PH8151 Engineering Physics Chapter 1

28 CHAPTER 1. PROPERTIES OF MATTER

M N

M’ N’

M N

N’

M’

(a) (b)

Compressive

Force

Tensile

Force

F

F

neutral

surface neutral^

surface

neutral

axis

neutral

axis

Figure 1.23: Neutral filament MNNÕMÕ of a beam -(a)before bending and(b)after
bending

which opposes the bending of the beam.

Bending Moment

The moment of internal restoring couple is called the ‘moment of the resistance’ or

the ‘moment of the restoring couple’ orBending Moment(BM) of the beam.

At equilibrium, moment of the external bending couple

= moment of the internal restoring couple (BM).

The action of the bending moment can be thought of as “trying to rotate the cross-

section about the neutral axis (NNÕ) back to its original vertical orientation.”

1.9 Bending Moment of a Beam

Consider a beam whose neutral filament MN is bent into an arc of radiusRwith centre
at O as shown in Figure1.24. Then,

Stress due to bending in beams

x

The neutral axis is an axis

in the cross section of a

beam along which there are

no longitudinal stresses or

strains.

Radius of curvature of the

Neutral surface = R

Strain in layer EF = x/R

Stress due to bending at

layer EF= σ

E F

R

Young’s modulus = Y = (Stress due to bending at layer EF) / (Strain in layer EF)

Or Y = σ /(x/R) = (σR) /x

Hence, stress due to bending = σ = (Yx)/R

O

P x

P’ Q’

Q

N N’

θ

δA

M

D

Compressive

force

Tensile

force

Figure 1.24: A beam whose neutral filament is bent into an arc of radiusR

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