 Welcome back MechanicalEI. Did you know that the PC, mobile phone, a tank and a trumpet all share the same theory of pure bending to achieve their final shape? This makes us wonder, what is the theory of pure bending? Before we jump in, check out the previous part of this series to learn about what are beams with internal hinges. Now, pure bending is a condition of stress where bending movement is applied to a beam without the simultaneous presence of axial, shear or torsional forces. Pure bending occurs only under a constant bending moment M since the shear force V which is equal to the first derivative of constant bending moment M with respect to distance x has to be equal to 0. In reality, this state of pure bending does not exist because such a state needs an absolutely weightless member. The state of pure bending is an approximation made to derive formulas. There are six assumptions to the theory of pure bending. First, the material of the beam is homogeneous and isotropic. Homogeneous means the material is of the same kind throughout and isotropic means that the elastic properties in all directions are equal. Second, the value of Young's modulus of elasticity E is the same in tension and compression. Third, a transfer section which are plain before bending remain plain after bending also. Fourth, the beam is initially straight and all longitudinal filaments bend into circular arcs with a common center of curvature. Fifth, the radius of curvature is too large when compared to the dimensions of the cross section. And sixth, each layer of the beam is free to expand or contract independently of the layer above or below it. In order to compute the maximum value of bending stress developed in a strain of loaded beam at a distance y, from the axis using the theory of pure bending, we obtain a relation between maximum bending stress, sigma max, internal bending moment m and the second moment of inertia i. It is expressed as sigma max equals the product of m and c divided by i. Hence, we first saw what theory of pure bending is, then saw the assumptions in pure bending and finally saw what flexural formula for straight beams is.