A wide variety of trusses exist for bridges and roofs. There are many different permutations when it comes to arranging the internal truss members. Depending on the direction, a diagonal member may be subjected to either compression or tension. Using this outline of a truss top chord and bottom chord, for example:
How does one goes about searching for the most efficient arrangement of internal web members within the truss, without going through a tedious trial-and-error process?
You say your members will be either in tension or compression. This is not entirely correct. The members supporting your UDL's will be in bending. If you design the entire structure as a pinned frame structure you will end up with the remaining members being either in tension or compression. In that case all your nodes have to be pinned to avoid moment transfer across the nodes. If you want to avoid designing for bending (except self weight of the member), your 'base' nodes would be all your corners around the perimeter of your frame as well as locations where the supports and any point loads are.
You would then have to look at the sectional properties of your members to ensure you don't end up with slender members for the compression members. This is the one of the reasons you might need an iterative (trial and error) process.
You would start by dividing the structure into triangles. Something like the image below. I think that these members would be the bare minimum.
This is an optimization problem, and specifically a topology optimization one. There are software packages that perform that task. However an optimal solution depends on the contraints of the problem, which sometimes are hard to quantify. Normally the objective is to minimize total cost, but other considerations can be valid (architectural style for example).
An insight about the factors that make a truss more cost effective is useful. These factors may contradict one another, so the optimal solution depends on the specific project. The most profound factors are mentioned next.
Material cost: Optimally should be minimized, but this can lead to a more complicated design, and increased labor costs.
Labor cost: Again optimally should be minimized, but this usually means members are not varying much, which results in increased material costs.
Joints. Joints are a considerable part of the total cost, so an optimal design should minimize them and keep them as simple. Also depending on the material some types of joints can be more difficult. For wood, it is harder to joint tensile members compared to compressive ones, so one should try to minimize such joints. These decisions can have an impact on material costs.
Sensitivity to buckling: Steel members usually suffer from buckling when in compression, so an optimal design should try to drive compression through the short members. Consider for example the Pratt truss in the figure. For gravity loads, the diagonal braces, which are the most lengthy ones, are in tension while the vertical braces, which are the shorter ones, are in compression. This solution seems suitable for a steel truss, since it drives compressive forces through the shorter members.
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Compare this to the Warren truss below, where all the braces have equal lengths and some of them are in compression. If the members are sensitive to buckling, then the increased length of the compression members (compared to the Pratt truss), may drive the material costs for them high. However, if buckling is not an issue (for wooden structure maybe) then this design is simpler and therefore more cost effective.
Life cycle costs. Maintenance costs, upgrade costs, demolition costs, environmental costs etc. can vary from one design to another. Often this cost is the bigger one but also the harder to predict.
