Real-Life Math
You're part of an engineering team that has designed a machine that
will operate in a railway tank where explosive gases are present. The machine
is designed to reach out and pull an object towards it. One component, a round
actuator arm, must transmit a force (applied load) of 10,000 pounds in tension.
Note: metallurgists still use imperial measurements.
Because the components used must be made of a spark-proof
material, the design team needs your expertise as a materials (or metallurgical)
technician in choosing a design for this component.
You must take into
consideration 2 factors:
- The material -- whether it is prone to sparking
- The diameter of the actuator -- you want the smallest diameter possible
that will withstand 10,000 pounds
Due to cost considerations, you have only 3 materials to choose from,
each with their own characteristics:
| Steel | Aluminum | Brass |
| Disposition to Spark | High | Low | Low |
| Yield Stress in Pounds per Square Inch | 50,000 | 40,000 | 60,000 |
With all designs, you must include a factor of
safety in your calculations. The industry standard is a factor of safety
of 5.
Evaluate each material and choose the one that most closely fits
your criteria.
Hint: Calculate the maximum design strength using
this formula:
Yield stress / factor of safety
Then use the
maximum design strength to calculate the diameter of the actuator.
Maximum
design strength = applied load / area
Area of a circle = pi x
r2