INTRODUCTION This Item presents data on stress concentration effects that occur in flat bars or strips when they are loaded in tension or bending. A stress concentration factor is defined here as the ratio of the highest principal stress to a reference stress calculable from simple two-dimensional theory. Throughout this Item@ the term ??bars or strips' applies to bodies having solid@ thin rectangular sections. The data apply only to isotropic materials that obey Hooke's Law. However@ over the practical working range most engineering materials conform substantially in these respects and for these the data may be used without significant error. If the stress concentration is such that the maximum stress is above the limit of proportionality of the material@ stress is redistributed and creates residual stress on unloading. The various geometries for which data are presented are listed on Table 1.1. The gross stress concentration factor@k' is based on a reference stress found using the gross cross-section of the bar or strip (ignoring the discontinuity). The symbol k'indicates that the stress concentration factor is based on the net cross-section at the discontinuity. Table 1.1 also indicates the methods used to obtain stress concentration factors in the various derivations. The term ??analytical' implies that the relevant elasticity equations were solved directly for the range of parameters indicated. For a bar or strip of any thickness@ loaded in tension and containing a hole@ the stress concentration is a maximum at the mid-plane of the bore of the hole (and is greatest for thick bar or strips when the ratio of the hole diameter@ @ to the thickness@ @ of the bar or strip@d/t @ is greater than 0.5) and is a minimum at the free surface: an effect that becomes more pronounced when@d/tlt;2.0 see ESDU 93030*. The term ??closed-form equation' is defined in this Item as an explicit expression for the stress concentration factor. The equations presented are based in some cases on empirical curve-fitting to finite element@ photoelastic or analytically based data@ and in the other cases@ designated ??based on crack solutions'@ the equations have a partially analytical basis. Curves from closed-form equations are presented for Figures 3@ 8a@ 8b@ 8c@ 11a@ 11b@ 11c@ 12a@ 12b@ 12c@ 15a and 15b (see Derivations 34@ 31@ 32@ 33 and 35) which deal with a centrally placed hole or variously shaped notches and fillets that lie within specified bounds. The fracture mechanics approach underlying the ??closed-form equations based on crack solutions' is a special case of the ??analytical' method@ as it is based on elastic solutions for sharp-ended ellipses@ cracks or sharp corners. If the radius of the notch involved is small@ so that the region of concentrated stress is small compared to the other in-plane dimensions of the geometry@ including the notch depth@ a solution based on results for a crack with rounded ends will be accurate@ becoming exact in the limit of a mathematically sharp crack. This method can therefore be applied to any sharp stress concentration for which a corresponding sharp-crack Linear Elastic Fracture Mechanics (LEFM) solution is available (see Derivation 8 and ESDU 80036?). Reference 36 discusses the use of photoelasticity for the determination of stress concentration factors at sharp notches and concludes that the method tends to underestimate stress concentration factors unless the thickness of the test specimen is reduced in step with the notch tip radius. It demonstrated that the thickness should be less than 1.5 times the radius to ensure accurate data and that this may be impractical for very sharp notches. The earlier photoelastic results used in this Item (see Figures 1 to 7 and 13 to 15a) tend to give stress concentration factors up to 10 per cent lower than those given by finite element analysis. Recent photoelastic data used in Figure 11a agree completely with the finite element data for fillets in tension@ for a ratio of maximum to minimum width W/w@ of 2.0 and greaterthan 0.1@ where is the minimum width of the bar or strip and is the radius of the fillet (see Derivations 29 and 30). For geometries outside this range@ and for other cases presented in Figures 8a to 12a@ the agreement between the results decreases as r/w decreases@ i.e. as the notch becomes sharper. These photoelastic stress concentration factors can be up to 17 per cent lower than those from the finite element determinations for r/w between 0.002 and 0.2. Given that the finite element results in this sharp notch regime align with the analytical solutions@ the presentations are based on finite element data@ where available@ and the photoelastic results are then used to validate the data in regions where the sharp notch theory is less applicable. ? ESDU 80036 ??Introduction to the use of linear elastic fracture mechanics in estimating fatigue crack growth rates and residual strength of components'.