Gross properties of solids

[Amin 6457]

GROSS PROPERTIES OF SOLIDS

 

We are all familiar with the matter that makes up the world and ourselves, as well as the fact that it comes in three different forms: as solid, liquid, or gas. This chapter discusses the properties of solid matter, with a focus on the applications of those principles to the design of structures. Liquids and gases are discussed in the next chapter

 

 

 

Solid matter covers a wide range of forms, everything from a compacted block of trash containing every form of household rubbish to a glittering diamond, consisting of carbon atoms arranged in an orderly, uniform "crystalline" arrangement.

 

At a high level of abstraction, chunks of matter have certain properties that can be characterized and measured, for example color; density, or ratio of mass to volume; and various measures of strength, or the ability of that chunk of matter to retain its structure or "integrity" when subjected to various forces. Obviously these things are much easier to characterize for, say, a diamond than for a block of compacted trash.

 

Solid matter also has certain properties of "scale" that are independent of what the matter is made up of. For example, let's take a set of cubes of solid matter without regard to what the matter is. Suppose one cube is a centimeter on a side. Now let's suppose Dexter stacks up the cubes to make a bigger cube that is two centimeters on a side. This doubles the linear dimensions of the cube. The surface area of the cube has expanded by a factor of four, while the volume and mass of the cube has expanded by a factor of eight. In more formal terms, doubling the linear dimensions of an object squares its surface area and cubes its volume and mass. This means that as an object grows bigger, its volume and mass increase much more rapidly than its surface area.

 

 

1950s horror movies such as THEM envisioned monster ants, but in fact such scaling effects prevent insects from becoming very large. For one thing, they don't have lungs, and have to acquire oxygen through pores in their chitinous skins. Doubling their size would increase their volume and mass twice as fast as it would increase their surface area, halving their ability to obtain oxygen for that mass, and at a certain size a giant insect would simply suffocate.

 

A more important scaling issue that rules out giant insects is the issue of "compressive strength", or the ability of a structural support to bear weight placed on top of it. The compressive strength of a structural support, such as a column that holds up a building, is proportional to the cross-sectional area of a horizontal slice through the column. A cross section is just one face of the surface of an object, and so like surface area increases with the square of a linear increase in size. However, the mass of the building increases with the cube of a linear increase in size.

 

Double the linear dimensions of a building and the ability of a column to support the building's weight is increased by four, while the mass and the load on the column is increased by eight. The column now has to proportionately bear twice as much load as it did at the smaller scale. This means that more, or disproportionately large, columns must be used to support a larger building. Insects generally have spindly bodies and legs, while an elephant has great stumpy massive legs. If an insect was scaled up to large size, it would simply collapse of its own weight. However, horror movie fans can still take comfort

that deadly venomous or parasitic insects are not ruled out by the laws of physics