What is Theory of Pure Bending?
Channel: MechanicaLEi
Date: 2018-06-16

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 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 moment 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 zero. 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 same kind throughout and Isotropic means that the elastic properties in all directions are equal. Second, the value of Young's Modulus of Elasticity is same in tension and compression. Third, the transverse sections which were plane before bending, remain plane after bending also. Fourth, the beam is initially straight and all longitudinal filaments bend into circular arcs with a common centre of curvature. Fifth, the radius of curvature is large as 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 value maximum value of bending stresses 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 area 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?
In the next episode of MechanicalEI find out what section modulus and moment of resistance is?

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Doh De Oh by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
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Subtle Library by Fabian Measures (http://freemusicarchive.org/music/Fabian_Measures/) is licensed under a Creative Commons Attribution licence ( https://creativecommons.org/licenses/by/4.0/)
Source: http://freemusicarchive.org/music/Fabian_Measures/Emotion_Music/Subtle_Library