Timeline for Why are arched bridges stronger than flat bridges?
Current License: CC BY-SA 3.0
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| Jan 3, 2017 at 14:56 | history | edited | Floris | CC BY-SA 3.0 |
added 654 characters in body
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| Jan 3, 2017 at 13:15 | vote | accept | user929304 | ||
| Jan 3, 2017 at 4:03 | comment | added | Euro Micelli | For a simplified version of the problem, imagine a miniature bridge made of rubber with a hefty load, sitting on a table top. It's not hard to visualize that the bridge will bend down quite a bit and the legs will try to separate. Except in a real arch, the legs are "tied down" encased in the foundations, so they can't move. The foundation is pushing sideways on the legs to keep them in place; that's where the horizontal forces come from. You can also see that the force amount necessarily depends on how much the bridge "wants to bend" (it's stiffness) and static analysis can't determine that. | |
| Jan 3, 2017 at 3:47 | comment | added | Euro Micelli | Why the horizontal forces? Static (Newtonian) analysis only proves that the horizontal force in the left pier and the one on the right pier are equal and opposite (in this symmetric case). It can't prove that they are zero and in fact they are not, unless the bridge is infinitely stiff. Forces like that are called "indeterminate". You need to look at the bridge deformation and stiffness to find out what those forces are. The details depend on the material's properties and bridge construction. If you assume uniform material, it's not that hard. This is a freshman engineering problem. | |
| Jan 2, 2017 at 21:33 | comment | added | Natecat | i) torques are caused whenever there is a force that is applied offset from a fixed suspension point. The suspension point here are the endpoints of the bridge. ii) Think about what happens when you bend something into an arc. The part on the inside of the arc has to get shorter relative to it's initial length and the outside has to get longer. Same action is happening here. iii) They come from the normal force of whatever the bridge is supported on. The shape of an arc naturally distributes some of it's weight laterally. | |
| Jan 2, 2017 at 17:02 | comment | added | user929304 | Thanks a lot Floris. If you don't mind, I have a couple of questions after reading your answer, mainly to better understand the arguments you've provided: i) in the flat case, why do we have torques when the endpoints of the bridge are fixed? Is this only of relevance when the load is off center? ii) why do we have tension only at the bottom? Last question: iii) where do the additional lateral forces come from in the arc case? Many thanks in advance for your explanations, and also very nice diagrams. | |
| Jan 2, 2017 at 15:55 | history | answered | Floris | CC BY-SA 3.0 |