Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 239

Transposing,

WK O =× °= sin. 22 8 400 × 0 388 . = 155 2 .

Thus, a force of 155.2 lb is necessary to pull the cart up the 22.8° angle of the ramp (friction
ignored). Note that the total amount of work is the same, whether the cart is lifted vertically (400 lb
× 5 ft = 2000 ft-lb), or pulled up the ramp (155.2 lb × 13 ft = 2000 ft-lb). The advantage gained in
using a ramp instead of a vertical lift is that less force is required—but through a greater distance.

11.5 PROPERTIES OF MATERIALS
When we speak of the properties of materials or a material's properties, what are we referring to
and why should we concern ourselves with this topic? The best way to answer this question is to
use an example where the environmental engineer, working with design engineers in a preliminary
design conference, might typically be exposed to engineering design data, parameters, and speci-
fications related to the properties of a particular construction material to be used in the fabrication
of, for example, a large mezzanine in a warehouse. In constructing this particular mezzanine, con-
sideration must be given to the fact that it will be used to store large, heavy equipment components.
The demands placed on the finished mezzanine create the need for the mezzanine to be built using
materials that can safely support a heavy load.
For illustration, let's say that the design engineers plan to use an aluminum alloy (structural, No.
17ST). Before they decide upon using No. 17ST and determining the required quantity required to
build the mezzanine, they must examine its mechanical properties to ensure that it will be able to
handle the intended load (they will also factor in, many times over, for safety, the use of a material
that will handle a load much greater than expected). Using a table on the mechanical properties of
engineering materials in Urquhart's Civil Engineering Handbook , they found the following infor-
mation for No. 17ST:

1. Ultimate strength (defined as the ultimate strength in compression for ductile materials,
usually taken as the yield point), including tension, 58,000 psi; compression strength,
35,000 psi; shear strength, 35,000 psi

2. Yield point tension, 35,000 psi

3. Modulus of elasticity, tension or compression, 10,000,000 psi

4. Modulus of elasticity, shear, 3,750,000 psi

5. Weight, 0.10 lb/in. 3

Is this information important to the environmental engineer? Well, in a specific sense, no—not
exactly; however, in a general sense, yes. What is important to the environmental engineer is that
procedures such as the one just described actually occur; that is, professional engineers do take
the time to determine the correct materials to use in constructing, for example, a mezzanine. Also,
when exposed to this type of information, the environmental engineer must know enough about
the language used to know what the design engineers are talking about—and to understand its sig-
nificance. A materials property is an intensive, often quantitative property of a material. Thus, it is
important for environmental engineers to understand the material property descriptor and also the
units used as metrics of value. In short, we must know and understand the meaning of nomenclature
of the materials to be used and their limits. This is important in order to compare the benefits of one
material vs. another when selecting the appropriate materials to be used. Remember Voltaire: “If
you wish to converse with me, define your terms.”
Let's take a look at a few other engineering terms and their definitions, so that we will be able to
converse. Keep in mind that many of these definitions are defined exactly and precisely in mathe-
matical formulas and computation. These exact and precise mathematical definitions are beyond the