William Haynes

Find the shear, normal force and bending moment at a point in a beam supporting a uniformly distributed load.

Draw shear and bending moment diagram for  beam with a uniformly distributed load and a concentrated force

Use this as a template to create Shear and Bending Moment diagram problems.   Supports concentrated forces and moments, uniformly distributed loads, and uniformly varying loads.

Draw shear and bending moment diagram for a symmetrically loaded beam resting on the ground.

Draw Shear and Bending Moment Diagrams for a simply supported beam with triangular loading

A demonstration of the Shear and Bending Moment Extension

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

Draw Shear and Bending Moment Diagrams for a simply supported or overhanging beam loaded with one or two concentrated forces.

Concept check on sign convention for shear and bending moment diagrams

Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

Shear and Bending Moment diagram for a beam with several concentrated loads.  Student can't see V & M diagrams a hints.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

Find roots and the area under a parabola

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.

Sum three force vectors based on a written description of the situation.

Determine the mechanical advantage of a pair of compound lopping shears.

An A-frame structure supporting a force or a moment.  One leg is a two force body.

Find all forces on a two-part, symmetrical frame supporting a load.