building a cardboard bridge

I am building a cardboard bridge that is supposed to span 7-9 feet and made of cardboard. I am having trouble however designing the abutments. The bridge will simply be placed on a table (no suspension designs btw) and will have a maximum 10% grade.

What will be the best way to design the edges of the bridge?
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 The design of abutments depends on the support reactions. These, in turn, depend upon the type of bridge chosen. Some more information about your ideas would help.

 Quote by Studiot The design of abutments depends on the support reactions. These, in turn, depend upon the type of bridge chosen. Some more information about your ideas would help.
I was thinking about designing an undertruss/arch bridge.

Here is a diagram of my concern.

Is this something I should worry about? How do I adequately prevent that part from folding in?

building a cardboard bridge

 The bridge will simply be placed on a table
How would this design fit on a table?

Is it supposed to be free standing on the table or to span between two tables or what?

Have you considered the horizontal and vertical reactions at the supports?
I think they have given you a clue here as you state the max grade is 10%

A simply supported beam has only vertical reactions.
No horizontal abutment reactions or moments.

An arch has no abutment moments but does have both horizontal and vertical abutment reactions.

How are you to fabricate this bridge?
Is it to be made from sheets of cardboard, cut to shape?
Glue? Pin joints?
I know you said you cannot use a suspension design, but can you use string to prestress the beam?

If you want to use a truss, and the above fabrication methods are available I would suggest cutting the cardboard into rectangles and rolling these into longish cylinders and gluing the joins. Also change the truss design so the compression members are much shorter and/or fatter than the tension ones, otherwise the cardboard will buckle.

We can look again at the abutment question when you clarify what the bridge is to stand on, as your current idea will not work well.

 Quote by Studiot How would this design fit on a table? Is it supposed to be free standing on the table or to span between two tables or what? Have you considered the horizontal and vertical reactions at the supports? I think they have given you a clue here as you state the max grade is 10% A simply supported beam has only vertical reactions. No horizontal abutment reactions or moments. An arch has no abutment moments but does have both horizontal and vertical abutment reactions. How are you to fabricate this bridge? Is it to be made from sheets of cardboard, cut to shape? Glue? Pin joints? I know you said you cannot use a suspension design, but can you use string to prestress the beam? If you want to use a truss, and the above fabrication methods are available I would suggest cutting the cardboard into rectangles and rolling these into longish cylinders and gluing the joins. Also change the truss design so the compression members are much shorter and/or fatter than the tension ones, otherwise the cardboard will buckle. We can look again at the abutment question when you clarify what the bridge is to stand on, as your current idea will not work well.
Thank you for your comments. This is only my second bridge and it is not clear to me that I may have no idea what I am doing when it comes to design.

First, it is to span between two tables.
Secondly, I have not considered the reactions at the supports. I am most likely not imagining the flow of pressure throughout the system. Now, the arch abutments in West Point Bridge Designer 2010 are vertical, but provide horizontal reactions?
Here is a reference picture:

However, seeing as how I will simple place the bridge onto the two tables, like so,

How should I design the abutments (highlighted in blue),
or rather,
I don't understand if this would suffice for 160lbs.

This bridge will be made from cardboard, and can be joined by any means possible. I believe the beam can be prestressed, but to be honest, I have no idea what you mean by using a string to prestress the beam.

Lastly, thank you for the idea. To roll up the cardboard, assuming the length of the card board is how long the member should be, how much would you recommend the width /the diameter of the member?

 I don't understand if this would suffice for 160lbs.
Is 160 lbs a requirement? This is the weight of a woman or small man and quite a significant load.
Is this load to be a point load in the middle or evenly distributed over the deck?

An indication of what you are studying and at what level, would certainly help.

Do you understand what the term 'abutment reactions' means?

You have correctly identified one weakness of your underslung design. The truss needs to continue beyond the abutment line.
Of course you have produced a planar drawing. To support 160 lbs worth of loading you will need more than one truss, may be several. Depending upon how the load is distributed you will need cross members to transfer the load evenly between the supporting trusses.

Incidentally for the purposes here a truss is a skeletal form of a beam.

I would not advise pursuing an arch. Arches are compression structures and sheet cardboard is weak in compression.
Most concrete bridges with curver undersides (soffits) are actually curved beams, not arches.

 Quote by Studiot Is 160 lbs a requirement? This is the weight of a woman or small man and quite a significant load. Is this load to be a point load in the middle or evenly distributed over the deck? An indication of what you are studying and at what level, would certainly help. Do you understand what the term 'abutment reactions' means? You have correctly identified one weakness of your underslung design. The truss needs to continue beyond the abutment line. Of course you have produced a planar drawing. To support 160 lbs worth of loading you will need more than one truss, may be several. Depending upon how the load is distributed you will need cross members to transfer the load evenly between the supporting trusses. Incidentally for the purposes here a truss is a skeletal form of a beam. I would not advise pursuing an arch. Arches are compression structures and sheet cardboard is weak in compression. Most concrete bridges with curver undersides (soffits) are actually curved beams, not arches.
The 160lb is a requirement (the teacher has to walk across the bridge) so it would have to hold 160 lbs across the deck.

Also, this is a high school engineering class, we have gone over reactions (each joint has to evened out at 0N, and each member has to "cancel out" the force of another member), I am possible confused as to why a standard abutment does not provide a horizontal reaction.

Thanks for confirming my problem about the weakness of an underslung design, I started the thread to try and solve this problem. I thought about continuing the truss under the table, but I could not think of a way to attach it under the table, and still have the bridge be "portable." Also, since the span of the bridge will be 3 1/2 feet long, I thought it would be okay if I had 2 trusses, but I haven't gotten to crossing the loads, my textbook did not explain it.

The arch approach was mainly an aesthetic one, but I can see how problems could arise especially towards the middle. On that note, do you have any suggested readings that can may be explain the designs of different bridges vs. the requirements of their members?
 Firstly you do not need to reproduce my entire post in quotes every time. Just any points or emphasis you wish to discuss. OK I get the picture about where you are at. This is a considerable task for high school. It will be a real feather if and when you achieve it. You did say at the outset that the span was to be 7 - 9 feet, now you say 3.5 feet??? I will post some sketches shortly to help matters. In order to understand what is going on you will need to understand Resolution of forces at a point Moments of a force about a point Friction Force as equal to $$\mu$$ times the normal reaction Please confirm you understand these? We will do what is commonly known as a line beam analysis in a simple form. I do not intend to try to calculate individual member forces - that is beyond high school - just to do enough simple mechanics to get a handle on things. Do you realise the difference between a point load and a distributed load? A teacher in the middle of the bridge constitutes a near point load. A real difficulty will be creating a walkway that a human can stand on without falling through, whether the bridge spans anything or not.
 Sorry for requoting the whole post, I wasn't aware I saw doing so. I don't think the tasks will be incredibly difficult considering we made a paper bridge that held 200 times its own weight (the difference was were given the blueprints.) As for the specs of the bridge I meant to say it is going to 7 feet long and 3.5 feet wide. I understand the three points you posted, and once I am able to finally grasp "why it works", I will be able to calculate individual member forces (I don't think this is beyond high school, and also provides a benchmark for how sturdy we should make members).
 Okay, took a while to get that all down, amazingly I understood most of it. 1.) How would I calculate, or how would I figure out an optimal distance of how much of the bridge should be touching the table? 2.) Seeing how I am just building a large corrugated beam, could I add my "useless" arch design? 3.) To build the cell walls, I would assume I would still have to roll the cardboard up to get an adequate compression member. Thanks for all you help.
 Please correct me if I am wrong, but for this cellular door application here is that I would mean I would create many "toilet paper rolls" and stack them vertically? Or b.) I am just stacking non corrugated cardboard on top of another to create one large beam?

A standard door is around inch and a quarter to inch and a half thick.
Since the veneer skins will be stronger than your cardboard I suggested looking at a figure of around 2 inches for your beam.

To be quite clear.

The main forces are in the skins. A single sheet of cardboard will be inadequate so I suggest gluing several together like plywood. Simply stacking them would not be enough they would not act as one.
I suggested some experiments to determine how many layers, sheets or laminations or plies your would need.

 Now you can see why engineers like beams to be as deep as practicable.