Engineering Statics

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

3D equilibrium of a particle problem.  Rectangular steel plate supported by three cables, dimensions and density given.

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Find the reactions of a rigid body (a truss) at a pin and roller.  All loads are either horizontal or vertical.

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

Friction

Friction

Friction

Replace two parallel forces with an equivalent single force

Friction

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Find the tensions is a system of cables supporting two loads.

Simple truss with a zero-force member

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

This just an equilibrium of a particle problem, but posed in context of a joint as a warm-up for the method of joints.

Advice is brief.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Find the forces in the members of a truss using the method of joints.

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

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.