Engineering 1 Structural Analysis Tom Rebold

To design a bridge, the internal forces must be understood

Outline Force vectors Adding vectors Tension and Compression Assumptions Method of Joints

Vectors help us understand forces Have a direction And a size Applied to bridges

Adding Vectors Imagine you walk N for 2 blocks, turn and walk E for 2 blocks turn and walk S for 2 blocks Where did you end up? That’s exactly how you add vectors For a bridge not to collapse, all the forces at each joint must add to zero i.e. you arrive back where you started

Tension and Compression Who knows the difference? In our diagrams, a force acting toward the center of a member (pulling on a pin) is tension. A force pushing a pin outward from a member is compression

Assumptions All loadings are applied to the joints The members are joined by smooth pins Conclusion 1: each truss member acts as a two force member Conclusion 2: forces can only elongate (tension) or shorten (compress) a member Also assume the weight of the members is small compared to the load At each joint, the sum of all forces must be zero (or the bridge would collapse)

Method of Joints Start at a joint with one known force and at most two unknown forces Draw the “free-body” diagram of a joint, removed from it’s surroundings Apply the known force to the joint, then zero out the known force by adjusting the force vectors along the other two members Once you determine the force at one end of a member, it’s the same force at the other end Continue to analyze each joint, where at most you have two unknown forces to solve

We now demonstrate on the homework examples 1 end is anchored to the ground 1 end is set on a roller

Problem 2

Computer Analysis Tool at http://www.jhu.edu/virtlab/bridge/bridge.htm

As the length increases, so do the forces…

Shifting the load…