Triangulated Strength Question

[46/71 Hybrid]

I'm building a platform and have a quick triangulated strength question.

All things considered equal, what percentage stronger does the joint X/Z become (i.e the amount of weight that can be placed at that point) for each percentage that Y is increased.

For example, if x=3,y=4,and z=5, how much percentage stronger does the joint of X/Z become if x=3,y=6,and z=6.71 ? Is there a calculator somewhere that will tell me this?

The reason I ask is that I'm building a cargo carrier in another thread and I'm wondering how much stronger the design will become if I increase the length of Z by adding a piece to weld too underneath the receiver tube.

http://i287.photobucket.com/albums/ll145/leswhitt/triangulatedstrength.jpg

[lotechman]

you can use vectors to figure out how much compressive force is exerted on the member. Often the brace folds/collapses before the welds fail. The forces are proportional to the lengths of your sides of the triangle. google vectors or vector analysis... no math when done graphically.

[DSW]

Welcome to the world of structural engineering. I'ts been quite a bit since I did any serious calcs on any of this. Here is a simple way to understand this somewhat.

Think of your design as a table. The top is X, one leg is Y and the other leg is Z. Half the weight on X goes to Y, the other half to Z if the loads are equally applied. (point loads and unequal distributions have special formulas that say how much goes to which side based on how far they are from the ends) If both legs are vert. both take the same load just like a table. If Z is flat parrallel to X it take no weight it all goes to Y. The closer to 90 Z is the more load it will take. At 45 deg it will support about 1/2 the load it will at vertical.

Many other things affect the ability of a joint to support a load. Type of conection, welded or bolted and how stiff the brace is will all change what is happening.

In general the longer you make Z the stronger the joint as long as everything else can take the load being transfered. As far as how much more weight can be added, thats a ton of complicated math, most of which you won't likely have the info to plug in.

[lotechman]

I'm building a platform and have a quick triangulated strength question.
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http://i287.photobucket.com/albums/ll145/leswhitt/triangulatedstrength.jpg

lets pretend that the load at the tip is 100 pounds. The diagonal brace would take a compressive load of 5/4 = 125 pounds

In the second case the load on the brace would be 6.7/6 x 100 = 111.7 pounds compressive force on the brace.

This only shows you how vectors work. You can draw out a scale drawing and develop the ratios from the lengths.
Rarely do the welds fail in a situation like this. What happens is the brace bends and buckles from the compressive force. Of course there are guidelines as to the size of compression members and limits on slenderness ratios.
This is why engineers get the big bucks. If they are wrong their career can go down the toilet instantly.

[46/71 Hybrid]

lets pretend that the load at the tip is 100 pounds. The diagonal brace would take a compressive load of 5/4 = 125 pounds

In the second case the load on the brace would be 6.7/6 x 100 = 111.7 pounds compressive force on the brace.

This only shows you how vectors work. You can draw out a scale drawing and develop the ratios from the lengths.
Rarely do the welds fail in a situation like this. What happens is the brace bends and buckles from the compressive force. Of course there are guidelines as to the size of compression members and limits on slenderness ratios.
This is why engineers get the big bucks. If they are wrong their career can go down the toilet instantly.

Whoa, I was following along decently until I read this. I don't understand how if you have 100lbs sitting on the tip, the load on the brace could be greater than 100lbs, i.e. 111.7 and 125.

[lotechman]

It is the same principle involved in a clothes line. If you were to pull the line so that it was absolutely straight and had zero sag the tension would reach infinity. If you had a sling with two legs angled out lifting a load once the legs angle out to 30 degrees the load on one sling leg alone is the weight of the object.
If this was not true then you would be able to hold your rifle out at arms length all day long as the sargent screams in your face.

[DSW]

46/71 Hybrid I'm not quite sure I follow lotechman's examples either even with my structural eng classes quite a while back.

As far as how you can have a load greater than 100lbs at the point XZ, I can not quite picture what he's thinking, but it may have to do with other factors. The load at XY however could be signifigantly different. Welded connections are moment joints and have a different set of calculations from simply supported structures, where you usually think of a hinge so the forces can even out. In a simply supported truss (bolted connetions) loads can transfer from one point to another so they could add up to a greater load than you might imagine. In a moment conection (cantilevered), the load at XY would be 4X100lb ( distance from XY times load) assuming that the brace took no load. So you could have signifigantly more load at a point than what is actually applied. You actually get an upward load at XY as the joint tries to twist at the weld.

In a simple angle brace (lets use 45 deg because it simplifies my math this early in the morning) the 100lb load at XZ wants to fall. The angle brace takes both vertical and horizontal loads. As you push down with 100 lb the brace wants to fall side ways. The load down equals the load to the side so the X member ends up with a horizontal tension load of 100lbs to offset the brace trying to fall. The more vertical the brace the less tension induced into the X member, The flatter the brace the more tension is added to the X member.

This example is not acurate as far as the #'s are concerned. (there's a reason why I didn't continue with engineering, The math just make my mind mush at certain times) The general concept is close however.

As mentioned above you have to be sure that loads don't bend the members, loads dont exceed the joints ability to transfer loads, and many other factors. That's why engineers make big bucks. The calculations to figure this sort of connection would fill about 1/2 a sheet of paper minimum to do it right.

[lotechman]

Resolving vectors is grade eleven science nowadays. This site might help with the concept. No math required.. just a scale drawing. This only tells you the magnitude of the forces along the frame members and the direction.
http://www.walter-fendt.de/ph11e/resultant.htm

Yes the compressive load along that brace is greater than the vertical load... Makes you think eh??? It is not something to be taken casually.

[46/71 Hybrid]

Welcome to the world of structural engineering. I'ts been quite a bit since I did any serious calcs on any of this. Here is a simple way to understand this somewhat.

Think of your design as a table. The top is X, one leg is Y and the other leg is Z. Half the weight on X goes to Y, the other half to Z if the loads are equally applied. (point loads and unequal distributions have special formulas that say how much goes to which side based on how far they are from the ends) If both legs are vert. both take the same load just like a table. If Z is flat parrallel to X it take no weight it all goes to Y. The closer to 90 Z is the more load it will take. At 45 deg it will support about 1/2 the load it will at vertical.

Many other things affect the ability of a joint to support a load. Type of conection, welded or bolted and how stiff the brace is will all change what is happening.

In general the longer you make Z the stronger the joint as long as everything else can take the load being transfered. As far as how much more weight can be added, thats a ton of complicated math, most of which you won't likely have the info to plug in.

This makes the most sense to me...that the greater the angle, the more weight it will support. As a "field" rule, I think this is what I'm looking for. In dealing with specifics, my horizontal bar is 30.5" and is made out of 1" x 1" x 3/16" angle. The angled support will be 3/4" pipe (I think sched 80).

Since the receiver tube is 2" thick, it will give me a X=30.5, Y=2, and Z=30.57. That gives an angle of 3.75. If I weld a 1" drop to the receiver tube, and X=30.5, Y=3, and Z=30.65, that gives me an angle of 5.62. Assuming that 90 deg = 100% of the load and 45 deg = 50% of the load, then 3.57 degrees = 3.97% of the load and 5.62 deg = 6.24%. Throw in all the variables such as strength of materials, strength of welds, reduced bowing, and everything else, and I'm sure that 2.24% difference becomes more and more substantial.

Since I'm guessing a sched 80 3/4" pipe would take at least 100 lbs of pressure at the XZ joint to bend it, I'm guessing my carrier will support at least 400 pounds (4 corners) once I've added the plywood floor to help distribute the weight. Once I get the supports welded and the floor in, I'll start adding weight until I see some bowing. I'll post back when it's good to go. Any guesses on how much it'll hold?

[46/71 Hybrid]

Yes the compressive load along that brace is greater than the vertical load... Makes you think eh??? It is not something to be taken casually.

It's been a long time since I've done any heavy duty math but my gut disagrees with this. When I think of it in simple minded terms, I imagine a guy with a 45 lb marble. It doesn't matter where on the structure he puts that marble, it's not going to create more than 45 lbs of pressure (assuming everything is stationary) anywhere on the structure. If it did, it seems like there'd be a way to harness that energy and possibly lift up the marble by using it's own energy against it.

[DSW]

I am haveing a bit of trouble visualizing how you are putting this all together. A 1" drop really won't gain you much with a diagonal brace. It all depends how you assemble it. A 3" "beam" under the carrier would add a large amount of strength.

If I was going to build what you are, ( Took me abit to remember your post on the Tahoe and put 2+2 together.) I would just get a chunk of 2" OD square tube say 1/8"-3/16" and go straight from the reciever to the back end of the carrier. 2"x3" angle with the 3" leg down would work also, but require more work.

If you choose to use tube, think truss. I would set the bottom and top cord at least 6" apart. The farther apart the stronger to a certain point. The key to this is tying the trusses into the reciever. That might take a bit of thought.


As far as you thoughts on the marble you are correct that the 45lb marble places 45 pounds of force on the floor. But I can use that 45 lb marble to lift 450lb IF I use a lever. It's like a seesaw. The 45 pound marble 10' from the piviot will = a 450 lb weight 1 ft from the piviot. Thats key to what you are doing. 100 lbs 30" from the reciever will equal aproximatly 250 lb of bending moment on your "beam" with out any other loads added.

In all honesty the calculations to figure this out isn't worth the time and energy to try and do it. It can certainly be done, but I lack most of the info to do it. Each shape of steel and each size in those shapes has a diferent set of numbers that corespond to its ability to bend in each axis as well as other info. The charts for this are large and complicated. Most standard charts don't list small sizes as they are rarely used for structural aplications. even in I bar trusses most members are 1 1/2 angle or larger and you would need to find a set of charts just for that special application.

If you want some help trying to design it I'll try and make a few sugestions but it will not be engineered. I would need to know what materials you have available. As I said I would use a piece of 2" tube as my #1 choice. Tall angle or C channel would be #2, and some sort of truss for the sides would be #3. All of these options gain strength from one thing, depth of the member.

[46/71 Hybrid]

It's my fault for not including pictures in my question, I would think they would add a huge amount of clarity to my question. Let me see what I can find online to illustrate my point and I'll post it up.

[46/71 Hybrid]

Okay, here's 3 pictures (they aren't the greatest but bear with me). The first is roughly what I built, the second is the braces attached to the receiver tube, and the third is the braces attached to a piece that drops 1" below the receiver tube. Which one is going to be stronger and what's your guess (doesn't need to be exact) of how much stronger?


1 (http://i287.photobucket.com/albums/ll145/leswhitt/draw-tite-hitch-mounted-cargo-carri.jpg)
2 (http://i287.photobucket.com/albums/ll145/leswhitt/option1.jpg)
3 (http://i287.photobucket.com/albums/ll145/leswhitt/option2.jpg)

[mjcutri]

So dropping a brace down 1" will make it marginally stronger, but not enough to justify it. I ran a quick and dirty model in solidworks with cosmos express, and dropping the supports 1" reduced the max von mises stress from 26333 to 22582 psi. The version without the supports had a max stress of 80842 psi.

If it were me, I would just run the supports to the 2" tube.

As far as the compressive forces in the diagonal legs being greater than the load, DSW is right, even though it seems counter intuitive at first.

[DSW]

Ok It makes more sense now. I was thinking you wanted to add the brace coming out from the hitch in place of the 2" tube not going left and right as shown. Lowering the brace will add some strength but not a signifigant amount.

If you were to build sides like this rack posted not long ago, and made them fixed rather than removeable you would add a lot more strength and rigidity to the rack.

21593

It make's loading items a bit more dificult but makes secureing them easier. This is what I meant when I suggested a truss. The sides act as a truss or shear panel to stiffen the frame below. This could be made with small tube and add a signifigan amount of strength but add little weight.

[46/71 Hybrid]

Mjcutri,
Thanks for taking the time to run it and produce numbers, I appreciate it. Based on your numbers, it doesn't seem like it's worth the time or materials to drop the supports down an inch.

DSW,
I had also planned to run round tube sides and a front, I think I may leave the back open though. That way if something is a *tad* too long, I can let it hang off the back.

[steve45]

It's been a long time since I've done any heavy duty math but my gut disagrees with this. When I think of it in simple minded terms, I imagine a guy with a 45 lb marble. It doesn't matter where on the structure he puts that marble, it's not going to create more than 45 lbs of pressure (assuming everything is stationary) anywhere on the structure. If it did, it seems like there'd be a way to harness that energy and possibly lift up the marble by using it's own energy against it.

When you have a force and a distance, you're creating a moment (foot-pounds). To balance that moment, you have to have an equal, but opposite moment. This can be a longer distance and lower force, or a shorter distance and greater force.

Does that make sense?