Engineering Statics

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.

An A-frame structure supporting a force and a moment. The feet are at the same vertical position, so taking moments at one foot yields the y component of the reaction at the other.

Developing concepts for shear and bending moment diagrams. 

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

Homework set.  Application of Parallel Axis Theorem to find area Moment of Inertia

Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

Homework set.  Basic concepts of Area Moment of Inertia.

Homework set.  Uniformly and uniformly varying distributed loads.

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

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

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

Given the specifications of two vectors, draw the parallelogram representing their sum, then estimate length of the diagonal. 

Homework set.  Vector addition in two dimensions by summing scalar components.

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

Homework set.  Identify student errors when drawing free body diagrams.

Homework set.  Rigid body equilibrium solved using the three-force body principle.

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.