Bridge Beam Shapes: Why Are They Different?

[rollingstein]

I pass a river with two bridges on it, right next to each other. One older, one newer.

The newer one is all concrete construction & the shape of its spans makes intuitive sense to me i.e. minimum thickness at mid span. Like this sketch:

The older one has sort of the opposite shape with max girder thickness at mid span. Intuitively I cannot figure why this would be chosen so? Any thoughts? I have a sketch below.

If it matters the girders in the older bridge are steel with concrete piers.

Basically, does it make sense to have a beam that is thickest (deepest?) at the center? I find odd that two bridges will have the optimal beam shape exactly opposite.

 

[SteamKing]

I pass a river with two bridges on it, right next to each other. One older, one newer.

The newer one is all concrete construction & the shape of its spans makes intuitive sense to me i.e. minimum thickness at mid span. Like this sketch:

This newer concrete bridge appears to be constructed as a shallow arch on the cantilever principle. As a load moves between the piers of this type of bridge, the bridge structure is designed to remain in compression, which concrete can withstand quite well. If concrete is put into tension, things get trickier, and steel must be added to take the tension, as concrete has very low tensile strength, and the design of the structure is more complicated.

Arch bridges have traditionally had a very solid and heavy appearance. With new pre-stressed concrete construction techniques becoming available over the last century or so, bridge engineers have been able to develop arch bridge designs which are quite light in appearance, while maintaining great strength.

http://en.wikipedia.org/wiki/Cantilever_bridge

The older one has sort of the opposite shape with max girder thickness at mid span. Intuitively I cannot figure why this would be chosen so? Any thoughts? I have a sketch below.

If it matters the girders in the older bridge are steel with concrete piers.

This older bridge appears to be a type of deck truss, where the truss work is built below the road surface. There are a dizzying array of different types of truss bridge construction, which can be seen in this article:

http://en.wikipedia.org/wiki/Truss_bridge

Truss bridges can be fabricated from a number of simple parts and erected rather quickly, in comparison with other methods of construction.

Basically, does it make sense to have a beam that is thickest (deepest?) at the center? I find odd that two bridges will have the optimal beam shape exactly opposite.

There are many factors which go into the design of a bridge. The length of span, amount of clearance below midspan for any other road or water traffic, aesthetics, cost, etc. Sometimes, the structural considerations wind up down the list.

 

[rollingstein]

This older bridge appears to be a type of deck truss, where the truss work is built below the road surface. There are a dizzying array of different types of truss bridge construction, which can be seen in this article:

Didn't seem like a truss to me. At least not what I think of as a truss. This below is what I think of as a truss:

But if it looks like a single solid steel plate from the side, is that a truss too? The older bridge spans looks more like this element below but in that trapezoidal shape. The main question I had was why one might want to put most metal at mid span instead of at the support.

 

[SteamKing]

Didn't seem like a truss to me. At least not what I think of as a truss. This below is what I think of as a truss:

But if it looks like a single solid steel plate from the side, is that a truss too? The older bridge spans looks more like this element below but in that trapezoidal shape. The main question I had was why one might want to put most metal at mid span instead of at the support.

No, that's a regular plate girder. The structural principle is similar, though, to a deck truss. The plate girder supports the loads on the bridge as a beam, which means that a bending moment is generated in the span, which will be a maximum midway between supports. The way to reduce bending stress in a beam is to increase its depth in way of where the maximum bending moment will occur.

 

[rollingstein]

No, that's a regular plate girder. The structural principle is similar, though, to a deck truss. The plate girder supports the loads on the bridge as a beam, which means that a bending moment is generated in the span, which will be a maximum midway between supports. The way to reduce bending stress in a beam is to increase its depth in way of where the maximum bending moment will occur.

Ah! That makes sense then.

I think I get where my confusion arose from:

The Bending Moment of a simple beam maxes out at its midpoint whereas for a cantilever it maxes out at the support. Correct?

If so, that explains intuitively why one bridge design needed max material at mid-span & the other at the support.

 

[SteamKing]

Ah! That makes sense then.

I think I get where my confusion arose from:

The Bending Moment of a simple beam maxes out at its midpoint whereas for a cantilever it maxes out at the support. Correct?

Correct.

If so, that explains intuitively why one bridge design needed max material at mid-span & the other at the support.

The bridge over the Firth of Forth in Scotland is one of the crowning achievements of Victorian engineering which is still in use today:

http://en.wikipedia.org/wiki/Forth_Bridge

This photo of the the 2 men supporting a third man suspended between them is a striking illustration of the cantilever concept: