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Glossary: Definitions Appendix B Glossary: Definitions The definitions given here apply to the terminology used throughout this book. Some of the terms may be defined differently by other authors; when this is the case, alternative terminology is noted. When two or more terms with identical or similar meaning are in general acceptance, they are given in the order of preference of the current writers. Allowable stress (working stress): If a member is so designed that the maximum stress as calculated for the expected conditions of service is less than some limiting value, the member will have a proper margin of security against damage or failure. This limiting value is the allowable stress subject to the material and condition of service in question. The allowable stress is made less than the damaging stress because of uncertainty as to the conditions of service, nonuniformity of material, and inaccuracy of the stress analysis (see Ref. 1). The margin between the allowable stress and the damaging stress may be reduced in proportion to the certainty with which the conditions of the service are known, the intrinsic reliability of the material, the accuracy with which the stress produced by the loading can be calculated, and the degree to which failure is unattended by danger or loss. (Compare with Damaging stress; Factor of safety; Factor of utilization; Margin of safety. See Refs. l–3.) Apparent elastic limit (useful limit point): The stress at which the rate of change of strain with respect to stress is 50% greater than at zero stress. It is more definitely determinable from the stress–strain diagram than is the proportional limit, and is useful for comparing materials of the same general class. (Compare with Elastic limit; Proportional limit; Yield point, Yield strength.) Apparent stress: The stress corresponding to a given unit strain on the assumption of uniaxial elastic stress. It is calculated by multi- 813 814 Formulas for Stress and Strain [APP.B plying the unit strain by the modulus of elasticity, and may differ from the true stress because the effect of the transverse stresses is not taken into account. Bending moment: Reference is to a simple straight beam, assumed for convenience to be horizontal and loaded and supported by forces, all of which lie in a vertical plane. The bending moment at any section of the beam is the moment of all forces that act on the beam to the left (or right) of that section, taken about the horizontal axis in the plane of the section. When considering the moment at the section due to the forces to the left of the section, the bending moment is positive when counterclockwise and negative when clockwise. The reverse is true when considering the moment due to forces to the right of the section. Thus, a positive bending moment bends the beam such that the beam deforms concave upward, and a negative bending moment bends it concave downward. The bending moment equation is an expression for the bending moment at any section in terms of x, the distance along the longitudinal axis of the beam to the section measured from an origin, usually taken to be the left end of the beam. Bending moments as applied to straight beams in two-plane symmetric or unsymmetric bending, curved beams, or plates are a bit more involved, and are discussed in the appropriate sections of this book. Bending stress (flexural stress): The tensile and compressive stress transmitted in a beam or plate that arises from the bending moment. (See Flexure equation.) Boundary conditions: As used in structural analysis, the term usually refers to the condition of stress, displacement, or slope at the ends or edges of a member, where these conditions are apparent from the circumstances of the problem. For example, given a beam with fixed ends, the zero displacement and slope at each end are boundary conditions. For a plate with a freely supported edge, the zero-stress state is a boundary condition. Brittle fracture: The tensile failure of a material with negligible plastic deformation. The material can inherently be a brittle material in its normal state such as glass, masonry, ceramic, cast iron, or high strength high-carbon steel (see Sec. 3.7); or can be a material normally considered ductile which contains imperfections exceeding specific limits, or in a low-temperature environment, or undergoing high strain rates, or any combination thereof. Bulk modulus of elasticity: The ratio of a tensile or compressive stress, triaxial and equal in all directions (e.g., hydrostatic pressure) to the relative change it produces in volume. APP. B]Glossary: Definitions 815 Central axis (centroidal axis): A central axis of a line, area, or volume is one that passes through the centroid; in the case of an area, it is understood to lie in the plane of the area unless stated otherwise. When taken normal to the plane of the area, it is called the central polar axis. Centroid of an area: That point in the plane of an area where the moment of the area is zero about any axis. The centroid coincides with the center of gravity in the plane of an infinitely thin homogeneous uniform plate. Corrosion fatigue: Fatigue aggravated by corrosion, as in parts repeatedly stressed while exposed to a corrosive environment. Creep: Continuous increase in deformation under constant or decreasing stress. The term is ordinarily used with reference to the behavior of metals under tension at elevated temperatures. The similar yielding of a material under compressive stress is called plastic flow,orflow. Creep at atmospheric temperature due to sustained elastic stress is sometimes called drift,orelastic drift. (See also Relaxation.) Damaging stress: The least unit stress of a given kind and for a given material and condition of service that will render a member unfit for service before the end of its useful life. It may do this by excessive deformation, by excessive yielding or creep, or through fatigue cracking, excessive strain hardening, or rupture. Damping capacity: The amount of energy dissipated into heat per unit of total strain energy present at maximum strain for a complete cycle. (See Ref. 4.) Deformation: Change in the shape or dimensions of a body produced by stress. Elongation is often used for tensile deformation, compression or shortening for compressive deformation, and distortion for shear deformation. Elastic deformation is deformation that invari- ably disappears upon removal of stress, whereas permanent deforma- tion is that which remains after the removal of stress. (Compare with Set.) Eccentricity: A load or component of a load normal to a given cross section of a member is eccentric with respect to that section if it does not act through the centroid. The perpendicular distance from the line of action of the load to the central polar axis is the eccentricity with respect to that axis. Elastic: Capable of sustaining stress without permanent deforma- tion; the term is also used to denote conformity to the law of stress– 816 Formulas for Stress and Strain [APP.B strain proportionality (Hooke’s law). An elastic stress or strain is a stress or strain within the elastic limit. Elastic axis: The elastic axis of a beam is the line, lengthwise of the beam, along which transverse loads must be applied to avoid torsion of the beam at any section. Strictly speaking, no such line exists except for a few conditions of loading. Usually the elastic axis is assumed to be the line through the elastic center of every section. The term is most often used with reference to an airplane wing of either the shell or multiple spar type. (Compare with Torsional center; Flexural center; Elastic center. See Ref. 5.) Elastic center: The elastic center of a given section of a beam is that point in the plane of the section lying midway between the shear center and center of twist of that section. The three points may be identical—which is the normal assumption. (Compare with Shear center; Torsional center; Elastic axis. See Refs. 5 and 6.) Elastic curve: The curve assumed by the longitudinal axis of an initially straight beam or column in bending where the stress is within the elastic limit. Elastic instability (buckling): Unstable local or global elastic deformations caused by compressive stresses in members with large length to lateral dimensions. (See Slenderness ratio.) Elastic, perfectly plastic material: A model that represents the stress–strain curve of a material as linear from zero stress and strain to the elastic limit. Beyond the elastic limit, the stress remains constant with strain. Elastic limit: The least stress that will cause permanent set. (Compare with Proportional limit; Apparent elastic limit, Yield point; Yield strength. See Sec. 3.2 and Ref. 7.) Elastic ratio: The ratio of the elastic limit to the ultimate strength. Ellipsoid of strain: An ellipsoid that represents the state of strain at any given point in a body. It has the shape assumed under stress by a sphere centered at the point in question (Ref 8). Ellipsoid of stress: An ellipsoid that represents the state of stress at any given point in a body; its semi-axes are vectors representing the principal stresses at the point, and any radius vector represents the resultant stress on a particular plane through the point. For a condition of plane stress, where one of the principal stresses is zero, the ellipsoid becomes the ellipse of stress (see Ref. 9). Endurance limit (fatigue strength): The maximum stress ampli- tude of a purely reversing stress that can be applied to a material an APP. B]Glossary: Definitions 817 indefinitely large number of cycles without producing fracture (see Sec.
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