William Haynes

Draw Shear and Bending Moment Diagrams for a cantilever beam with two forces and a concentrated moment load.

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

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

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

End of chapter exercises for Engineering Statics: Open and Interactive 

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.

Find moment of inertia and radius of gyration for a built-up beam made of two channels and two plates.

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

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

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

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

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

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.

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

Write expressions for the moment of inertia of simple shapes about various axes.

Find moment of inertia wrt the x- and y- axes for a shape made up of two rectangles.

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

End of chapter exercises for Engineering Statics: Open and Interactive 

Find the force required to produce a given moment, or vice-versa.

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.

demonstrates bug on geogebra diagram

Homework set.  Identify zero force members and utilize special loading conditions to simplify trusses.

Determine the forces in the pistons of a hydraulicly operated excavator.

Student calculates $\bar{y}$ for a triangle.  Must use similar triangles get element $dA$.

Equilibrium of a rigid body.  Find tension to raise a pole.