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Fig. 43.1(b)
planes of these two sections will remain perpendicular to the plane AB but will now be inclined at an angle dy to each other. The parts of the beam above the layer AB are in compression and those below the layer AB are in tension. Thus the layer AB is neither in compression or tension and this layer is called the Neutral Axis.
Let the radius of curvature of the neutral axis layer be R.
Consider a layer of thickness dy which is situated at distance y from the plane of the Neutral Axis.
Original length of layer dx
After bending, this length REdy no stress or strain here
Length of layer after bending R y dy at a distance y below A B But
Strain Elongation Orig. length
R y dy RdEy RdEy
Strain y/R
This equation indicates that strain varies directly as the distance from the neutral axis. Also, if the modules of elasticity is constant throughout the
Bending and shear stresses 357
beam, then: or
E Stress Strain
Stress E Strain