In the structural engineering beam theory, the term "plastic hinge" is used to describe the deformation of a section of a beam where plastic bending occurs. [1] In earthquake engineering plastic hinge is also a type of energy damping device allowing plastic rotation [deformation] of an otherwise rigid column connection. [2]
In plastic limit analysis of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between Myp and Mp is considered to be elastic. When Mp is reached, a plastic hinge is formed in the member. In contrast to a frictionless hinge permitting free rotation, it is postulated that the plastic hinge allows large rotations to occur at constant plastic moment Mp.
Plastic hinges extend along short lengths of beams. Actual values of these lengths depend on cross-sections and load distributions. [3] But detailed analyses have shown that it is sufficiently accurate to consider beams rigid-plastic, with plasticity confined to plastic hinges at points. While this assumption is sufficient for limit state analysis, finite element formulations are available to account for the spread of plasticity along plastic hinge lengths. [4]
By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism. For each degree of static indeterminacy of the beam, an additional plastic hinge must be added to form a collapse mechanism.
Sufficient number of plastic hinges(N) required to make a collapse mechanism (unstable structure):
N=Degree of static indeterminacy + 1
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).
In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.
In physics and materials science, plasticity is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.
The field of strength of materials typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.
A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile, equilibrium conditions, length, and their material.
In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column.
In applied mechanics, bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
Plastic bending is a nonlinear behavior particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analysis. In both the plastic and elastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the neutral axis. In an elastic analysis this assumption leads to a linear stress distribution but in a plastic analysis the resulting stress distribution is nonlinear and is dependent on the beam’s material.
In structural engineering, the plastic moment (Mp) is a property of a structural section. It is defined as the moment at which the entire cross section has reached its yield stress. This is theoretically the maximum bending moment that the section can resist – when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation. In practice most materials are work-hardened resulting in increased stiffness and moment resistance until the material fails. This is of little significance in structural mechanics as the deflection prior to this occurring is considered to be an earlier failure point in the member.
This is an alphabetical list of articles pertaining specifically to structural engineering. For a broad overview of engineering, please see List of engineering topics. For biographies please see List of engineers.
A deformation mechanism, in geology, is a process occurring at a microscopic scale that is responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from their original position within a crystal lattice structure. These small changes are preserved in various microstructures of materials such as rocks, metals and plastics, and can be studied in depth using optical or digital microscopy.
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.
In physics and continuum mechanics, deformation is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body.
In structural engineering, the P-Δ or P-delta effect refers to the abrupt changes in ground shear, overturning moment, and/or the axial force distribution at the base of a sufficiently tall structure or structural component when it is subject to a critical lateral displacement. A distinction can be made between P-delta effects on a multi-tiered building, written as P-Δ, and the effects on members deflecting within a tier, written as P-δ.
Structural engineering depends upon a detailed knowledge of loads, physics and materials to understand and predict how structures support and resist self-weight and imposed loads. To apply the knowledge successfully structural engineers will need a detailed knowledge of mathematics and of relevant empirical and theoretical design codes. They will also need to know about the corrosion resistance of the materials and structures, especially when those structures are exposed to the external environment.
Moment redistribution refers to the behavior of statically indeterminate structures that are not completely elastic, but have some reserve plastic capacity. When one location first yields, further application of load to the structure causes the bending moment to redistribute differently from what a purely elastic analysis would suggest.
In Earth science, ductility refers to the capacity of a rock to deform to large strains without macroscopic fracturing. Such behavior may occur in unlithified or poorly lithified sediments, in weak materials such as halite or at greater depths in all rock types where higher temperatures promote crystal plasticity and higher confining pressures suppress brittle fracture. In addition, when a material is behaving ductilely, it exhibits a linear stress vs strain relationship past the elastic limit.
Johannes Ferdinand "Hans" Besseling was professor emeritus of Engineering Mechanics at the Delft University of Technology, worked in the field of the application of solid mechanics to the analysis of structures; constitutive equations for the mathematical description of material behaviour. His specialities are finite element methods, continuum thermodynamics, creep and plasticity of metals.
This glossary of structural engineering terms pertains specifically to structural engineering and its sub-disciplines. Please see glossary of engineering for a broad overview of the major concepts of engineering.