Shear flow

The term shear flow is used in solid mechanics as well as in fluid dynamics. The expression shear flow is used to indicate: The term shear flow is used in solid mechanics as well as in fluid dynamics. The expression shear flow is used to indicate: For thin-walled profiles, such as that through a beam or semi-monocoque structure, the shear stress distribution through the thickness can be neglected. Furthermore, there is no shear stress in the direction normal to the wall, only parallel. 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. This corresponds to units of newtons per meter in the SI system and pound-force per foot in the US. When a transverse shear force is applied to a structure, such as a beam, the result is variation in bending normal stresses along the length of the beam. This variation necessitates an internal horizontal shear stress within the beam that varies with position y' from the neutral axis in the beam. The concept of complementary shear then dictates that a shear stress also exists along the front face of the beam. As described above, in thin-walled structures the variation with thickness can be neglected, and the shear stress along the front face of the structure can be examined as shear flow, or the shear stress multiplied by the thickness of the element. 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. 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. 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: By definition, shear flow through a section of thickness t is calculated using q = τ ∗ t {displaystyle q= au *t} , where τ = V Q I t {displaystyle au ={frac {VQ}{It}}} . Thus the equation for shear flow in a particular web section of the cross-section of a thin-walled structure (in this case symmetric across the x-axis) is: