Preview text and Solutions Manual to accompany Vector Mechanics for Engineers, Statics Eleventh Edition Ferdinand P. Beer Late of Lehigh University E. Russell Johnston, Jr. Late of University of Connecticut David F.

Mazurek United States Coast Guard Academy Prepared Amy Mazurek PROPRIETARY AND CONFIDENTIAL This Manual is the proprietary property of Education and protected copyright and other state and federal laws. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. Alaska bm 2000 bedienungsanleitung pdf file online. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. TO THE INSTRUCTOR As indicated in its preface, Vector Mechanics for Engineers: Statics is designed for the first course in statics offered in the sophomore year of college.

New concepts have, therefore, been presented in simple terms and every step has been explained in detail. However, because of the large number of optional sections which have been included and the maturity of approach which has been achieved, this text can also be used to teach a course which will challenge the more advanced student. The text has been divided into units, each corresponding to a topic and consisting of one or several theory sections, one or several Sample Problems, a section entitled Solving Problems on Your Own, and a large number of problems to be assigned. To assist instructors in making up a schedule of assignments that will best fit their classes, the various topics covered in the text have been listed in Table I and a suggested number of periods to be spent on each topic has been indicated. Both a minimum and a maximum number of periods have been suggested, and the topics which form the standard basic course in statics have been separated from those which are optional. The total number of periods required to teach the basic material varies from 26 to 39, while covering the entire text would require from 41 to 65 periods. If allowance is made for the time spent for review and exams, it is seen that this text is equally suitable for teaching a basic statics course to students with limited preparation (since this can be done in 39 periods or less) and for teaching a more complete statics course to advanced students (since 41 periods or more are necessary to cover the entire text).

In most instances, of course, the instructor will want to include some, but not all, of the additional material presented in the text. In addition, it is noted that the text is suitable for teaching an abridged course in statics which can be used as an introduction to the study of dynamics (see Table I).

The problems have been grouped according to the portions of material they illustrate and have been arranged in order of increasing difficulty, with problems requiring special attention indicated asterisks. We note that, in most cases, problems have been arranged in groups of six or more, all problems of the same group being closely related.

This means that instructors will easily find additional problems to amplify a particular point which they may have brought up in discussing a problem assigned for homework. Accessible through Connect are problem sets for each chapter that are designed to be solved with computational software. Solutions for these problems, including analyses of the problems and problem solutions and output for the most widely used computational programs, are also available through Connect. To assist in the preparation of homework assignments, Table II provides a brief description of all groups of problems and a classification of the problems in each group according to the units used. It should also be noted that the answers to all problems are given at the end of the text, except for those with a number in italic.

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Because of the large number of problems available in both systems of units, the instructor has the choice of assigning problems using SI units and problems using U.S. Customary units in whatever proportion is found to be most desirable for a given class. To illustrate this point, sample lesson schedules are shown in Tables IV, and V, together with various alternative lists However, the traditional use of commas to separate digits into groups of three has been maintained for and larger numbers involving U.S.

Customary units. Chapter 2 Statics of Particles This is the first of two chapters dealing with the fundamental properties of force systems.

A simple, intuitive classification of forces has been used: forces acting on a particle (Chap. 2) and forces acting on a rigid body (Chap. Chapter 2 begins with the parallelogram law of addition of forces and with the introduction of the fundamental properties of vectors. In the text, forces and other vector quantities are always shown in type. Thus, a force F (boldface), which is a vector quantity, is clearly distinguished from the magnitude F (italic) of the force, which is a scalar quantity.

On the blackboard and in handwritten work, where lettering is not practical, vector quantities can be indicated underlining. Both the magnitude and the direction of a vector quantity must be given to completely define that quantity. Thus, a force F of magnitude F 280 lb, directed upward to the right at an angle of with the horizontal, is indicated as F 280 lb when printed or as F 280 lb when handwritten. Unit vectors i and j are introduced in Sec. 2.7, where the rectangular components of forces are considered. In the early sections of Chap. 2 the following basic topics are presented: the equilibrium of a particle, first law, and the concept of the diagram.

These first sections provide a review of the methods of plane trigonometry and familiarize the students with the proper use of a calculator. A general procedure for the solution of problems involving concurrent forces is given: when a problem involves only three forces, the use of a force triangle and a trigonometric solution is when a problem involves more than three forces, the forces should be resolved into rectangular components and the equations 0, 0 should be used. The second part of Chap.

2 deals with forces in space and with the equilibrium of particles in space. Unit vectors are used and forces are expressed in the form F Fxi Fyj Fzk where i, j, and k are the unit vectors directed respectively along the x, y, and z axes, and is the unit vector directed along the line of action of F. Note that since this chapter deals only with particles or bodies which can be considered as particles, problems involving compression members have been postponed with only a few exceptions until Chap.

4, where students will learn to handle problems in a uniform fashion and will not be tempted to erroneously assume that forces are concurrent or that reactions are directed along members. It should be observed that when SI units are used a body is generally specified its mass expressed in kilograms.

The weight of the body, however, should be expressed in newtons. Therefore, in many equilibrium problems involving SI units, an additional calculation is required before a diagram can be drawn (compare the example in Sec.

2.3C and Sample Probs. 2.5 and 2.9). This apparent disadvantage of the SI system of units, when compared to the U.S. Customary units, will be offset in dynamics, where the mass of a body expressed in kilograms can be entered directly into the equation F ma, whereas with U.S.

Customary units the mass of the body must first be determined in (or slugs) from its weight in pounds. Chapter 3 Rigid Bodies: Equivalent Systems of Forces The principle of transmissibility is presented as the basic assumption of the statics of rigid bodies. However, it is pointed out that this principle can be derived from three laws of motion (see Sec. 16.1D of Dynamics). The vector product is then introduced and used to define the moment of a force about a point. The convenience of using the determinant form (Eqs. 3.19 and 3.21) to express the moment of a force about a point should be noted.

The scalar product and the mixed triple product are introduced and used to define the moment of a force about an axis. Again, the convenience of using the determinant form (Eqs. 3.41 and 3.44) should be noted. The amount of time which should be assigned to this part of the chapter will depend on the extent to which vector algebra has been considered and used in prerequisite mathematics and physics courses. It is felt that, even with no previous knowledge of vector algebra, a maximum of four periods is adequate (see Table I). 3.12 through 3.15 couples are introduced, and it is proved that couples are equivalent if they have the same moment. While this fundamental property of couples is often taken for granted, the authors believe that its rigorous and logical proof is necessary if rigor and logic are to be demanded of the students in the solution of their mechanics problems.

In Section 3.3, the concept of equivalent systems of forces is carefully presented. This concept is made more intuitive through the extensive use of equations (see Figs. 3.34 through 3.41). Note that the moment of a force is either not shown or is represented a green vector (Figs. 3.10 and 3.22). A red vector with the symbol is used only to represent a couple, that is, an actual system consisting of two forces (Figs.

3.33 through 3.41). Section 3.4D is it introduces the concept of a wrench and shows how the most general system of forces in space can be reduced to this combination of a force and a couple with the same line of action. Since one of the purposes of Chap. 3 is to familiarize students with the fundamental operations of vector algebra, students should be encouraged to solve all problems in this chapter as well as using the methods of vector algebra. However, many students may be expected to develop solutions of their own, particularly in the case of problems, based on the direct computation of the moment of a force about a given point as the product of the magnitude of the force and the perpendicular distance to the point considered. Such alternative solutions may occasionally be indicated the instructor (as in Sample Prob.

3.9), who may then wish to compare the solutions of the sample problems of this chapter with the solutions of the same sample problems given in Chaps. 3 and 4 of the parallel text Mechanics for Section 5.2A explains the use of differential elements in the determination of centroids integration. The theorems of are given in Sec. Sections 5.3A and 5.3B are they show how the resultant of a distributed load can be determined evaluating an area and locating its centroid. Section 5.4 deals with centers of gravity and centroids of volumes.

Here again the determination of the centroids of composite shapes precedes the calculation of centroids integration. It should be noted that when SI units are used, a given material is generally characterized its density (mass per unit volume, expressed in rather than its specific weight (weight per unit volume, expressed in The specific weight of the material can then be obtained multiplying its density g 9.81 (see footnote, page 234 of the text). Chapter 6 Analysis of Structures In this chapter students learn to determine the internal forces exerted on the members of structures. The chapter starts with the statement of third law (action and reaction) and is divided into two parts: (a) trusses, that is, structures consisting of members only, (b) frames and machines, that is, structures involving multiforce members. After trusses and simple trusses have been defined in Sec.

6.1A, the method of joints and the method of sections are explained in detail in Sec. 6.1B and Sec.

6.2A, respectively. Since a discussion of diagram is not included in this text, the use of notation has been avoided, and a uniform notation has been used in presenting the method of joints and the method of sections. In the method of joints, a diagram should be drawn for each pin.

Since all forces are of known direction, their magnitudes, rather than their components, should be used as unknowns. Following the general procedure outlined in Chap. 2, joints involving only three forces are solved using a force triangle, while joints involving more than three forces are solved summing x and y components. Sections 6.1C and 6.1D are optional. It is shown in Sec.

6.1C how the analysis of certain trusses can be expedited recognizing joints under special loading conditions, while in Sec. 6.1D the method of joints is applied to the solution of trusses.

It is pointed out in Sec. 6.1B that forces in a simple truss can be determined analyzing the truss joint joint and that joints can always be found that involve only two unknown forces. The method of sections (Sec. 6.2A) should be used (a) if only the forces in a few members are desired, or (b) if the truss is not a simple truss and if the solution of simultaneous equations is to be avoided (for example, Fink truss).

Students should be urged to draw a separate diagram for each section used. The free body obtained should be emphasized shading and the intersected members should be removed and replaced the forces they exerted on the free body. It is shown that, through a judicious choice of equilibrium equations, the force in any given member can be obtained in most cases solving a single equation. Section 6.2B is it deals with the trusses obtained combining several simple trusses and discusses the statical determinacy of such structures as well as the completeness of their constraints. Structures involving multiforce members are separated into frames and machines. Frames are designed to support loads, while machines are designed to transmit and modify forces.

It is shown that while some frames remain rigid after they have been detached from their supports, others will collapse (Sec. In the latter case, the equations obtained considering the entire frame as a free body provide necessary but not sufficient conditions for the equilibrium of the frame. It is then necessary to dismember the frame and to consider the equilibrium of its component parts in order to determine the reactions at the external supports.

The same procedure is necessary with most machines in order to determine the output force Q from the input force P or inversely (Sec. Students should be urged to resolve a force of unknown magnitude and direction into two components but to represent a force of known direction a single unknown, namely its magnitude. While this rule may sometimes result in slightly more complicated arithmetic, it has the advantage of matching the numbers of equations and unknowns and thus makes it possible for students to know at any time during the computations what is known and what is yet to be determined.

Chapter 7 Forces in Beams and Cables This chapter consists of five groups of sections, all of which are optional. The first three groups deal with forces in beams and the last two groups with forces in cables. Most likely the instructor will not have time to cover the entire chapter and will have to choose between beams and cables. Section 7.1 defines the internal forces in a member. While these forces are limited to tension or compression in a straight member, they include a shearing force and a bending couple in the case of multiforce members or curved members.

Problems in this section do not make use of sign conventions for shear and bending moment and answers should specify which part of the member is used as the free body. In Section 7.2 the usual sign conventions are introduced and shear and diagrams are drawn. All problems in these sections should be solved drawing the freebody diagrams of the various portions of the beams. The relations among load, shear, and bending moment are introduced in Sec. Problems in this section should be solved evaluating areas under load and shear curves or formal integration (as in Probs. 7.85 through 7.88).

Some instructors may feel that the special methods used in this section detract from the unity achieved in the rest of the text through the use of the diagram, and they may wish to omit Sec. Others will feel that the study of shear and diagrams is incomplete without this section, and they will want to include it. Sergdriver mr double. The latter view is particularly justified when the course in statics is immediately followed a course in mechanics of materials. Sections 9.5 and 9.6 deal with the moments of inertia of masses. Particular emphasis is placed on the moments of inertia of thin plates (Sec. 9.5C) and on the use of these plates as differential elements in the computation of moments of inertia of symmetrical threedimensional bodies (Sec. Section 9.6 is optional but should be used whenever the following dynamics course includes the motion of rigid bodies in three dimensions.

Sections 9.6A and 9.6B introduce the moment of inertia of a body with respect to an arbitrary axis as well as the concepts of mass products of inertia and principal axes of inertia. Section 9.6C discusses the determination of the principal axes and principal moments of inertia of a body of arbitrary shape.

When solving many of the problems of Chap. 5, information on the specific weight of a material was generally required. This information was readily available in problems stated in U.S. Customary units, while it had to be obtained from the density of the material in problems stated in SI units (see the last paragraph of our discussion of Chap. 9, when SI units are used, the mass and mass moment of inertia of a given body are respectively obtained in kg and directly from the dimensions of the body in meters and from its density in However, if U.S.

Customary units are used, the density of the body must first be calculated from its specific weight or, alternatively, the weight of the body can be obtained from its dimensions and specific weight and then converted into the corresponding mass expressed in (or slugs). The mass moment of inertia of the body is then obtained in (or Sample Problem 9.12 provides an example of such a computation.

Attention is also called to the footnote on page of the 530 regarding the conversion of mass moments of inertia from U.S. Customary units to SI units.

Chapter 10 Method of Virtual Work While this chapter is optional, the instructor should give serious consideration to its inclusion in the basic statics course. Indeed, students who learn the method of virtual work in their first course in mechanics will remember it as a fundamental and natural principle. They may, on the other hand, consider it as an artificial device if its presentation is postponed to a more advanced course. Section 10.1 is devoted to the derivation of the principle of virtual work and to its direct application to the solution of equilibrium problems.

Section 10.2 introduces the concept of potential energy and shows that equilibrium requires that the derivative of the potential energy be zero. Section 10.1D defines the mechanical efficiency of a machine and Sec. 10.2D discusses the stability of equilibrium. The first groups of problems in each assignment utilize the principle of virtual work as an alternative method for the computation of unknown forces.

Subsequent problems call for the determination of positions of equilibrium, while other problems combine the conventional methods of statics with the method of virtual work to determine displacements (Probs. 10.55 through 10.58). TABLE I: LIST OF THE TOPICS COVERED IN VECTOR MECHANICS FOR ENGINEERS: STATICS Suggested Number of Periods Sections Topics Basic Course Additional Topics Abridged Course to be used as an introduction to 1. INTRODUCTION This material may be used for the first assignment or for later reference 2. STATICS OF PARTICLES 2.1 Addition and Resolution of Forces 2.2 Rectangular Components 2.3 Equilibrium of a Particle 2.4 Forces in Space 2.5 Equilibrium in Space 3. RIGID BODIES: EQUIVALENT SYSTEMS OF FORCES 3.1 Vector Moment of a Force about a Point 3.2 Scalar Moment of a Force about an Axis 3.3 Couples Equivalent Systems of Forces 3.4D Reduction of a Wrench 1 1 1 1 1 1 1 1 4.

EQUILIBRIUM OF RIGID BODIES Equilibrium in Two Dimensions 4.1C Indeterminate Partial Constraints 4.2 and Bodies 4.3 Equilibrium in Three Dimensions 1 2 5. CENTROIDS AND CENTERS OF GRAVITY 5.1 Centroids and First Moments of Areas and Lines 5.2 Centroids Integration 5.3 Beams and Submerged Surfaces 5.4 Centroids of Volumes 2 6. ANALYSIS OF STRUCTURES Trusses Method of Joints 6.1C Joints under Special Loading Conditions 6.1D Space Trusses 6.2A Trusses Method of Sections 6.2B Combined Trusses 6.3 Frames 6.4 Machines 7.

INTERNAL FORCES AND MOMENTS 7.1 Internal Forces in Members 7.2 Shear and Moment Diagrams FB Diagram 7.3 Shear and Moment Diagrams Integration 7.4 Cables with Concentrated Parabolic Cable 7.5 Catenary 1 1 8. FRICTION 8.1 Laws of Friction and Applications 8.2 Wedges and Screws 8.3 Axle and Disk Rolling Resistance 8.4 Belt Friction 1 1 9. MOMENTS OF INERTIA 9.1 Moments of Inertial of Areas 9.2 Composite Areas 9.3 Products of Principal Axes 9.4 Circle 9.5 Moments of Inertia of 9.6 Mass Products of Principal Axes and Principal Moments of Inertia 1 1 10. METHOD OF VIRTUAL WORK Principle of Virtual Work 10.1D Mechanical Efficiency 10.2 Potential Stability Total Number of Periods A sample assignment schedule for a course in dynamics including this minimum amount of introductory material in statics is given Table V.

It is recommended that a more complete statics course, such as the one outlined in Tables and IV of this manual, be used in curricula which include the study of mechanics of materials. Mass moments of inertia have not been included in the basic statics course since this material is often taught in dynamics. Xiv TABLE II: CLASSIFICATION AND DESCRIPTION OF PROBLEMS (CONTINUED) Problem SI Units U.S.

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