Think Triangles
One of the most important things to remember in Bridge Builder is to think in triangles. Triangles are one of the strongest shapes in nature. Think back on bridges you've seen over wide gorges. You may have noticed that the beams make many triangle shapes. Keep this in mind while you are building your bridge. If you notice an area that doesn't have a triangle above or below it, try to make a triangle. These will help boost the strength of your bridge can even help widen it. Avoid shapes like squares or rectangles. These shapes have more sides and add more money to the cost of your bridge. They are also simply not as strong as a triangle, making them inefficient and wasteful.
Stress
With every piece you add to your bridge, you should be trying to support every other area. Minimizing stress on the links your bridge is crucial to keeping it up. Too much stress on one link will cause it to break, creating a chain reaction that will bring your bridge down. If you are unsure of how strong your bridge is, hit the analyze stress button. It will run a quick diagnostic on your bridge to tell you where it is suffering from the most stress. Green areas are safe while red areas are suffering from severe stress and are in danger of falling down. Build triangles underneath of these areas to help remove stress. Keep running your stress test until every link in your bridge is green. Your train will then be safe.
Optimize
Once you have a working bridge, you can try to optimize its efficiency. This will help you save money and get a better score. You can optimize your cost by removing excess pieces that may not need to be on the bridge. Deciding which pieces need to go and which have to stay can be a very difficult process. Run a stress test to see what areas of the bridge are fully supported. Start carefully removing pieces you think are excessive, such as supporting beam to an area that already has at least two. After you've removed a few pieces, run a stress test to see how the stress has started to redistribute. Keep the pieces orange, which means moderate stress. A bridge filled with orange pieces will stay up better than a bridge that is mostly green but with a few red parts. Once your bridge starts to fall down again, place as few supporting beams as necessary to keep it back up.