Why do arches and triangles make truss bridges stronger?

Answer 1

The triangle is a unique geometric shape in that it is stable structurally when the nodes are "pinned". This means that if you load a triangle structure at a node, as long as 2 nodes are fixed against translation (but free to rotate), the legs of the triangle will develop axial forces to transfer the load to the supports and maintain equilibrium.

In an ideal truss, the nodes are pinned, the external loads and supports are applied to the nodes, and the supports prevent translation but allow rotation. Additionally, only axial forces are developed in the truss members. An ideal truss made of squares will collapse.

Truss bridges are typically made up of triangles, and the gravity loads from the traffic are transferred through a floor frame to the nodes of the truss. When designing the truss, it is usually assumed that the nodes are "pinned". The connections are designed for axial forces only, usually with an allowance for eccentricities which may arise due to the details.

Arches are a different type of structural member, and are beneficial structurally because they transfer gravity loads along the length of the span into compression loads at the end reactions. A perfect arch will be entirely in compression (although not equal compression across the cross-section of the member), and is inherently stable. The drawback to arches is that the high compression at the end of the arch must be accounted for in the design to prevent against buckling of the member. This usually results in beefy members, but are still often economical for long spans. Arches can be made up of trusses (see the New River Gorge Bridge), or single members (see the Hoover Dam Bridge). The deck can hang below the arch or be supported about it.