Engineering Statics

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

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

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.

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

Determine the mechanical advantage of a pair of compound lopping shears.

Determine the forces in the pistons of a hydraulicly operated excavator.

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

Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

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

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

Concept check on sign convention for shear and bending moment diagrams

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

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

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

Find the sum of two couples in a plane.

Find the moment of a couple formed by two equal and opposite forces.

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

Calculate the moment of a force.  Must calculate perpendicular distance based on simple geometry, and recognize direction.

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.

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

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.

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.

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