Machinery's Handbook, 31st Edition
212 Stress and Strain 2–2.5 For use with ordinary materials where loading and environmental conditions are not severe. 2.5–3 For less tried and for brittle materials where loading and environmental conditions are not severe. 3–4 For applications in which material properties are not reliable and where loading and environmental conditions are not severe, or where reliable materials are to be used under difficult loading and environmental conditions. Stress and Strain.—Stress is force per unit area of a material associated with a given strain (stress = force/area), normally expressed in pounds per square inch (psi) or new- tons per square meter (N/m 2 , or pascals, Pa). Strain is the deformation or extension of a material or part under load (strain = extension/length). Stress and strain are linearly related in some materials over all or part of their elastic ranges. This linear relationship is expressed as Hooke’s law, where stress/strain = E , with E being the elastic modulus of the material. Stresses can be axial (tensile or compressive), shear (simple or torsional), isotropic (uniform loading on all surfaces), or combined (any combination of types). Tensile and compressive stress act at right angles to (normal to) the stressed area; shear stress acts along the plane of the affected area (at right angles to compressive or tensile stresses). Working Stress.— Calculated working stresses are the products of calculated nomi- nal stress values and stress concentration factors. Calculated nominal stress values are based on the assumption of idealized stress distributions. Such nominal stresses may be simple stresses, combined stresses, or cyclic stresses. Depending on the nature of the nominal stress, one of the following equations applies: where K is a stress concentration factor; σ and τ are, respectively, simple normal (tensile or compressive) and shear stresses; σ ′ and τ ′ are combined normal and shear stresses; σ cy and τ cy are cyclic normal and shear stresses. Where uneven stress distribution occurs, as illustrated in the table (on page 216 ) of simple stresses for Cases 3, 4 and 6, the maximum stress is the one to which the stress concentration factor is applied in computing working stresses. The location of the maxi- mum stress in each case is discussed under the section Simple Stresses and the formulas for these maximum stresses are given in the Table of Simple Stresses on page 216 . Stress Concentration Factors.— Stress concentration is related to type of material, the nature of the stress, environmental conditions, and the geometry of parts. When stress concentration factors that specifically match all of the foregoing conditions are not avail- able, the following equation may be used: (8) K t is a theoretical stress concentration factor that is a function only of the geometry of a part and the nature of the stress; q is the index of sensitivity of the material. If the geometry is such as to provide no theoretical stress concentration, K t = 1. Curves for evaluating K t are on pages 213 through 216 . For constant stresses in cast iron and in ductile materials, q = 0 (hence, K = 1). For constant stresses in brittle materials such as hardened steel, q may be taken as 0.15; for very brittle materials such as steels that have been quenched but not drawn, q may be taken as 0.25. When stresses are suddenly applied (impact stresses) q ranges from 0.4 to 0.6 for ductile materials; for cast iron it is taken as 0.5; and, for brittle materials, 1. (2) (3) (4) (5) (6) (7) s w = K σ s w = K τ s w = K σ′ s w = K τ′ s w = K σ cy s w = K τ cy K q K 1 1 t = + − ^ h
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