Explanation of Shear w/o any Math
Hi guys, as promised here is my non-math qualitative explanation of shear diagrams. It was a topic of great frustration to me while studying and I realized many explanations are over-complicated.
I. the shear diagram graph space is just the regular old XY graph we have been using since high school. They chopped off an axis and renamed Y to V for shear. Then it is superimposed over a literal real world beam in elevation view.
II. Then the BEAM EQUATION is used to calculate shear. How does it do this? It runs every section (dx) of the beam through a function that outputs the shear force at that section. It run from the start point (left) to the stop point (right)
III. When it is finished the output is a graph that looks like this. But what is really going on? At each section (dx) there is an offset force-reaction pair pushing on opposite sides. Just as we all know it squishes the rectangle into a parallelogram. BUT as you can see in IIIa, the direction of the force-reaction pair has two possible configurations. The reaction force can be on the Righthand or Lefthand side of the load force. By convention one is (+) shear and the other is (-) shear.
IV. And this lead us to the Ant Analogy of Shear. The direction of shear predicts what happens at the point of failure from the POV of an ant walking backwards along the beam. If the beam shears off at that section, the ant will be looking in the direction of shear. Which makes sense if you think about it. The side closer to the support stays put and the longer side falls away.
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