that 'plane sections remain plane'. In other words, any deformation due to shear across the section is not accounted for (no shear deformation). Also, this linear distribution is only applicable if the maximum stress is less than the yield stress of the material. For stresses that exceed yield, refer to article plastic bending. At yield, the maximum stress experienced in the section (at the furthest points from the neutral axis of the beam) is defined as the flexural strength. Consider beams where the following are true: The beam is originally straight and slender, and any taper is slight The material is isotropic (or orthotropic), linear elastic, and homogeneous across any cross section (but not necessarily along its length) Only small deflections are considered In this case, the equation describing beam deflection () can be approximated as: where the second derivative of its deflected shape with respect to is interpreted as its curvature, is the Young's modulus, is the area moment of inertia of the cross-section, and is the internal bending moment in the beam. If, in addition, the beam is homogeneous along its length as well, and not tapered (i.e. constant cross section), and deflects under an applied transverse load , it can be shown that: This is the Euler–Bernoulli equation for beam bending. After a solution for the displacement of the beam has been obtained, the bending moment () and shear force () in the beam can be calculated using the relations Simple beam bending is often analyzed with the Euler–Bernoulli beam equation. The conditions for using simple bending theory are: The beam is subject to pure bending. This means that the shear force is zero, and that no torsional or axial loads are present. The material is isotropic (or orthotropic) and homogeneous. The material obeys Hooke's law (it is linearly elastic and will not deform plastically). The beam is initially straight with a cross section that is constant throughout the beam length. The beam has an axis of symmetry in the plane of bending. The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. Cross-sections of the beam remain plane during bending. Compressive and tensile forces develop in the direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam