Statics

Frontmatter

1. Introduction

Abstract

Nearly, each “Statics” book starts with the statement similar to this one: “the main objective of the book is to provide a student with a clear understanding of mechanics and develop the ability to analyze the problem in a simple and logical manner.” It is indeed hard to argue with such a statement. And if any of the “Statics” books would “provide a clear understanding and ability to analyze the problem,” this book would be unnecessary.

Igor Emri, Arkady Voloshin

2. Laws of Nature and Fundamental Concepts

Abstract

Basic concepts and definitions

Igor Emri, Arkady Voloshin

3. From Reality to a Free Body Diagram

Abstract

How to single out the structure element of interest from its surrounding

Igor Emri, Arkady Voloshin

4. Resultant and Equilibrium of Forces Acting at a Point

Abstract

This chapter deals with forces acting at a point. This, however, does not imply that the rigid body has to be small. Sometimes lines of action of all forces applied to a body intersect at the same point. Thus, the effect of these forces may be studied as if they would act at a point. Such forces are called concurrent. Any two nonparallel in-plane forces acting on a rigid body will always intersect in a point. When two forces are parallel and are opposite in direction, they are called a couple of forces (Sect. 2.​2.​2) and they form a moment that tends to rotate the body. The effect of moments on rigid bodies will be discussed in Chap. 5. When a moment is small, in engineering practice we often neglect its effect and consider forces as if they are acting at a point.

Igor Emri, Arkady Voloshin

5. Equilibrium of Rigid Bodies

Abstract

In Chap. 4, we discussed equilibrium of objects loaded by concurrent forces. Such objects were modeled as a particle (point). In these cases, the principle of parallelogram of forces may be applied to find the resultant force. Setting the resultant force equal to zero, according to the First Newton’s law, leads to equilibrium equations. In reality, however, there are many situations when a body cannot be modeled as a particle, i.e., forces acting upon it are not concurrent, Fig. 5.1a.

Igor Emri, Arkady Voloshin

6. Distributed Forces: Center of Gravity and Centroids

Abstract

In previous chapters, we have learned about the equilibrium of rigid bodies loaded by concentrated forces and moments. In this chapter, we will discuss the difference between the concentrated forces, i.e., force acting on a body at a given point, and the distributed forces. It is obvious that the notion of a concentrated force is a simplification of the load acting on a small area. This may be a valid representation when the area of the contact between the load and the body is small. However, when the contact area is not small, relative to the rigid body size, we have to account for the actual force distribution.

Igor Emri, Arkady Voloshin

7. Classification of Structural Elements

Abstract

In previous chapters, we were dealing with equilibrium of objects modeled either as particles (points) or rigid bodies depending on their size and loading conditions. As we already know the actual geometry of a rigid body has no effect on its equilibrium. The latter depends only on the moments and the relative location of the forces acting upon the body.

Igor Emri, Arkady Voloshin

8. Analysis of Truss Structures

Abstract

As we described in Chap. 7, there are several main types of structural elements. In this chapter, we will discuss ways to find the internal forces acting in structures. Structures may be spatial or planar. For example, if all of the structure members and loads belong to the same plane, we will call such a structure planar.

Igor Emri, Arkady Voloshin

9. Beams

Abstract

In Chap. 7, we have introduced three classes of structural elements: truss members, beams, and cables. For each class, we have discussed the requirements that structural element has to meet in order to belong to a particular class. In Chap. 8, we have discussed trusses, and frames. Frames and mechanisms (Chap. 11) are built from truss members and beams.

Igor Emri, Arkady Voloshin

10. Cables

Abstract

How to calculate the internal forces in cables loaded by concentrated forces?

Igor Emri, Arkady Voloshin

11. Compound Structures

Abstract

How to identify a compound structure

Igor Emri, Arkady Voloshin

12. Friction

Abstract

About the origin of friction

Igor Emri, Arkady Voloshin

Backmatter