Stress Concentration Factors Machinery's Handbook, 31st Edition
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3.0
2.8
M
M
2.6
d
a
2.4
2.2
2.0
0
0.05
0.10
0.15
0.20
0.25
0.30
a / d Fig. 10. Stress-Concentration Factor K t for a Shaft with a Transverse Hole in Bending a a Source: R. E. Peterson, Design Factors for Stress Concentration, Machine Design, vol. 23, 1951. For other stress concentration charts, see Lipson and Juvinall, The Handbook of Stress and Strength, The Macmillan Co., 1963. Simple Stresses.—Simple stresses are produced by constant conditions of loading on ele- ments that can be represented as beams, rods, or bars. Table 2 summarizes information per- taining to the calculation of simple stresses, including symbols used in simple stress formulae: σ = simple normal (tensile or compressive) stress, in psi (Mpa) τ = simple shear stress, in psi (Mpa) F = external force in pounds (Newtons, or N) V = shearing force in pounds (N) M = bending moment in inch-pounds (N-mm) T = torque in inch-pounds (N-mm) A = cross-sectional area perpendicular to the axial force or parallel to the shear force, in in 2 (mm 2 ) I = moment of inertia in in 4 (mm 4 ) J = polar moment of inertia in in 4 (mm 4 ) a = area of the web of wide flange and I beams in in 2 (mm 2 ) y = perpendicular distance from axis through center of gravity of cross-sectional area to the most-stressed fiber in inches (mm) c = radial distance from center of gravity to the most-stressed fiber (usually the farthest point from the neutral axis) in in. (mm). Table 2. Table of Simple Stresses Case Type of Loading Illustration Stress Distribution Stress Equations 1 Direct tension F F Uniform (9) 2 Direct compression Uniform (10) A F σ = F F A F σ=− Z = section modulus in in 3 (mm 3 ) Z p = polar section modulus in in 3 (mm 3 )
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