214 Budynas-Nisbett:Shigley's ll.Failure Prevention 5.Failures Resulting from T©The McGraw-Hill Mechanical Engineering Static Loading Companies,2008 Design,Eighth Edition 210 Mechanical Engineering Design A load of 30 kip induces a tensile stress of 30 kpsi in the shank at point B.The fillet stress is still 40 kpsi(point D),and the SCFK Omax/onom Sy/o =40/30 1.33. At a load of 40 kip the induced tensile stress (point C)is 40 kpsi in the shank. At the critical location in the fillet,the stress (at point E)is 40 kpsi.The SCF K =Omax /onom Sy/=40/40 =1. For materials that strain-strengthen,the critical location in the notch has a higher Sy. The shank area is at a stress level a little below 40 kpsi,is carrying load,and is very near its failure-by-general-yielding condition.This is the reason designers do not apply K:in static loading of a ductile material loaded elastically,instead setting K:=1. When using this rule for ductile materials with static loads,be careful to assure yourself that the material is not susceptible to brittle fracture (see Sec.5-12)in the environment of use.The usual definition of geometric (theoretical)stress-concentration factor for normal stress K,and shear stress Kis is Omax K1Onom (a) Tmax =Kistnom (6 Since your attention is on the stress-concentration factor,and the definition of onom or Thom is given in the graph caption or from a computer program,be sure the value of nominal stress is appropriate for the section carrying the load. Brittle materials do not exhibit a plastic range.A brittle material"feels"the stress concentration factor K,or Ks,which is applied by using Eq.(a)or(b). An exception to this rule is a brittle material that inherently contains microdiscon- tinuity stress concentration,worse than the macrodiscontinuity that the designer has in mind.Sand molding introduces sand particles,air,and water vapor bubbles.The grain structure of cast iron contains graphite flakes(with little strength),which are literally cracks introduced during the solidification process.When a tensile test on a cast iron is performed,the strength reported in the literature includes this stress concentration.In such cases K,or Kis need not be applied. An important source of stress-concentration factors is R.E.Peterson,who com- piled them from his own work and that of others.'Peterson developed the style of pre- sentation in which the stress-concentration factor K,is multiplied by the nominal stress nom to estimate the magnitude of the largest stress in the locality.His approximations were based on photoelastic studies of two-dimensional strips(Hartman and Levan, 1951:Wilson and White,1973),with some limited data from three-dimensional photoelastic tests of Hartman and Levan.A contoured graph was included in the pre- sentation of each case.Filleted shafts in tension were based on two-dimensional strips. Table A-15 provides many charts for the theoretical stress-concentration factors for several fundamental load conditions and geometry.Additional charts are also available from Peterson. Finite element analysis(FEA)can also be applied to obtain stress-concentration factors.Improvements on K,and Kis for filleted shafts were reported by Tipton,Sorem, and Rolovic.3 R.E.Peterson,"Design Factors for Stress Concentration,"Machine Design,vol.23.no.2.February 1951; no.3.March 1951;no.5.May 1951;no.6.June 1951;no.7,July 1951. 2Walter D.Pilkey,Peterson's Stress Concentration Factors.2nd ed.John Wiley&Sons,New York.1997. 3S.M.Tipton,J.R.Sorem Jr.,and R.D.Rolovic."Updated Stress-Concentration Factors for Filleted Shafts in Bending and Tension,"Trans.ASME,Journal of Mechanical Design,vol.118.September 1996,pp.321-327.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition II. Failure Prevention 5. Failures Resulting from Static Loading 214 © The McGraw−Hill Companies, 2008 210 Mechanical Engineering Design • A load of 30 kip induces a tensile stress of 30 kpsi in the shank at point B. The fillet stress is still 40 kpsi (point D), and the SCF K = σmax/σnom = Sy/σ = 40/30 = 1.33. • At a load of 40 kip the induced tensile stress (point C) is 40 kpsi in the shank. At the critical location in the fillet, the stress (at point E) is 40 kpsi. The SCF K = σmax/σnom = Sy/σ = 40/40 = 1. For materials that strain-strengthen, the critical location in the notch has a higher Sy . The shank area is at a stress level a little below 40 kpsi, is carrying load, and is very near its failure-by-general-yielding condition. This is the reason designers do not apply Kt in static loading of a ductile material loaded elastically, instead setting Kt = 1. When using this rule for ductile materials with static loads, be careful to assure yourself that the material is not susceptible to brittle fracture (see Sec. 5–12) in the environment of use. The usual definition of geometric (theoretical) stress-concentration factor for normal stress Kt and shear stress Kts is σmax = Ktσnom (a) τmax = Ktsτnom (b) Since your attention is on the stress-concentration factor, and the definition of σnom or τnom is given in the graph caption or from a computer program, be sure the value of nominal stress is appropriate for the section carrying the load. Brittle materials do not exhibit a plastic range. A brittle material “feels” the stress concentration factor Kt or Kts, which is applied by using Eq. (a) or (b). An exception to this rule is a brittle material that inherently contains microdiscon￾tinuity stress concentration, worse than the macrodiscontinuity that the designer has in mind. Sand molding introduces sand particles, air, and water vapor bubbles. The grain structure of cast iron contains graphite flakes (with little strength), which are literally cracks introduced during the solidification process. When a tensile test on a cast iron is performed, the strength reported in the literature includes this stress concentration. In such cases Kt or Kts need not be applied. An important source of stress-concentration factors is R. E. Peterson, who com￾piled them from his own work and that of others.1 Peterson developed the style of pre￾sentation in which the stress-concentration factor Kt is multiplied by the nominal stress σnom to estimate the magnitude of the largest stress in the locality. His approximations were based on photoelastic studies of two-dimensional strips (Hartman and Levan, 1951; Wilson and White, 1973), with some limited data from three-dimensional photoelastic tests of Hartman and Levan. A contoured graph was included in the pre￾sentation of each case. Filleted shafts in tension were based on two-dimensional strips. Table A–15 provides many charts for the theoretical stress-concentration factors for several fundamental load conditions and geometry. Additional charts are also available from Peterson.2 Finite element analysis (FEA) can also be applied to obtain stress-concentration factors. Improvements on Kt and Kts for filleted shafts were reported by Tipton, Sorem, and Rolovic.3 1 R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951; no. 3, March 1951; no. 5, May 1951; no. 6, June 1951; no. 7, July 1951. 2 Walter D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed, John Wiley & Sons, New York, 1997. 3 S. M. Tipton, J. R. Sorem Jr., and R. D. Rolovic, “Updated Stress-Concentration Factors for Filleted Shafts in Bending and Tension,” Trans. ASME, Journal of Mechanical Design, vol. 118, September 1996, pp. 321–327