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In fluid dynamics, shear flow is the flow induced by a force in a fluid. In solid mechanics, shear flow is the shear stress over a distance in a thin-walled structure. [1]
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In fluid dynamics, shear flow is the flow induced by a force in a fluid. In solid mechanics, shear flow is the shear stress over a distance in a thin-walled structure. [1]
For thin-walled profiles, such as that through a beam or semi-monocoque structure, the shear stress distribution through the thickness can be neglected. [2] Furthermore, there is no shear stress in the direction normal to the wall, only parallel. [2] In these instances, it can be useful to express internal shear stress as shear flow, which is found as the shear stress multiplied by the thickness of the section. An equivalent definition for shear flow is the shear force V per unit length of the perimeter around a thin-walled section. Shear flow has the dimensions of force per unit of length. [1] This corresponds to units of newtons per meter in the SI system and pound-force per foot in the US.
When a transverse force is applied to a beam, the result is variation in bending normal stresses along the length of the beam. This variation causes a horizontal shear stress within the beam that varies with distance from the neutral axis in the beam. The concept of complementary shear then dictates that a shear stress also exists across the cross section of the beam, in the direction of the original transverse force. [3] As described above, in thin-walled structures, the variation along the thickness of the member can be neglected, so the shear stress across the cross section of a beam that is composed of thin-walled elements can be examined as shear flow, or the shear stress multiplied by the thickness of the element. [2]
The concept of shear flow is particularly useful when analyzing semi-monocoque structures, which can be idealized using the skin-stringer model. In this model, the longitudinal members, or stringers, carry only axial stress, while the skin or web resists the externally applied torsion and shear force. [3] In this case, since the skin is a thin-walled structure, the internal shear stresses in the skin can be represented as shear flow. In design, the shear flow is sometimes known before the skin thickness is determined, in which case the skin thickness can simply be sized according to allowable shear stress.
For a given structure, the shear center is the point in space at which shear force could be applied without causing torsional deformation (e.g. twisting) of the cross-section of the structure. [4] The shear center is an imaginary point, but does not vary with the magnitude of the shear force - only the cross-section of the structure. The shear center always lies along the axis of symmetry, and can be found using the following method: [3]
By definition, shear flow through a cross section of thickness t is calculated using , where . Thus the equation for shear flow at a particular depth in a particular cross-section of a thin-walled structure that is symmetric across its width is
where
Unlike in solid mechanics where shear flow is the shear stress force per unit length, in fluid mechanics, shear flow (or shearing flow) refers to adjacent layers of fluid moving parallel to each other with different speeds. Viscous fluids resist this shearing motion. For a Newtonian fluid, the stress exerted by the fluid in resistance to the shear is proportional to the strain rate or shear rate.
A simple example of a shear flow is Couette flow, in which a fluid is trapped between two large parallel plates, and one plate is moved with some relative velocity to the other. Here, the strain rate is simply the relative velocity divided by the distance between the plates.
Shear flows in fluids tend to be unstable at high Reynolds numbers, when fluid viscosity is not strong enough to dampen out perturbations to the flow. For example, when two layers of fluid shear against each other with relative velocity, the Kelvin–Helmholtz instability may occur.
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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).
Shear stress is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.
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.
In structural engineering, a shear wall is a two-dimensional vertical element of a system that is designed to resist in-plane lateral forces, typically wind and seismic loads.
Aerodynamic heating is the heating of a solid body produced by its high-speed passage through air. In science and engineering, an understanding of aerodynamic heating is necessary for predicting the behaviour of meteoroids which enter the earth's atmosphere, to ensure spacecraft safely survive atmospheric reentry, and for the design of high-speed aircraft and missiles.
In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. The plug flow model assumes there is no boundary layer adjacent to the inner wall of the pipe.
Euler–Bernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral loads only. By ignoring the effects of shear deformation and rotatory inertia, it is thus a special case of Timoshenko–Ehrenfest beam theory. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution.
I-beam is a generic lay term for a variety of structural members with an I or H-shaped cross-section. Technical terms for similar items include H-beam, w-beam, universal beam (UB), rolled steel joist (RSJ), or double-T. I-beams are typically made of structural steel and serve a wide variety of construction uses.
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.
The first moment of area is based on the mathematical construct moments in metric spaces. It is a measure of the spatial distribution of a shape in relation to an axis.
In materials science, a sandwich-structured composite is a special class of composite materials that is fabricated by attaching two thin-but-stiff skins to a lightweight but thick core. The core material is normally low strength, but its higher thickness provides the sandwich composite with high bending stiffness with overall low density.
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.
In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed ; therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end. In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely.
The neutral axis is an axis in the cross section of a beam or shaft along which there are no longitudinal stresses or strains.
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 mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral plane is the surface within the beam between these zones, where the material of the beam is not under stress, either compression or tension.
Skin friction drag is a type of aerodynamic or hydrodynamic drag, which is resistant force exerted on an object moving in a fluid. Skin friction drag is caused by the viscosity of fluids and is developed from laminar drag to turbulent drag as a fluid moves on the surface of an object. Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force.
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.