Engineering Statics

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

Find the force of the piston and the reaction at the pin for the boom of a bucket truck.

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 forces acting on the raised bed of a dump truck.

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

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

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

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

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

Standard rigid body equilibrium problem.  Inclined bar, prevented from slipping by a cable.  

Find the coefficient of friction between a rope and a post.  

Student calculates $\bar{y}$ for a triangle.  Must use similar triangles get element $dA$.

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

A vertical force and an force at an angle act on a L shaped bracket supported by a pin.  The vertical force is known. Use Verignon's theorm to find the magnitude of the unknown force by taking moments about the pin.

Two weights are connected together and rest on inclined surfaces.  Must solve for tension in the cable, then find the angle of the second incline.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

Equilibrium of a rigid body.  Find tension to raise a pole.

Two known forces, and a third with known magnitude act on a rigid body.  Apply $\Sigma M = 0$ about a pin restraint to determine the direction of the third force.  The problem has two valid answers.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

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

Triangular Plate with weight, supported by a pin and roller and subjected to a vertical and a horizontal load.  No angles.

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

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.

Equilibrium of a particle, solution by rotating coordinate system.

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

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

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

Pulley supported by a cable, so the tension in the rope is constant.    Advice is a youtube video showing how to solve the problem.