Engineering Statics

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.

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.

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

Find the reactions of a simply-supported beam with a trapazoidal distributed load.

Find the reactions for a beam with a uniformly distributed load.

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 of a shape made from a rectangle, triangle, and circle.

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

Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.

Given three vectors with integer components, find the corresponding magnitude and direction.

Find roots and the area under a parabola