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Ebook Mark’s calculations for machine design: Part 2

(BQ) Part 2 book "Mark’s calculations for machine design" has contents: Static design and column buckling, fatigue and dynamic design, machine assembly, machine energy, machine motion. Invite you to reference. | CHAPTER 6 STATIC DESIGN AND COLUMN BUCKLING 6.1 STATIC DESIGN The question now arises as to whether the values of the principal stresses (σ1 ) and (σ2 ) and the maximum and minimum shear stresses (τmax ) and (τmin ) found for a machine element in Chap. 5, either mathematically or using the Mohr’s circle graphical process, represent a safe operating condition. Depending on whether the material used for the machine element can be considered ductile or brittle, the most commonly accepted criteria, or theories, predicting that a design is safe under static conditions will be presented. The most common ways to define a factor-of-safety (n) for a machine element will also be presented, again based on whether the material being used is ductile or brittle. Static Design Coordinate System. For the static design theories that follow, all the theories can be represented by mathematical expressions; however, as was the case with Mohr’s circle, a graphical picture of these expressions provides a significant insight into what the theory really means in terms of predicting that a design is safe under static conditions. Figure 6.1 shows the coordinate system that will be used, where the horizontal axis is the maximum principal stress (σ1 ) and the vertical axis is the minimum principal stress (σ2 ). For ductile materials, the yield strength (S y ) in tension and in compression are relatively equal in magnitude, whereas for brittle materials the ultimate compressive strength (Suc ) is significantly greater in magnitude than the ultimate tensile strength (Sut ). Figure 6.1 reflects the difference between the yield and ultimate strengths, and the difference between the magnitudes of the ultimate tensile and compressive strengths. (Note that capital S is used for the term strength of a material, whereas the Greek letter σ is used for the calculated normal stresses and the principal stresses and τ for the calculated shear stresses and the maximum and minimum shear stresses.) The four .