6b. Bending in Beams (SSES Ch. 6.1) • MomentShearLoad • Beam Bending • Bending Stress 
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Beam Bending
When a beam is subjected to pure bending (constant moment), it deforms in the manner shown at right. Viewed from the side, the deflection takes the form of a circular arc with a radius of curvature of R (measured to the neutral axis of the beam). The neutral axis is a line along the beam axis that does not change length and so has zero strain. From geometry, the strain in the beam must be:

Bending Stress
From Hooke's Law, the stress due to bending is related to the bending strain: Applying the equilibrium conditions and making a couple of algebraic
substitutions, the Bending Stress  a normal stress in the xdirection  is:  
 

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