Unit 1 Engineering Physics

40 CHAPTER 1. PROPERTIES OF MATTER

In order to maximise the section modulus for a given cross-sectional area A and heightd,wedistribute
each halfA/ 2 of the area at a distanced/ 2 from the neutral axis, as shown in Figure1.36(b). The
geometric moment of inertia of this ideal shape is given by

Ig=A 2

3

d

2

(^42)
+A 2
3
d
2
(^42)
=Ad
2
4
and the distancec=(d/2), the sectional modulus of the ideal shape is
S=Icg=(Ad
(^2) )/ 4
(d/2) =0.^5 Ad (1.47)
Because of the necessity of putting part of the material vertically in the middle part of the beam, the ideal
shape in Figure1.36(b) and hence the limiting condition of eqn (1.47)) can never be realized. However,
this ideal limit may be approximated in practice by the use of a ‘wide- flange section’ (or ‘I-section’).
Figure 1.37: Cross-section of an
I-Beam.
An I-beam is a beam with an ‘I’- or ‘H’-shaped
cross-section, as shown in Figure1.37, with most of
its material in the ‘flanges’, which are the horizontal
elements of the beam.
The vertical element of an I-beam is termed the
‘web’. The web resists shear forces, while the flanges
resist most of the bending moment experienced by
the beam. For standard I-beams, the section mod-
ulus is approximately
S=0. 35 Ad (1.48)
Comparison of eqn (1.46) with eqn (1.48) shows that
a wide-flange section is more ecient than a rectangular section of the same area and same
height. The reason is that more of the material in a rectangular beam is located near the
neutral axis where it is under-stressed. By contrast, in a wide flange beam, most of the
material is located in the flanges, where it is highly stressed. An additional consideration
is the fact that a wide-flange beam is wider and therefore more stable with respect to
sideways buckling than a beam of rectangular section of the same height and section
modulus. Of course, if the web of a wide-flange beam is too thin, it will be susceptible to
localized buckling or it may be overstressed in shear.
Advantage:I-shaped section is a very ecient form for carrying both bending and shear
loads in the plane of the web. There is a good amount of material saving with no
loss in strength.
Disadvantage:I-beam has a reduced load bearing capacity in the transverse direction.
It is also inecient in carrying torsion.
Learning Resource : I-Shaped Beams
A pretty good video introduction to the Physics of I-shaped
beams byDesign Squad GlobalYoutube channel.
URL:https://www.youtube.com/watch?v=UspM9qOdAmI

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