Building a truss bridge
You have a challenge. You are to construct a 2D truss bridge model which can hold the maximum weight at the centre with the smallest bridge mass. You have to follow the following conditions:
Minimum length of 500 millimetres
Maximum height of 90 millimetres
Maximum weight of 50 grams
You can only build out of the following materials:
Timber which has a mass of 5.5 grams per 300 millimetres
Glue with weight of 1.5 grams per 200 millimetres
How would you make the bridge?
Note by
Sharky Kesa
6 years, 10 months ago
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You need to specify how the bridge is to be loaded. It makes a big difference whether all the load is at the center of the bridge or evenly distributed. If I had a choice of loading the bridge at any point, then of course I'd load it right at the end of the bridge, so that I don't even need a bridge!
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I edited it to the centre.
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Then the next critical factor is the cross-section dimension of the timber, which is presumably uniform in all the pieces to be used. Given that all the members are of uniform cross section, then most likely a simple Warren type truss would be optimal. But how many sections it should have does depend on the resistance to buckling the timber piece have.
More optimal truss designs uses members of varying cross sections, to match actual stress on each member.
To fine tune this further, what's the tensile and/or shear strength of the glue? It could very well be that this could be the limiting factor, and not the strength of the timber members. If glue has to be applied along the length of the timber members, then the shear strength of the glue dominates the design.
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Oh yeah, another very important detail, are the ends of the bridges fixed, i.e., can the forces be transmitted to foundations at either end? Or all resultant loading at the ends must be directly downwards? Most bridge designs assume the latter.
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BTW, are you a civil engineer?
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I've passed the examinations for that a long time ago, but never found the time to work 2 years full time for a licensed structural engineer, which is a State of California requirement. I just have a General Contractor's License, have had that a long time now. Been too busy with other things.
No, it is directly downwards but you can have this sort of structure:
_ ...
|/
Where the | is either side, _ is the bridge base and / is a foundation. The foundation is not glued to the side.
Assuming that the resultant loading at both ends of the bridges must be vertically downwards, ruling out a simple "bent arch" bridge design (which would give the maximum load capacity per weight of bridge), the next best design would probably be a simple A frame, where there is a single chord straight between the 2 points of support, using up 500 of the 2727 millimeters of allowed timer, leaving 1727 to use. The distance from the one end of the bridge to the center apex is 266 millimeters, which means we can use box girders for the compressive members for maximum buckling resistance, using 2 straight chords each side or 4 x 266 =1063, leaving 1727 - 1063 = 664, or 332 millimeters of timber left to use as webbing in fabricating such box girders. This final design wouldn't be practical for a real bridge for any traffic from end to end, but it'd be a top performer in carrying loads at the center, relative to the total weight of the bridge. As a rule, slender members (of almost any structural material except unreinforced concete) buckle far more easily than fail from tensile forces, so this design focuses on maximizing buckling resistance.
A more sophistical (and harder to fabricate) design would be to use 3 long members in each box girder, arranged in an equilateral triangle in cross section, but with varying spacing, with maximum spacing at the center, as to make best use of limited material left for webbing, while coming to a point at both ends of the girder. This is the best design, but requires the most work. However, this wouldn't any longer be a "2D truss", it'd fall under the class of "space trusses", even though it'd work much better than a 2D one. Would it be cheating to simply glue together 3 straight members in a equilateral triangle bundle and call it "2D"?
How well this "bridge" works critically depends on the properties of the glue and how it's used. The analogy to using multiple rivets or welding seams is making use of side-by-side joins of timber, instead of putting "a dab of glue where members come to a point", which would make the whole structure iffy because such inadequately glued joints can easily tear apart. Extra short members for this purpose would be recommended at the apex and at the ends.
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That looks awesome, better than what I had done (a simple chain of equilateral triangles). Would you mind drawing up a diagram of this? :D
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Skarky, let me tell you, the devil is in the details. It all critically depends on a number of factors, including "design limitation rules". if we're allowed to imagine that this bridge is to work in a 2D flatland so that we wouldn't have to worry about side buckling (I mean, who really builds 2D bridges anyway?), then the simpler box girders using 2 members would be optimum. I need to get out the door real soon and won't be back later this afternoon or so. Please give me more specifics.
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OK, we are trying to build a bridge truss (frame) basically. I call it 2D because there is no road. We are working only on the frame. The sides are about 6mm width and height of radiata pine (the wood) is 5.5 grams. There is a loading zone where the bridge must span. There are sides on either end as so
| . . . . . . .. . . . . . . . . . . . . . . . . . . . . .|
| . ............ ......................................|
except no disconnection. The dots are the ravine area and it spans 500 millimetres. There is a slot in the middle where the bridge goes. The load is to be put on the centre of the truss.
Is timber Australian for wood? I'm wondering what kind of wood, but since this is an abstract sort of 2D challenge I guess that is insignificant compared to the design.. I would probably go with a traditional triangle lattice.
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Timber is wood, yeah. Could you draw a diagram of your triangle lattice? It probably is different to my triangle lattice.
Sharky,
1) Are you actually going to fabricate a bridge, instead of simulating it by computer?
2) Are there any provisions to keep the bridge from flopping or twisting over to the side?
3) You must provide a means of attachment at the center bottom of the truss to hang the load? Some "slot"?
4) Can you tell me what kind of glue you're using, white glue or epoxy? I hope it's not Gorilla glue or Krazy Glue.
5) Are you allowed to use the 3rd dimension in any way, or is that forbidden?
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1) You are to fabricate the bridge.
2)There are none apart from the sot edges at either end.
3)There is some sort of object which is hung on to the centre of the bridge. The weights are then suspended on this object.
4) Hot glue, quick set.
5) No 3rd dimension usage.
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Okay, 2) is a real problem, because such a bridge can be strong in 2D, but weak in the 3rd dimension. Worse, we're not supposed to "use the 3rd dimension", which we need to cure this weakness? It's detials like this that make or break the design. The tiny, little details, including exactly how the joints are fabricated, and exaclty how the load is actually attached to the structure. I'll work up a proposal, and you can tell me if you see any problems in actual implementation in the lab. Gimmie more time.
Of course, hot glue is just about the worst possible glue for this kind of application. The only good thing about it is that it simplifies joint gluing, because you simply build up a ball of (almost useless) glue with it. Joints glued this way is very likely to fail long before any wood snaps or cracks.
Okay, here's one draft
Now, but this design depends on being able to cross members over each other as shown, so that at each crossing there is a dab of glue. This design attempts to maximize the number of such glued joints, because this will be the weakest part of the structure---the dabs of glue itself. It's better to have 3 dabs handling 3 crossed members instead of trying to bind them all with a single dab, however large.
This is far from a conventional truss design, this is strictly for the purpose of competition loading right at the centerline, given the limitations of "hot glued joints". The total length of members here is somewhere under 2727 millimeters, the maximum allowed. The principle behind this design is that it's a "tied-arch", probably one of the oldest structural design, dating back to Roman times, whereby an arch is stabilized by a tie chord at the bottom, i.e., the arch consists of members under compression while the tie is a member with tensile stress. The load at the center bottom is supported by angle members under tensile stress, which are attached at two points in the arch section of this design. Extra stiffeners have been added at the sides and center to provide more opportunities for glued joints.
As the load pulls down from the bottom center, all of the side members and the 2 horizontal top chord will experience compression forces, which could lead to buckling. However, it's more likely that some glued joint will fail first. Hence, it is strongly advised that all joints be glued and dried at least a few days before the competition. This will be the key to maximum performance. Attention to the gluing of the joints cannot be emphasized enough! Given the very poor structural performance of "hot glue" used on WOOD!
If crossed members are not allowed per rules, wow. Then this will really become a challenge, especially considering the difficulties of making good glued joints. A different design will have to be used, and this one junked.
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Have you taken into count that the glue has weight as well? Also, how tall is this? It seems like a good design.
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It's exactly 500 by 90 millimeters, width by height. As for the glue, we're kind of limited to using "dabs of glue" at joints, so you can cheat by shaving some of the webbing to save weight when completed. Or eliminate the center pair of members, even though I put those there in order to make sure the load at the center bottom doesn't simply pull the truss apart.
But first, the most important question---are crossed members allowed? Once that's settled, then we can further refine this design.
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No, if you want to cross members, you will have to cut one of the members into 2, then glue them on in a crossed version as so:
\ /
/ \
except one of the members are one piece. You cannot overlap, basically.
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Well that's going to seriously impact the performance of the final structure. Then it's ALL about those stupid glued joints, which will be the weakest and least reliable parts of the structure. What I have to do now is to first figure out the best way to make bombproof "hot glue" joints, and then design something around that. Give me until morning to come up with something. We'll have to just junk the other design that has a lot of crossed members.
Sharky, I have more very important question, which will have a huge impact the final design. Where, exactly, is the loading to be applied? We know that it's concentrated at the centerline of the structure, but is it at the top center or bottom center? It's easier to design something that will handle loading at the top center than the bottom center, because we have few effective ways of handling tensile stresses at the joints, because hot glue on wood is a joke for that.
As I said earlier, joint design is now critical, and the wood, which is 6 x 6 mm in cross section, is just thick enough to allow cut-out indentations for members to be glued into. Thus, we don't depend on the glue for structural strength, but the shear strength of the wood itself. The final design will be simpler than the last, but there's more details to be considered at the joints.
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The top centre, should've mentioned that. How deep would the indentations be?
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Well, that's good, the 2nd draft which has a center vertical beam, should be suitable for that kind of loading. Notches should be no deeper than about 25% of the thickness of the timber. It's kind of hard to work with pieces of wood only 6 mm square, so be careful not to overcut.
The exception is where the 2 crossed members overlaps. The notches have to be 1/2 deep, for them to fit together to stay 6 mm thick overall.
The more I think about this problem, the more refinements, I can come up with to boost performance.
Okay, have a look at this design
The width and height is still 500 mm x 90 mm, but the wood timber widths are greatly exaggerated to show joint details and how the pieces are fitted into notches. It is critical that wood members extend beyond the notchs by roughly the thickness of the wood member or more, because we want to use the shear strength of the wood where there is a force along the length of it, as exerted by the piece(s) glued to the joint. Note that the bottom chord has no notching at the center. Where the 2 members meeting at roughly 45 degrees at the bottom center of the truss, they need to be overlapped, i.e., both have to have side notches to half depth so that they fit together. The reason for this is that we need to make a splice of those two members, because both will experience tensile stresses and will want to tear apart. Hot glue will be insufficient to hold the slice together, unless we have this notching and overlapping. The load is best applied anywhere on the center vertical piece, which rests on top of the overlapped members.
For extra strength, and if allowed timber usage permits, repeat the outside sloping members, but with notches spaced from the notches used for the outside members, so that the side members run parallel but with a space between. In this way, the shear stresses on the bottom chord where notched will be halved. This is the weakest part of the structure, so this will help. Also, buckling forces on this side member will be halved as well. Glue in some webbing here and there to further stiffen it, making a sort of a box girder on both sides.
This design is further improved if the top two horizontal pieces are at a very slight angle downwards on both sides, so that the 5 joints on top trace out a circular arc. This design is a mix between a "Tied-Arch" and a more conventional Warren Truss.
As always, and which cannot be repeated enough here, special attention must be given to the joints. Failure will most probably occur at one of the joints. Care should be taken to not notch the members too deeply, which should be less than 25% of the thickness of the timber. The best kind of notch design is the way the ends of the bottom chord are notched. Note that the member "pushing" the chord is exerting a force on a face that is perpendicular to the wood grain. If instead there is an acute angle "wedge", then it will literally wedge apart the grain of the wood, hastening shear failure.
Sharky, let me say that in the architectural business, there's "always at least six different ways to do a thing, all of them correct." It forces us to look more closely why we choose any one way over others, and often it's a matter of esthetics
Here is a chart of a few common truss designs. Note the similarity with the 2nd draft. But what dominates the design for this wooden model is the problem of making dependably strong joints. You can't just bolt or weld members together, or use special reinforcing plates, which is common in truss construction. Also, these common truss designs are to have uniformly distributed loads.
Dear Michael Mendrin ,
I am new to this site. Your posts about truss constructions and knowledge attracted my attention. To be honest with you i am assinged a similar problem about constructing a truss bridge of 76cm length holding a weight of 100kg at the center with the smallest bridge mass. I am familiar with the formulas applied to calculate the bending moment, moment of inertia, bending stress etc (Simple Beam theory i think is called) but what i dont know is the ideal design with respect to the weight of the bridge. I would like to seek your advice for the design. Please let me know if you could help me
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