1.13. I-SHAPED GIRDERS

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=
  Ig
  c

  
  

  (Ad^2 )/ 4
  (d/2)
  =0. 5 Ad (1.48)
  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 equation (1.48)) 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 (1.49)
  Comparison of equation (1.47) with equation (1.49)
  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

  
  

PH8151 41 LICET