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

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

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.

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

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.

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

Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.

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.

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Homework set.  Determine the moment of a force using the definition of the moment, $M = F d_\perp$.

Find the tension required to hold a pole at a specified angle.

Homework set.  Calculate resultant moment of one or more couples. 

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

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

Find the sum of two couples in a plane.

Find the moment of a couple formed by two equal and opposite forces.

This question tests to see if students can recognise an alternating series and based on the alternating series test and the divergence test determine if it is convergent or divergent.

At the moment there is no example included with $b_n\rightarrow 0$ which isn't eventually monotonically convergent.