Shear flow
Encyclopedia
The term shear flow is used in solid mechanics
as well as in fluid dynamics
. Loosely speaking, shear flow is defined as:
In this article the first definition from solid mechanics is used. See Viscosity
for a fuller treatment about the term from fluid dynamics.
, shear flow is given in dimensions of force per length. This corresponds to units of newtons per meter in the SI
system and pound-force
per foot in the English Engineering and British Gravitational systems.
where
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...
as well as in fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
. Loosely speaking, shear flow is defined as:
- the gradient of a shear stressShear stressA shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
force through the body (in solid mechanics); - the flow induced by such a force gradient (in a fluid).
In this article the first definition from solid mechanics is used. See Viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
for a fuller treatment about the term from fluid dynamics.
Dimensions
In solid mechanicsSolid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...
, shear flow is given in dimensions of force per length. This corresponds to units of newtons per meter in the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
system and pound-force
Pound-force
The pound force is a unit of force in some systems of measurement including English engineering units and British gravitational units.- Definitions :...
per foot in the English Engineering and British Gravitational systems.
Shear flow in semi-monocoque structures
The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is:where
- q - the shear flow through a particular web section of the cross-section
- Vy - the shear force perpendicular to the neutral axis x through the entire cross-section
- Qx - the first moment of areaFirst moment of areaThe first moment of area, sometimes misnamed as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment of area equals the summation of area times distance to an axis [Σ]...
about the neutral axis x for a particular web section of the cross-section - Ix - the second moment of areaSecond moment of areaThe second moment of area, also known as the area moment of inertia, moment of inertia of plane area, or second moment of inertia is a property of a cross section that can be used to predict the resistance of beams to bending and deflection, around an axis that lies in the cross-sectional plane...
about the neutral axis x for the entire cross-section
External links
Sources
- Riley, W. F. F., Sturges, L. D. and Morris, D. H. Mechanics of Materials. J. Wiley & Sons, New York, 1998 (5th Ed.), 720 pp. ISBN 0-471-58644-7