Shear in critical beams
Introduction
The shear stress, shear stress, shear stress or tangential stress[1] is that which, once a plane is fixed, acts tangentially to it. It is usually represented with the Greek letter tau (Fig 1). In prismatic pieces, shear stresses appear in case of application of a shear force or a torsional moment "Torsion (engineering)").[2][3].
In elongated members, such as beams and columns, the reference plane is usually parallel to the cross section (i.e., one perpendicular to the longitudinal axis). Unlike normal stress, it is more difficult to appreciate in beams, since its effect is less evident.
Average shear stress
A problem that arises in its calculation is due to the fact that the stresses are not distributed uniformly over an area. If you want to obtain the average tension, the formula is applied:.
where V (letter commonly used to designate this force) represents the shear force and A represents the area of the section on which it is being applied. In this case, shear stress, as the name suggests, cuts a piece. In this image (Fig 2.), the screw and bolt present shear stress when cut by the pieces they join (green line).
Collignon-Jourawski formula
Contenido
Si se requiere encontrar la tensión cortante debida a una fuerza cortante en un punto específico, lo cual es común en vigas, se usa la siguiente fórmula, conocida como fórmula de Collignon (1877):.
donde V representa la fuerza cortante, m primer momento de área parcial (que coincide con el producto del centroide y el área que se abarca desde un extremo hasta el punto donde se quiere encontrar el esfuerzo):.
I el momento de inercia de la sección total respecto a un eje perpendicular a la dirección del cortante y t el espesor de la figura a lo largo de un eje perpendicular a la dirección del cortante. En esta fórmula tanto el segundo momento de área, como el primer momento de área parcial se toman con respecto a la fibra neutra de la pieza.