Want to travel across a valley? Want to cross an ocean? Want to span from one end to another? Whatever might be the need, bridge is required for that need. But it is a preliminary decision taken on the basis of budget, location, type of soil and surrounding to built a particular type of bridge. This can result in a most commonly used simply supported bridge or a suspension bridge or a cable stayed bridge or an arch bridge. Today we will be discussing about arch bridges. How they are designed? Where they shall be used? Why they are used?
First let us ask a basic question to ourselves. What is an arch? Arch is a member which takes majority of the stresses in compression while spanning a gap. The definition of a column and arch is very near to each other except the last words "spanning a gap". (Yeah, these last two words created majority of the complications in structural engineering). It can be of any shape, a parabolic, catenary, straight lines, etc. But how can we decide the shape?
A shape of an arch is one of the most critical thing. The shape depends on the type of load applied on the arch. If it is just a point load at the center then it will be two straight lines as shown in figure 2. If two point loads then the shape will be as shown in figure 4. If it is uniformly distributed load then the shape of the arch will be a parabolic one. How can we come up with such shapes and why? Take a normal cable or a thread and tie it up at two ends but don't pretension it. Then apply different loading like a point load, half uniformly distributed and a point load, full uniformly distributed, etc whatever you can imagine and see the shape of the cable. If you invert this shape and see it will be the best possible shape of the arch for that particular loading. These arches are called funicular arches. Funicular means a particular shape of chord in tension which you already found when applied a type of load. These particular shapes are the most efficient. Now one can ask why?
What happens when you load a cable? It takes all the load in pure tension and it is because of it's flexibility. This gives the most efficient design possible. So that is why if we give a similar shape to arch for a particular loading you will find only compression acting in the arch. Isn't that awesome? We will not be dealing with bending and shear forces anymore..!! But wait that is not possible. We cannot give any desired shape to an arch. Why? Because it is in compression. Take the example of case 1. A point load. What will be a funicular shape? Two straight lines connected at the location of the load. Now imagine the length of the member if the bridge is spanning for 100m. The effect of slenderness will come into picture. So you will not build such shape in such cases except modifying them by adding braces and everything. Well it all depends on the span that the bridge need to cover.
Now, where can we can see one important reason that why arches aren't built everywhere. Arches exhibit a horizontal reaction at it's ends and this reaction is immense. In order to resist this reaction we need strong foundation, like a rocky mountain. If you are planning to design it on a river, than you need strong piles which can resist shear equivalent to the horizontal reactions and this task becomes pretty tedious. So that is why arch bridges are found across very deep valleys or places with strong rocks at the ends. This is where we construct the arches.