6.7 Thin-Wall Torsion Members with Restrained Ends 266
6.8 Numerical Solution of the Torsion Problem
6.9 Fully Plastic Torsion 277
274
Problems
283
References
291
7 Nonsymmetrical Bending of Straight Beams
7.1 Definition of Shear Center in Bending. Symmetrical and Nonsymmetrical Bending 293
7.2 Bending Stresses in Beams Subjected to Nonsymmetrical Bending 302
7.3 Deflections of Straight Beams Subjected to Nonsymmetrical Bending 312
7.4 Effect of Inclined Loads 316
7.5 Fully Plastic Load for Nonsymmetrical Bending
Problems
References
320
330
318
8 Shear Center for Thin-Wall Beam Cross Sections
8.1 Approximations for Shear in Thin-Wall Beam Cross Sections 331
8.2 Shear Flow in Thin-Wall Beam Cross Sections
8.3 Shear Center for a Channel Section 336
334
8.4 Shear Center of Composite Beams Formed from Stringers and
Thin Webs 342
8.5 Shear Center of Box Beams
346
Problems
350
References
361
9. Curved Beams
9.1 Introduction 362
9.2 Circumferential Stresses in a Curved Beam
363
9.3 Radial Stresses in Curved Beams 373
9.4 Correction of Circumferential Stresses in Curved Beams Having I-, T-, or Similar Cross Sections 379
9.5 Defections of Curved Beams 385
9.6 Statically Indeterminate Curved Beams. Closed Ring Subjected to a Concentrated Load 391
INTRODUCTION
In this chapter, we present general concepts and definitions that are fundamental to many of the topics discussed in this book. The chapter serves also as a brief guide and introduction to the remainder of the book. The reader may find it fruitful to refer to this chapter, from time to time, in conjunction with the study of topics in other chapters.
THE ROLE OF DESIGN
This book emphasizes the methods of mechanics of materials and applications to the analysis and design of components of structural/machine systems. As such, it is directed to aeronautical, civil, mechanical, and nuclear engineers, as well as to specialists in the field of theoretical and applied mechanics. As engineers, we are problem solvers. The problems that we solve encompass practically all fields of human activity. We solve problems related to buildings, transportation (including automotive, rail, water, air and outer-space travel), water systems (e.g., dams and pipelines), manufacturing, specialized medical equipment, communication systems, computers, hazardous wastes, etc. These problems are generally encountered in the design, manufacture, and construction of engineering systems. Ordinarily, these systems are not built or manufactured before the design process is completed. The design process usually involves the development of many drawings and/or CAD files to describe the final system. One of the major purposes of the design process is to analyze or evaluate various design alternatives before a final design is selected. One of the simplest objectives of the analysis is to ensure that all components of the system will fit together and function properly. More complicated analysis involves the evaluation of forces in the proposed design to ensure that each component of the system functions properly (for instance, safely withstands loads or does not undergo excessive displacements). This analysis is essential in the process of refining the design to meet required conditions such as adequate strength, minimum weight, and minimum cost of production.
The process of refining the design can be very complicated and extremely time-consuming. For example, consider the design of a space vehicle, such as the shuttle. After the shuttle's mission or use has been established, the designer must decide on the shape of the vehicle and the materials to be used. The designer must analyze the vehicle's structure to determine if it is strong and stiff enough to withstand the aerodynamic and thermal loads to which it will be subjected.