider your own bike rack and the load you apply to it in tying something down. i'd imagine that the load of the bike (inertial, aero.) would be small and that stiffness is your biggest concern.

to answer your next question, how stiff ? stiff enough that the user has confidence in the robustness of the rack; again, how would you feel if your bike rack seemed to deflect as you were tightening it up ??

why "as thin as possible" ? sure you want to control the weight, but "as thin as possible" is really unachieveable and impractical. your goal could be "as thin as practical" so you can use standard tubes.

prepare to make prototypes, real or virtual (FEA), to see how things work. there enough examples of bike racks out there for you to get an idea of what works.

good luck !

 

[sethro5hc]

Yea, I meant as thin as practical, obviously not as thin as possible, meaning 1 extra pound would break it. I'd really just like to haev a few calculations proving that I think a thickness of X millimeters at the hitch receiver will sustain 44kgs of bikes. I've already found the thicknesses of other similar racks, I'd just like to have a couple calculations for my own benefit and curiosity.

 

[drawoh]

sethro5hc,

Why are you so picky about the weight of the a rack? If it is going on a car, five to ten extra pounds should not matter anywhere near as much as the rack not failing and deposting a $5000 bicycle on a highway somewhere.

I even question the value of bicycle weight for non-racers. I figure my bicycle and I weigh around 230lb. For another $2K or $3K, my bicycle and I can weigh around 225lb.

JHG

 

[rb1957]

44kgs (=100 lbs) represents a lot of bikes, so this wouldn't be a bumper mounted rack; or you're just being very conservative.

but your question is too basic to be sensibly answered this side of quitting time. you obviously got someting in mind; in laying out your structure remember triangles are good.

not meaning to be snarky, but does "free body diagram" mean anything to you ?

 

[sethro5hc]

Yes, I've got all the FBD's and everything I just don't have any of my books with me and the proper equations aren't as easy to locate online as one might think. I'm not trying to really accurately determine everything here, just the most basic equation(s) that would lead to the assumption that a thickness of t will be sufficient to support roughly 100 lbs of bikes.

If you'd like to imagine a free body diagram, start at the (0,0) point of origin, draw a horizontal line to the right 400 mm, then from that end point draw a straight line up about 1000 mm, then from that point another one to the right about 450 mm and the 44kg force acts straight down toward the X axis from the end of that line. The bottom segment can be assumed to be rigid and modeled as cantilever to make things simpler. It is square tubing of width b and thickness t. simple stuff here is all I'm looking for.

 

[rb1957]

it sounds like you've got some of the knowledge required (again, not being snarky; you'd know if i was !).

are you really carrying a 44kg bike, or 4+ bikes (a 22lb bike is pretty heavy) ? or is this where you're factoring the bike's weight ?

if you're not factoring the bike's weight, you have to. i'd suggest something like 2.

you have to consider other things than just weight; eg, the load the guy places on the rack as he reefs in the straps (holding the bike onto the rack).

if you're using a simple cantilever, then you want My/I = M/(pi*r^2*t) < 25ksi (Al), 75ksi (steel, annealled).

 

[NomLaser]

Don't forget the jarring of going over a pot hole with your car. You could easily see 2-3g in those cases.

 

[sethro5hc]

I was just being cautious with the weight and assumed four 25 lb bikes, heavy I know, but just a safe estimate. I've measured and study a million other bike racks so I know which thicknesses will work, I'm just looking for a couple calculations for my own sake basically. I was thinking about the My/I, but it's square tubing not round so the I won't be pi*r^2*t.

So far I've just thrown around Sigma(t)=T/2(tAr) and Tau(max)= (.75(V/t)[b^3-(b-2t)^3])/(b^4-(b-2t)^4), V is the transverse shear force.

Oh and by the way, I tried this question in the materials forum but got no response. For the straps, they'll be held together with a plastic cam, and I need an inexpensive plastic that's UV resistant, holds color well and is also fairly resilient. One that's going to bend or break isn't ideal. Any suggestions? I'm currently comparing ASA, PC, PMMA, Acrylic and Methyl Methacrylate. The straps themselves are polypropolene, I'm strictly asking about the plastic cams.

 

[rb1957]

ok My/I for square tubing is M*6b/(b^4-(b-2t)^4)
your "sigma(t)" looks like shear stress due to torque.
i don't think you need to worry about "Tau(max)" maximum shear stress due to shear ... this occurs on the neutral axis where the bending stress is zero.

your next concern is allowables ... thin wall tube doesn't necessarily work up to ftu/fty, particularly in compression.