Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

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

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

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

Find the shear, normal force and bending moment at a point in a beam supporting a uniformly distributed load.

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

Draw shear and bending moment diagram for a symmetrically loaded beam resting on the ground.

Draw shear and bending moment diagram for  beam with a uniformly distributed load and a concentrated force

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

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

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

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

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

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

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

Find roots and the area under a parabola

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 up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

An A-frame structure supporting a load at the top.  Simple because both legs are two force bodies.

Classic machine problem.  Find the mechanical advantage of a pair of pliers and the force on the hinge pin.

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

Determine the single force which is equivalent to a force and a couple.

Replace two forces with a equivalent force-couple system at a specified point.

Replace two parallel forces with an equivalent single force

Find the sum of two couples in a plane.

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

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

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Determine the resultant of three random 2-D vectors.