Engineering Statics

Calculate the moment of a force about three points using the definition of a Moment.  All forces and points are in the same plane.

Solve a random oblique triangle for sides and angles.

Determine the resultant of three random 2-D vectors.  

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

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

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Find the rectangular (scalar) components of a force for two coordinates systems.

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

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

Find reactions for a particle in equilibrium

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

Given a point and a line, determine the distance between them.

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

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.

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

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

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

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.

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

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

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.

Friction

Friction

Friction