PH8151EPUnit1

1.11. UNIFORM BENDING AND NONUNIFORM BENDING

which means that the shear force is zero. Nonuniform bending refers to flexure of beams
in the presence of shear forces, which means that the bending moment changes as we
move along the axis of the beam. For a uniformly bent beam, the radius of curvatureRof
the neutral filament (in the plane of bending) is constant, and for a beam in nonuniform
bending,Rchanges with distance along the axis of the beam.

1.11.1 Uniform Bending: Theory and Experiment

Consider a beam (or bar) AB arranged horizontally on two knife-edges C and D symmet-
rically so that AC = BD =a,as shown in Figure1.28. The beam is loaded with equal
weights W and W at the ends A and B such that any given filament of the bent beam
forms an arc of a single circle. This bending can be shown to be of uniform type. The

l

Load

Pin

Load

a a

A B

C E D

F

Figure 1.28: Uniform bending - experimental set up

forces acting on the neutral filament of the beam are shown in Figure1.29. The reactions
on the knife-edges at C and D are equal to W and W acting vertically upwards. The

a a

l

A B

C E D

F

W W

W W

Figure 1.29: Uniform bending - forces acting on the neutral filament

moment of external bending couple on the part AC of the beam is=W◊AC=W◊a

Internal bending moment =

YIg

R

(1.36)

whereY - Youngs’ modulus of the material of the bar
Ig- Geometrical moment of inertia of the cross-section of beam

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