Design Envelopes for Worst-Case Demands with Movable Live Loads

A design envelope provides the worst-case shear and moment demands along the length of a structure for a suite of load scenarios. In this video, we examine the combination of a static dead load, a patterned (distributed) live load, and a single movable point load. We use the influence lines to find the critical load patterns and positions for the live load. The effect of a distributed load is equal to the magnitude of that distributed load multiplied by the area under the influence line, while the effect of a point load is simply the magnitude of the load multiplied by the value of the influence line at the location of the load. These previous videos show how to find the influence lines: Influence Lines (statics method) - https://youtu.be/cNdEgnCmNU0 Muller-Breslau Method (the graphical/easy method!) - https://youtu.be/1VcwsaQeUMY 0:00 Introduction and Influence Lines 2:28 Placing loads 3:26 Computing worst case shear 6:31 Computing worst case moment 9:40 Generalizing shear envelope 14:24 Generalizing moment envelope