Advanced SHEAR and MOMENT DIAGRAMS Example Problem (with Curved Distributed Load)

This advanced Shear and Moment Diagrams example problem shows the hardest problem you could see in a Statics or Mechanics of Materials course. If you can solve this one – you can solve any of them. This problem contains every type of loading you can expect to see (Point Force, Point Moment, Rectangular distributed load, Triangular distributed load, and a distributed load represented by a function). Note – trapezoidal distributed loads are also common – but these are just an overlapped rectangle and triangle that you can treat separately. You will learn how to find the Centroid of an Area by Integration, how to use the Shear and Moment Diagram Graphical Method, Shear and Moment Diagram Area Method, and Shear and Moment Diagram Equation Method – all of which will be used for different portions of this drawing. The most complex part is dealing with the arbitrary distributed load, which crosses the x-axis of the shear diagram, resulting in a maximum in the moment diagram. This video steps through the calculus required to create the required functions that will be integrated and solved to complete the problem. TIMECODES 0:00 Introduction 0:55 Purpose of Shear and Moment Diagrams 2:00 Centroid of Triangle and Rectangle 2:50 Centroid of a Curved Function 3:52 Reaction Forces 5:02 How to Draw Shear Diagram 7:58 Moment of Rectangle Distributed Load – Area Method 10:03 Moment of Triangle Distributed Load – Equation Method 13:02 Moment of Curved Distributed Load – Equation Method