Engineering Statics

Solve for the internal force in three members of a truss.

Find the rectangular (scalar) components of a force for two coordinates systems.

Friction

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

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.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

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.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

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

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.

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.