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Work equivalent loading theory

Distributed loads are very common but unfortunately FEA requires that loads are only applied at nodes. The purpose of this video is to demonstrate how distributed loads are translated into nodal forces and moments on a beam element using work equivalency. 0:00 - Introduction 0:48 - Statically equivalent loading 2:13 - Introduction to work equivalent loading and equation derivation 7:16 - General equations for work equivalent nodal forces and moments to represent distributed loads 8:22 - Solved work equivalent loads for a uniform distributed load case and a triangular distributed load case. 9:29 - Comparison between work equivalent and statically equivalent nodal load representations. 11:40 - Reflection questions Correction: 9:45 - Each diagram should have total length "2L" instead of "L". Suggested answers to reflection questions: 1.) Work-equivalent loads may produce moments in addition to forces at nodes where static-equivalent loads would only account for forces. 2.) To determine work-equivalent loads for trapezoidal distributed loading, simply add the loads one would get from uniform loading (magnitude = w2 in example) and triangular loading (peak magnitude = (w1-w2) in example).