Are arcs stronger than beams

Why are arch bridges stronger than flat bridges?

A break occurs under tension - that is, if you pull on something hard enough it will tear. The key to understanding the arc design is to understand that it will lower the maximum pull force.

Take a simple beam, prop it up at the ends, and hang a little off-center:

The tension at the bottom and compression at the top are required to balance the torque created by the vertical forces of the supports and the load in the center. Of course, the further the supports are apart or the greater the load, the greater the tension. When this voltage reaches a critical value, the beam fails.

Now if we shape the bridge into an arch, we get the following:

The additional side forces on the arc cause compression in the beam, this reduces the net stress on the floor and makes the beam better able to carry the load. You can make things even better by distributing the load more evenly, designing the shape of the arch to better optimize load distribution, and so on. However, the diagram should give you an idea of ​​the underlying principle.

To update

Side forces are perhaps the easiest to understand when looking at a V-shaped structure: you intuitively know that such a structure would collapse unless you put some torque at the tip to hold the legs together, or enough friction on it Deploy the base of the legs hold them together. You can also see that the force needed near the hinge (which is provided by the red "tension" tension in my top diagram) needs to be much greater than the force provided by friction on the floor (Lateral forces from the column on the arches).

user929304

Thank you Floris. If you don't mind, after reading your answer, I have a few questions, mainly to better understand the arguments you are making: i) Why do we have torques in the flat case when the endpoints of the bridge are fixed? Is this only relevant if the load is off-center? ii) Why do we only have tension below? Last question: iii) Where do the additional side forces come from in the event of an electric arc? Thank you in advance for your explanations and also very nice diagrams.

Natecat

i) Torques are always caused when a force is applied that is offset from a fixed suspension point. The suspension point here is the end point of the bridge. ii) Think what happens when you bend something into an arch. The part on the inside of the arch must be shorter in relation to its original length and the outside longer. The same action takes place here. iii) They come from the normal force of what the bridge is supported on. The shape of an arch naturally distributes part of its weight laterally.

Euro Micelli

Why the horizontal forces? The static (Newtonian) analysis only shows that the horizontal force in the left pillar and that on the right pillar are equal and opposite (in this symmetrical case). It cannot prove that they are zero, and in fact not, unless the bridge is infinitely stiff. Such forces are called "indefinite". You need to study the deformation and stiffness of the bridge to find out what these forces are. The details depend on the material properties and the bridge construction. If you adopt a uniform material, it is not that difficult. This is a novice engineering problem.

Euro Micelli

For a simplified version of the problem, imagine a miniature rubber bridge with a heavy load sitting on a tabletop. It's not hard to imagine that the bridge will bend quite a bit and the legs will try to separate. Except in a real arch, the legs are "tied" in the foundations so that they cannot move. The foundation pushes the legs sideways to keep them in place. This is where the horizontal forces come from. You can also see that the amount of force necessarily depends on how much the bridge wants to "bend" (its stiffness), and static analysis cannot determine this.