# MECHANICAL ENGINEERING LIBRARY

## BY FERDINAND P. BEER,E. RUSSELL JOHNSTON JR,JOHN T. DEWOLF, DAVID F. MAZUREK

CONTENTS
1. INTRODUCTION - CONCEPT OF STRESS
3. TORSION
4. PURE BENDING
5. ANALYSIS AND DESIGN OF BEAMS FOR BENDING
6. SHEARING STRESSES IN BEAMS AND THIN WALLED MEMBERS
7. TRANSFORMATIONS OF STRESS AND STRAIN
9. DEFLECTION OF BEAMS
10. COLUMNS
11. ENERGY METHODS

INTRODUCTION TO MECHANICS OF MATERIALS

OBJECTIVES AND GENERAL APPROACH OF THIS BOOK :

OBJECTIVES

The main objective of a basic mechanics course should be to develop in the engineering student the ability to analyze a given problem in a simple and logical manner and to apply to its solution a few fundamental and well-understood principles. This text is designed for the first course in mechanics of materials—or strength of materials—offered to engineering students in the sophomore or junior year. The authors hope dial it will help instructors achieve this goal in that particular course in the same way that meir other texts may have helped them in statics and dynamics.

GENERAL APPROACH

In this text the study of the mechanics of materials is based on the understanding of a few basic concepts and on the use of simplified models. This approach makes it possible to develop all the necessary formulas in a rational and logical manner, and to clearly indicate the conditions under which diey can be safely applied to the analysis and design of actual engineering structures and machine components. Free-body Diagrams Are Used Extensively. Throughout the text free-body diagrams are used to determine external or internal forces. The use of "picture equations" will also help the students understand (he superposition of loadings and the resulting stresses and deformations. Design Concepts Are Discussed Throughout the Text Whenever Appropriate. A discussion of the application of the factor of safety to design can be found in Chap. 1, where the concepts of both allowable stress design and load and resistance factor design are presented. A Careful Balance Between SI and U.S. Customary Units Is Consistently Maintained. Because it is essential that students be able to handle effectively both SI metric units and U.S. customary units, half the examples, sample problems, and problems to be assigned have been stated in SI units and half in U.S. customary units. Since a large number of problems are available, instructors can assign problems using each system of units in whatever proportion they find most desirable for their class. Optional Sections Offer Advanced or Specialty Topics. Topics such as residual stresses, torsion of noncircular and thin-walled members, bending of curved beams, shearing stresses in non-symmetrical
members, and failure criteria, have been included in optional sections for use in courses of varying emphases. To preserve the integrity of the subject, these topics are presented in the proper sequence, wherever they logically belong. Thus, even when not covered in die course, diey are highly visible and can be easily referred to by the students if needed in a later course or in engineering practice. For convenience all optional sections have been indicated by asterisks.

CHAPTER ORGANIZATION

It is expected that students using this text will have completed a course in statics. However. Chap. 1 is designed to provide them with an opportunity to review the concepts learned in that course, while shear and bending-momenl diagrams are covered in detail in Sees. 5.2 and 5.3. The properties of moments and centroids of areas are described in Appendix A; this material can be used to reinforce the discussion of the determination of normal and shearing stresses in beams (Chaps. 4. 5. and 6).
The first four chapters of the text are devoted to the analysis of the stresses and of the corresponding deformations in various structural members, considering successively axial loading, torsion, and pure bending. Each analysis is based on a few basic concepts, namely, the conditions of equilibrium of the forces exerted on the member, the relations existing between stress and strain in the material. and the conditions imposed by the supports and loading of the member. The study of each type of loading is complemented by a large number of examples, sample problems, and problems to be assigned, all designed to strengthen the students' understanding of
the subject.

The concept of stress at a point is introduced in Chap. 1. where it is shown that an axial load can produce shearing stresses as well as normal stresses, depending upon the section considered. The fact that stresses depend upon the orientation of the surface on which they are computed is emphasized again in Chaps. 3 and 4 in the
cases of torsion and pure bending. However, the discussion of computational techniques—such as Mohr's circle—used for the transformation of stress at a point is delayed until Chap. 7, after students have had the opportunity to solve problems involving a combination of the basic loadings and have discovered for themselves the need for such techniques. The discussion in Chap. 2 of the relation between stress and strain in various materials includes fiber-reinforced composite materials.
Also, the study of beams under transverse loads is covered in two separate chapters. Chapter 5 is devoted to the determination of the normal stresses in a beam and to the design of beams based on the allowable normal stress in the material used (Sec. 5.4). The chapter begins with a discussion of the shear and bending-moment diagrams

STRESS - INTRODUCTION

INTRODUCTION

The main objective of the study of the mechanics of materials is to provide the future engineer with the means of analyzing and designing various machines and load-bearing structures. Both the analysis and the design of a given structure involve the determination of stresses and deformations. This first chapter is devoted to the concept of stress. Section 1.2 is devoted to a short review of the basic methods of statics and to their application to the determination of the forces in the members
of a simple structure consisting of pin-connected members. Section 1.3 will introduce you to die concept of stress in a member of a structure, and you will be shown how that stress can be determined from the farce in the member. After a short discussion of engineering analysis and design , you will consider successively the normal stresses in a member under axial loading , the shearing stresses caused by the application of equal and opposite transverse forces , and the bearing stresses created by bolts and pins in the members they connect . These various concepts will be applied in Sec. 1.8 to the determination of the stresses in the members of the simple structure considered earlier in Sec. 1.2. The first part of the chapter ends with a description of die method you should use in the solution of an assigned problem  and with a discussion of the numerical accuracy appropriate in engineering calculations.
In Sec. 1.11, where a two-force member under axial loading is considered again, it will be observed that the stresses on an oblique plane include both normal and shearing stresses, while in Sec. 1.12 you will note that six components are required to describe the state of stress at a point in a body under the most general loading conditions. Finally. Sec. 1.13 will be devoted to the determination from test specimens of the ultimate strengih of a given material and to the use of a factor
of safety in the computation of the allowable load for a structural component made of that material.

STRAIN - INTRODUCTION

In Chap. 1 - Concepts of Stress we analyzed die stresses created in various members and connections by the loads applied lo a structure or machine. We also learned to design simple members and connections so that they would not fail under specified loading conditions. Another important aspect of the analysis and design of structures relates to the deformations caused by the loads applied to a structure. Clearly, it is important to avoid deformations so large that they may prevent the structure from fulfilling the purpose for which it was intended. But the analysis ol deformations may also help us in the determination of stresses. Indeed, it is not always
possible lo determine die forces in die members of a structure by applying only the principles of statics. This is because statics is based on the assumption of undeformable, rigid structures. By considering engineering structures as deformable and analyzing the deformations in their various members, ii will be possible for us to compute forces thai are statically indeterminate, i.e., indeterminate within die framework of statics. Also, as we indicated in Sec. 1.5, the distribution of stresses in a given member is statically indeterminate, even when the force in that member is known. To determine die actual distribution of stresses within
a member, it is thus necessary to analyze die deformations that lake place in thai member. In this chapter, you will consider the deformations of a structural member such as a rod, bar, or plate under axial loading.

TORSION - INTRODUCTION

In the two preceding chapters you studied how to calculate the stresses and strains in structural members subjected to axial loads, that is, to forces directed along the axis of the member. In this chapter structural members and machine parts that are in torsion will be considered. More specifically, you will analyze the stresses and strains in members of circular cross section subjected to twisting couples, or torques, T and T'. These couples have a common magnitude 7, and opposite senses. They are vector quantities and can be represented either by curved arrows. or by couple vectors.

PURE BENDING - INTRODUCTION

In the preceding chapters you studied how to determine the stresses in prismatic members subjected to axial loads or to twisting couples. In this chapter and in the following two you will analyze the stresses and strains in prismatic members subjected to bending. Bending is a major concept used in the design of many machine and structural components, such as beams and girders. This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are said to be in pure bending. In most of the chapter, the members will be assumed to possess a plane of symmetry
and the couples M and M' to be acting in that plane

DEFLECTION IN BEAMS - INTRODUCTION

In the preceding chapter we learned to design beams lor strength. In this chapter we will be concerned with another aspect in the design of beams, namely, the determination of the deflection. Of particular interest is the determination of the maximum deflection of a beam under a given loading, since the design specifications of a beam will generally include a maximum allowable value for its deflection. Also of interest is that a knowledge of the deflections is required to analyze indeterminate beams. These are beams in which the number of reactions at the supports exceeds the number of equilibrium equations available to determine these unknowns.

COLUMNS - INTRODUCTION

In the preceding chapters, we had two primary concerns: (I) the strength of the structure, i.e., its ability to support a specified load without experiencing excessive stress: (2) the ability of the structure to support a specified load without undergoing unacceptable deformations. In this chapter, our concern will be with Ihe stability of the structure, i.e., with its ability to support a given load without experiencing a sudden change in its configuration. Our discussion will relate chiefly to columns, i.e., to the analysis and design of vertical prismatic members supporting axial loads.

## BY REGIS BLONDEAU

CONTENTS
2. High Density Energy Beam Welding Processes: Electron Beam and Laser Beam
3. Thermal, Metallurgical and Mechanical Phenomena in the Heat Affected Zone
4. Molten Metal
5. Welding Products
6. Fatigue Strength of Welded Joints
7. Fracture Toughness of Welded Joints
8. Welding of Steel Sheets, With and Without Surface Treatments
9. Welding of Steel Mechanical Components
10. Welding Steel Structures
11. Welding Heavy Components in the Nuclear Industry
12. Welding Stainless Steels
13. Welding Aluminum Alloys
14. Standardization: Organization and Quality Control in Welding

Introduction to Metallurgy and Mechanics of Welding by Regis Blondeau

Welding: The Permanent Bond Between Two Solid Bodies

What a long story welding is! Seeing the light of day at the end of the 19th century in the mind of scientists, it passed quickly into the hands of technicians, first
of all with the oxyacetylene technique, then with arc welding and resistance welding techniques. Other processes (we will not quote them all in this introduction) then
followed and the 20th century ended with laser welding which had its origins in the 1980s. However, it must be said that only since the 1950s has welding been the main
means of assembly, as riveting was the most used method up to that point.

Introduction

To avoid any misunderstandings, the definitions of the terms which appear in this text are those proposed in the document entitled “Terms and definitions used in
welding and related techniques” published by the “Publications of Autogeneous Welding and the International Council of the French Language” [COL 96]. It has been specified in the preface to this book that welding makes it possible to reconstitute metallic continuity between the components to be assembled. This reconstitution involves the re-establishment of the interatomic metal bonding forces which requires at the same time a connection of the nodes of the crystal lattices and the absence of any foreign body likely to constitute a screen. This chapter will successively cover the physical conditions necessary to create the metallic bond and the industrial processes which make it possible to establish this bond.

Conditions to create metallic bonding : Creating the metal bond consists, theoretically, of bringing the surfaces to be linked closer so that the surface atoms are at a distance of the order of the inter-nodal distances of their own crystalline system.

This operation, which would assume at the beginning that surfaces are chemically clean and in a specular state of polish, is not practically feasible. To mitigate this industrial impossibility, the surfaces to be joined will have to be activated with a view to eliminating the foreign bodies and elements likely to obstruct the creation of the bond.

Activation of surfaces : The most effective surface activation is fusion which can simultaneously ensure their cleaning. The metallic bond is created by solidification. Different procedures can be employed:

--> the two parts to be assembled undergo a surface fusion and thus contribute to the formation of a molten metal pool (possibly with the addition of a filler) which
solidifies without mechanical action;

--> the two parts to be assembled undergo a surface fusion but an external mechanical action expels the molten metal and creates the assembly by placing the surfaces in contact at the solidus temperature;

--> the two parts to be assembled undergo a localized fusion and take part in the formation of a captive molten metal core which during its solidification is compacted by the action of an external effort of compression.

The activation of surfaces can also be obtained by heating without fusion. In general it is then supplemented by a mechanical action which enables, moreover, cleaning and improvement in contact of the surfaces to be assembled. It is possible to distinguish between:

a) the case where the heating and the cleaning of surfaces to be assembled are simultaneously carried out by mechanical friction (which implies the assembly of axisymmetric parts) and is followed, after stopping the latter, by a crushing (“forging”) by axial compression; and

b) the case where the heating is carried out by external heating and the close contact is ensured by an effort perpendicular to the joint plane. Finally, activation can result from a mechanical action without total heating of the parts to be assembled. This mechanical action causes a plasticization of the outer layer of each surface and generates a very localized heating which finally allows the establishment of the metallic bond. This process simultaneously requires a relative displacement of the surfaces to be assembled, parallel to the mating plane, coupled with a compressive force perpendicular to this same plane. It is necessary to carry

.

Elimination of obstacles to bond creation

Obstacles to the creation of the metallic bond can be of various kinds:

– geometrical surface irregularities,
– pollution of the surface (oxides, grease, moisture, etc.),
– chemical elements brought in by the surrounding air.

Surface irregularities are likely to disrupt the creation of metallic bonds in all the cases where there is not surface fusion of the parts to be assembled. It will then be necessary to carry out a surface preparation by mechanical means (grinding, machining, etc.).

All pollution of surfaces to be assembled will have to be eliminated by mechanical action (sanding, grinding) or by chemical means (solvents, scouring, drying, etc.).
It is necessary to neutralize the possible effects of chemical elements brought in by the surrounding air. Welding operations generally being carried out in atmospheric conditions, it is especially oxygen, nitrogen and hydrogen (carried in the air’s humidity) which can be harmful. Oxygen can react with the elements volatilized by the arc and in this way contribute to the creation of welding fumes. Furthermore, it can especially dissolve in the molten metal and, during solidification, contribute to the formation of:

– metallic oxides which constitute inclusions in solidified metal;

– porosities in the molten metal due to the drop in solubility which accompanies cooling and solidification. This formation of porosities can be aggravated by a
reaction developing with an element contained in the metal and leading to the formation of a gas compound (for example, formation and release of CO during steel
welding without protection against the atmosphere).

Protection against oxygen in the air can be ensured by the interposition of a neutral gas, a molten slag or by fixing in the form of oxides by the addition of oxygen hungry elements (silicon especially). In the vicinity of the molten metal, the surface of the parent metal raised to a high temperature can also react with oxygen and be covered with oxides, which is a further justification for using protective means, including at the back of the weld.

Aluminothermic welding

In this process the welding is carried out by running a metal in fusion (filler) into a mold built around the two faces of the parts to be assembled, placed face to face, at a specified distance. These two faces are often pre-heated with a flame via holes provided in the mold. The molten metal is created on the spot by aluminothermy, i.e. exothermic reaction between oxides (of the metal filler) and powdered aluminum. This operation is carried out in a crucible placed at the top of the mold. As the molten filler is run in, the surface of the parts to be assembled melts, preceding solidification of the assembly. The protection of the molten metal is ensured by the slag which is formed during the aluminothermic reaction. Afterwards, it is necessary to remove the mold and grind the assembled parts, so as to eliminate any excess deposits.

Resistance welding with containment of the molten metal

This process combines the Joule effect and a mechanical pressure applied to the outside of the assembly, perpendicular to it and right where the molten metal zone
is. This force has the aim of ensuring a good electrical contact between the parts to be assembled, thereby confining the molten metal in the zone where it is formed and applying pressure to it after its solidification in order to improve its compactness by avoiding shrinkage (an operation known as spot forging). Generally the electrodes carrying the current apply this effort. These considerations show that they are overlapping assemblies of products of limited thickness. The containment of the molten metal within the joint avoids any contact with the air; the problem of its protection thus does not arise . The effectiveness of this process is related to the localization of the zone heated by the Joule effect, which depends on the electric contact resistance between the parts; precautions must be taken so that, on the one hand, other resistances in series in the electric circuit are much lower and that, on the other hand, there is no possibility of the welding current being diverted to one or more parallel circuits.

High Density Energy Beam Welding :

Processes: Electron Beam and Laser Beam

Welding processes using high density energy beams result from the application, in the second half of the 20th century, of work conducted by physicists in the fields
of x-rays and vacuum techniques for the process of electron beam welding and optronics for laser beam welding. The possibility of concentrating these beams on points having a very small surface area led engineers to use this property to melt materials to achieve welds or cuts.

Compared to traditional arc welding processes, these two processes are characterized by a very high energy density at the impact point on the work piece. Rykaline [RYK 74] gave a representation comparing for several processes the heat flows at the center of the heat sources and the diameters of these sources. We can observe that the energy density measured at the focal point of a laser beam or an electron beam is 10,000 times higher than that reached in an oxy-fuel flame

Laser beam welding

History

Einstein surely did not suspect the technological revolution to which his stimulated emission theory, established in 1917, would give rise. The technological adventure could only really start in 1954 when Professor Townes and his team developed the first stimulated emission amplifier and oscillator, which they baptized “MASER” (Microwave Amplifier by Stimulated Emission of Radiation). This discovery was followed by many others. In 1958, Schawlow and Townes demonstrated the theoretical possibility of producing coherent light by stimulated emission of radiation. The first laser source was a ruby laser produced by Maiman in 1960. It was very quickly followed by the development of the first gas laser by Javan (helium-neon laser). Many mediums were then studied and used for the manufacture of lasers: doped crystals, semiconductors, ionized gases, molecular gases, liquids, dyes. Laser is currently experiencing an extraordinary development. It is used in many spheres of activity.

Principle Laser is an acronym formed by the initial letters of Light Amplification byStimulated Emission of Radiation :

An atom can pass from a fundamental state E1 to excited state E2 by the absorption of a certain energy quantity . This energy contribution can be mechanical or kinetic in origin. This atom will revert to its fundamental state by the restitution of this energy quantity, it is “the spontaneous emission”

These randomly emitted photons produce a light known as “incoherent”. There is no relationship of phase, direction and polarization between all these photons. If an incident photon causes a return to the fundamental state of the excited atom, there is “stimulated emission”. The two emerging photons are in phase, they have the same direction and same polarization as the incident photon: there is light amplification by stimulated emission of radiation. The excitation of the medium is called “pumping”. It allows the population inversion between excited and non-excited atoms. Pumping requires an external energy source which can be assured by electrical discharge or radio frequency in the case of gas lasers, and by lamps or laser diodes in the case of solid lasers. A laser source must thus be made up of three principal elements:

– an active medium made up of particles (atoms, ions, molecules),

– an energy source to carry out the pumping of the medium and thus to obtain the population inversion,

– a resonator cavity made up of two mirrors ensuring photon oscillation.

If one of the mirrors is partially reflective, it will allow some of the photons to escape which will constitute the coherent light beam. The laser beam thus obtained will have certain characteristics of divergence, polarization and energy distribution which will define the quality of the laser beam.

Fatigue Strength of Welded Joints

Fatigue strength

Introduction

The observation of many failures in welded structures generally points the finger at fatigue as the main cause. Moreover, it has become apparent that for welded structures, admissible service stresses were very low in respect of the static stresses (yield strength, breaking strength) and that it was not enough to apply a safety coefficient based, for example, on a fraction of the yield strength to be certain of avoiding failure. Indeed, welds can introduce severe stress concentrations and which differ from one structural element to another.