Principles of Engineering
Learning materials for Berkeley Carroll's Upper School Principles of Engineering class.
- Engineering Design
- Civil Engineering
- Types of Forces
- Stress and Strain
- Elastic Modulus
- Stress-Strain Curves
- Material Selection
- Truss Design
- Mechanical Engineering
- Electrical Engineering
- Software Engineering
Engineering Design
Learn how to think like an engineer and start turning your ideas into reality.
Design Cycle
Failing Forward
Perspective Drawing
Reverse Engineering
Civil Engineering
Civil Engineering is concerned with the design, construction and maintenance of the public works we use everyday such as roads, bridges, dams, skyscrapers, and even the less glamorous like wastewater treatment and sewage.
Types of Forces
Learning Outcome: Identify the type of force acting on a structural member.
Stress and Strain
Learning Outcome: Predict how a structural member will react under a particular load given its shape and material.
Elastic Modulus
Learning Outcome: Use a material's Elastic Modulus to calculate a structural member's stress and/or strain.
Stress-Strain Curves
Learning Outcome: Use a stress-strain curve to identify the relationship between stress and strain, and the different strengths of a material.
Material Selection
Learning Outcome: Select a material for a given application considering cost, weight, and strength.
Truss Design
Learning Outcome: Identify the shapes and patterns that allow for a structure to efficiently hold a given load.
Mechanical Engineering
Learn how to design and make machines that both move and make tasks easier.
Energy
Energy is something that is found all over the physical and life sciences. Thermal Energy is what you experience when you burn your hand on the stove (again). Chemical Energy is what causes that (safely contained) explosion in chemistry class. In this section, we will focus solely on mechanical energy, or energy due to the movement (or potential movement) of an object.
Types of Mechanical Energy
Kinetic
Kinetic energy is the amount of energy an object has due to its movement (velocity).
Example
Mr. Box, who has a mass of 10 kilograms (kg), is sliding on a patch of ice at 2 meters per second (m/s) of velocity. How much kinetic energy would he have?
Mr. Box would have 20 Joules of Kinetic Energy.
Potential
Potential energy is the energy of an object or system due to its position relative to other objects.
Gravitational
Gravitational potential energy is calculated using an object's position within a gravitational field. Typically, this is considered to be the height (h) above the surface of the earth, which provides a constant gravitational acceleration (g) of around 9.8 meters per second squared.
Example
Mr. Box, who has a mass of 10 kg, is lifted 5 meters into the air above the surface of the Earth, which provides a gravitational acceleration of 9.8 meters per second squared. How much gravitational potential energy would Mr. Box have?
Mr. Box would have 490 Joules of gravitational potential energy.
Elastic Potential
Although similar to gravitational potential energy, elastic potential energy instead deals with the energy provided by a spring (or elastic) rather than gravity. A spring's constant (k), also known as "stiffness", is determined by its shape and material.
Example
Mr. Box (mass of 10 kg) is pressed against a spring with a spring constant of 1 N/m for 10 centimeters (or 0.1 meters). How much elastic potential energy does Mr. Box now have?
Mr. Box would have an elastic potential energy of 0.005 Joules.
Conservation of Energy
The conservation of energy is a fundamental principle of physics, which states:
The total energy of an isolated system is constant despite internal changes.
What this means within the context of our work in mechanical engineering is that the type of energy a system experiences may change, but the total amount of energy in that system will not.
For example:
In a previous question, we lifted Mr. Box (mass of 10 kg) to a height of 5 meters, which gave him a gravitational potential energy of 490 Joules. Dropping him from that height would begin to convert the potential energy into kinetic energy. When Mr. Box gets back to the ground (height of 0 meters) his potential energy will have been entirely converted to kinetic energy.
How much velocity is he moving with when he hits the ground (GPE = 0 J, KE = 490 J)?
Work
Background
In the previous unit on Civil Engineering, we discussed the principle of force, and the idea that:
When the forces acting on Mr. Box add up to zero, he will not accelerate.
With things like bridges, roads, and buildings this (usually) means the object is not moving, and will continue not to move. Trouble arises when the forces are no longer balanced, and things start to move.
But what happens when if do want Mr. Box to move? What happens when we remove one of the forces on purpose?
Calculating Work using Force
Now that the forces are no longer balanced, Mr. Box will be allowed to accelerate. How much he accelerates depends on how long (in length) the force is applied for. We call this: doing work on Mr. Box. To calculate the amount of work done, we multiply the amount of force (in Newtons) by the length (in meters) the force is applied. The unit for work is Newton-meter, or Joule.
Example
If you were to pull Mr. Box with a force of 10 Newtons for a length of 1 meter, you will have done 10 Joules of work on Mr. Box.
Note: Similar to our working calculating Stress and Strain, it is important to always use proper units when calculating work. For example, 200 cm should be converted to 2 m, 2 kN should be converted to 2,000 N, etc.
Calculating Work using Energy
Alternatively, you may calculate the work performed on an object using its change in total energy.
Note: In math, the symbol Δ (or delta) is typically used as a shorthand to say "change in". For example, ΔE is a short way of saying "change in energy."
Previously, we discussed the different types of energy, such as kinetic and potential. When an object changes the total energy of another object, it is said to have done work on that object.
Examples
You lift Mr. Box (10 kg) in the air. Originally his gravitational potential energy was 0 Joules. By raising him in the air 0.98 meters, you have done 100 Joules of work on him.
This can also apply to changes in kinetic energy:
Mr. Box is sliding with 50 Joules of kinetic energy. He hits a wall that brings him to a stop (0 Joules). The wall did 50 Joules of work on Mr. Box.
NOTE: The work is negative because the wall is taking energy away from Mr. Box.
Mechanical Advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. This is calculated as the ratio between the input force, and the output force of the device/tool.
For example, "Some Device" that is able to turn a 10 N input force into a 20 N output force is said to have a mechanical advantage of 2.
NOTE: Because mechanical advantage is a ratio, it does not have a unit.
Simple Machines
Typically, we will achieve mechanical advantage by employing simple machines. A simple machine is a mechanical device that changes the direction and/or magnitude of a force and come in a few varieties.
Inclined Plane
An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, with one end higher than the other, used as an aid for raising or lowering a load.
Examples: Ramps, slides, roofs
Levers
A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. Levers are then classified by the relative positions of the fulcrum, input, and output forces.
Examples: See-saws (first-class), wheelbarrows (second-class), fishing rod (third-class)
Wedge
A wedge is a triangular shaped tool that is typically used to separate two objects or portions of an object. It can also be used to hold objects in place, and resembles a portable inclined plane.
Examples: Axes, door-stoppers, knives
Wheel & Axle
The wheel and axle is a simple machine, consisting of a wheel attached to a smaller axle so that these two parts rotate together, in which a force is transferred from one to the other. The wheel and axle can be viewed as a version of the lever, with a drive force applied tangentially to the perimeter of the wheel, and a load force applied to the axle supported in a bearing, which serves as a fulcrum.
Screw
The screw is a simple machine that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. The amount of mechanical advantage achieved by a screw depends on both the input radius, and the pitch length.
The input radius is considered to be the distance from where the force is applied, to the axis around which the screw spins. The pitch length is the distance between each threads of the screw, or how long the screw has moved after one rotation.
Other Types of Machines
Up until this point, we have discussed simple machines which are well... simple. They are comprised of very few parts -- sometimes only one. There are also machines that, by their nature, require (at least) a few moving parts to achieve mechanical advantage.
Gears
Pulleys
Conservation of Energy
An important thing to note when dealing with simple machines
Collisions
Learning Outcome: Identify whether a collision is elastic or inelastic, and calculate the velocities of the objects involved before and after.
Machine Elements
Learning Outcome: Identify various machine elements, describe their function, and include them in the construction of simple and complex machines.
Fasteners
A fastener is a machine element that joins or affixes two or more objects together. Some fasteners do this using chemical properties (like glue), or heat (like soldering), but this page will focus specifically on mechanical fasteners.
A mechanical fastener holds two (or more) pieces together using the mechanical advantage of a simple machine. In order to separate the pieces, the simple machine must be overcome or undone.
Nails
A nail is a (typically) metal device that is driven through two (or more) pieces, acting as a wedge and using friction to keep them fastened together.
| Name | Description | Example | |
| Nail |
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| Screw |  |
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| Bolt |
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Bolts vs. Screws
You may have noticed that
Screws fasten objects together on their own.
Bolts fasten objects together with the help of a nut on the other side.
The Machinery's Handbook describes the distinction between bolts and screws in more detail:
A bolt is an externally threaded fastener designed for insertion through holes in assembled parts, and is normally intended to be tightened or released by torquing a nut. A screw is an externally threaded fastener capable of being inserted into holes in assembled parts, of mating with a preformed internal thread or forming its own thread, and of being tightened or released by torquing the head. An externally threaded fastener which is prevented from being turned during assembly and which can be tightened or released only by torquing a nut is a bolt. (Example: round head bolts, track bolts, plow bolts.) An externally threaded fastener that has thread form which prohibits assembly with a nut having a straight thread of multiple pitch length is a screw. (Example: wood screws, tapping screws.)[60]
Screws
NOTE: We are talking here about screws as a physical machine element, rather than a theoretical simple machine screw.
Contrary to Nails which rely solely on friction to fasten two pieces together, screws use the mechanical advantage provided by their threading.
They come in a wide variety types and sizes. Which you choose varies drastically depending
Bolts
Nuts
When combined with a Bolt,
Shafts
Bearings
A bearing is a machine element