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Unformatted text preview: Load and Stress Analysis Chapter Outline 31 Equilibrium and Free-Body Diagrams 68 32 Shear Force and Bending Moments in Beams 71 33 Singularity Functions 73 34 Stress 75 35 Cartesian Stress Components 75 36 Mohrs Circle for Plane Stress 76 37 General Three-Dimensional Stress 82 38 Elastic Strain 83 39 Uniformly Distributed Stresses 84 310 Normal Stresses for Beams in Bending 85 311 Shear Stresses for Beams in Bending 90 312 Torsion 95 313 Stress Concentration 105 314 Stresses in Pressurized Cylinders 107 315 Stresses in Rotating Rings 110 316 Press and Shrink Fits 110 317 Temperature Effects 111 318 Curved Beams in Bending 112 319 Contact Stresses 117 320 Summary 121 3 67 68 Mechanical Engineering Design One of the main objectives of this book is to describe how specific machine components function and how to design or specify them so that they function safely without failing structurally. Although earlier discussion has described structural strength in terms of load or stress versus strength, failure of function for structural reasons may arise from other factors such as excessive deformations or deflections. Here it is assumed that the reader has completed basic courses in statics of rigid bodies and mechanics of materials and is quite familiar with the analysis of loads, and the stresses and deformations associated with the basic load states of simple prismatic elements. In this chapter and Chap. 4 we will review and extend these topics briefly. Complete derivations will not be presented here, and the reader is urged to return to basic textbooks and notes on these subjects. This chapter begins with a review of equilibrium and free-body diagrams associated with load-carrying components. One must understand the nature of forces before attempting to perform an extensive stress or deflection analysis of a mechanical com-ponent. An extremely useful tool in handling discontinuous loading of structures employs Macaulay or singularity functions . Singularity functions are described in Sec. 33 as applied to the shear forces and bending moments in beams. In Chap. 4, the use of singularity functions will be expanded to show their real power in handling deflections of complex geometry and statically indeterminate problems. Machine components transmit forces and motion from one point to another. The transmission of force can be envisioned as a flow or force distribution that can be fur-ther visualized by isolating internal surfaces within the component. Force distributed over a surface leads to the concept of stress, stress components, and stress transforma-tions (Mohrs circle) for all possible surfaces at a point....
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This note was uploaded on 03/22/2010 for the course MEEN ISEN 302 taught by Professor Kim during the Spring '10 term at Texas A&M University–Commerce.
- Spring '10