Shigley-s-Mechanical-Engineering-Design

In the development of the basic stress equations for tension, compression, bending, and torsion, it was assumed that no geometric irregularities occurred in the member under consideration. But it is quite difficult to design a machine without permitting some changes in the cross sections of the members. Rotating shafts must have shoulders designed on them so that the bearings can be properly seated and so that they will take thrust loads; and the shafts must have key slots machined into them for securing pulleys and gears. A bolt has a head on one end and screw threads on the other end, both of which account for abrupt changes in the cross section. Other parts require holes, oil grooves, and notches of various kinds. Any discontinuity in a machine part alters the stress distribution in the neighborhood of the discontinuity so that the elementary stress equations no longer describe the state of stress in the part at these locations. Such discontinuities are called stress raisers, and the regions in which they occur are called areas of stress concentration. Stress concentrations can also arise from some irregularity not inherent in the member, such as tool marks, holes, notches, grooves, or threads. 1 in T 18 in Figure 3–28 The cross-section of a thin strip of steel subjected to a torsional moment T. bud29281_ch03_071-146.qxd 11/24/09 3:02PM Page 110 ntt 203:MHDQ196:bud29281:0073529281:bud29281_pagefiles: Load and Stress Analysis 111 A theoretical, or geometric, stress-concentration factor Kt or Kts is used to relate the actual maximum stress at the discontinuity to the nominal stress. The factors are defined by the equations K t = σ max σ0 K ts = τ max τ0 (3–48) where Kt is used for normal stresses and Kts for shear stresses. The nominal stress σ0 or τ0 is the stress calculated by using the elementary stress equations and the net area, or net cross section. Sometimes the gross cross section is used instead, and so it is always wise to double check the source of Kt or