Part I
Setting the Stage for Mechanics of Materials
In this part . . .
This part introduces you to the basic concepts of mechanics of materials and its relationship to and differences from basic statics and dynamics (known simply as mechanics). You get a short refresher in several mathematics areas, including geometry, trigonometry, and basic calculus, that you may need along the way, and I discuss the basic unit systems while showing you the base units mechanics of materials uses from each system.
But thatâs not all! I also provide a short review of basic statics skills and of computing internal forces of structural members, which are critical to your continued analysis of mechanics of materials. I round out the part with chapters on computing section properties such as the cross-sectional area, centroid location, and the first and second moments of area, all of which are integral to mechanics of materials.
Chapter 1
Predicting Behavior with Mechanics of Materials
In This Chapter
Defining mechanics of materials Introducing stresses and strains Using mechanics of materials to aid in design Mechanics of materials is one of the first application-based engineering classes you face in your educational career. Itâs part of the branch of physics known as mechanics, which includes other fields of study such as rigid body statics and dynamics. Mechanics is an area of physics that allows you to study the behavior and motion of objects in the world around you.
Mechanics of materials uses basic statics and dynamics principles but allows you to look even more closely at an object to see how it deforms under load. Itâs the area of mechanics and physics that can help you decide whether you really should reconsider knocking that wall down between your kitchen and living room as you remodel your house (unless, of course, you like your upstairs bedroom on the first floor in the kitchen).
Although statics can tell you about the loads and forces that exist when an object is loaded, it doesnât tell you how the object behaves in response to those loads. Thatâs where mechanics of materials comes in.
Tying Statics and Mechanics Together
Since the early days, humans have looked to improve their surroundings by using tools or shaping the materials around them. At first, these improvements were based on an empirical set of needs and developed mostly through a trial-and-error process. Structures such as the Great Pyramids in Egypt or the Great Wall of China were constructed without the help of fancy materials or formulas. Not until many centuries later were mathematicians such as Sir Isaac Newton able to formulate these ideas into actual numeric equations (and in many cases, to remedy misconceptions) that helped usher in the area of physics known as mechanics.
Mechanics, and more specifically the core areas of statics and dynamics, are based on the studies and foundations established by Newton and his laws of motion. Both statics and dynamics establish simple concepts that prove to be quite powerful in the world of analysis. You can use statics to study the behavior of objects at rest (known as equilibrium), such as the weight of snow on your deck or the behavior of this book as it lies on your desk. Dynamics, on the other hand, explains the behavior of objects in motion, from the velocity of a downhill skier to the trajectory of a basketball heading for a winning shot.
What statics and dynamics both have in common is that at their fundamental level, they focus on the behavior of rigid bodies (or objects that donât deform under load). In reality, all objects deform to some degree (hence why theyâre called deformable bodies), but the degree to which they deform depends entirely on the mechan...
