Engineering Statics

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

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

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

An A-frame structure supporting a force and a moment. The feet are at the different vertical positions so the solution will require simultaneous equations, unless you rotate the coordinate system.

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

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

Find an interior angle and length of a diagonal of a random parallelogram.

Solve for the internal force in three members of a truss.

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

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

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

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

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.