{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chap3_0130473928 - ch03.qxd 7:20 AM Page 95 CHAPTER 3...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
95 C H A P T E R 3 Two-Dimensional Problems in Elasticity 3.1 INTRODUCTION As has been pointed out in Sec. 1.1, the approaches in widespread use for determin- ing the influence of applied loads on elastic bodies are the mechanics of materials or elementary theory (also known as technical theory ) and the theory of elasticity . Both must rely on the conditions of equilibrium and make use of a relationship be- tween stress and strain that is usually considered to be associated with elastic mate- rials. The essential difference between these methods lies in the extent to which the strain is described and in the types of simplifications employed. The mechanics of materials approach uses an assumed deformation mode or strain distribution in the body as a whole and hence yields the average stress at a section under a given loading. Moreover, it usually treats separately each simple type of complex loading, for example, axial centric, bending, or torsion.Although of practical importance, the formulas of the mechanics of materials are best suited for relatively slender members and are derived on the basis of very restrictive condi- tions. On the other hand, the method of elasticity does not rely on a prescribed de- formation mode and deals with the general equations to be satisfied by a body in equilibrium under any external force system. The theory of elasticity is preferred when critical design constraints such as minimum weight, minimum cost, or high reliability dictate more exact treatment or when prior experience is limited and intuition does not serve adequately to supply the needed simplifications with any degree of assurance. If properly applied, the theory of elasticity should yield solutions more closely approximating the actual distribution of strain, stress, and displacement. Thus, elasticity theory provides a check on the limitations of the mechanics of materials solutions.We emphasize, however, that both techniques cited are approxi- mations of nature, each of considerable value and each supplementing the other.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
96 Chapter 3 Two-Dimensional Problems in Elasticity The influences of material anisotropy, the extent to which boundary conditions de- part from reality, and numerous other factors all contribute to error. 3.2 FUNDAMENTAL PRINCIPLES OF ANALYSIS To ascertain the distribution of stress, strain, and displacement within an elastic body subject to a prescribed system of forces requires consideration of a number of conditions relating to certain physical laws, material properties, and geometry. These fundamental principles of analysis, also referred to as the three aspects of solid mechanics problems , are summarized as follows: 1. Conditions of equilibrium. The equations of statics must be satisfied throughout the body.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern