Length of flange

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Chapter 7

• Length of flange

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6.1 Introduction As the bending moment decreases
towards the support, the flange plate may be
varied and a smaller flange plate may be used.
There is not much difference in the effective
depth after variation of flange plate and will
nearly be equal. Therefore,
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moment of resistance will be proportional to
(area of flange plate Aweb/6). Graphically or
by analytical calculations, theoretical cut off
points can be determined. The flange plates are
butt welded at junction to form continuous
flange. Where the difference in thickness of the
two plates is 6 mm or more, thicker plate shall
rather be beveled so that the slop of surface
from one part to the other is not steeper
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than one in five as shown in Fig. (6.1.a) or the
weld metal shall be built up between the two
parts as shown in Fig. (6.1.b), provided the
thickness of the thicker plate is not more than
50 greater than that of the thinner plate. The
flange width bf and or the flange thickness tf
can be reduced at the cut-off point. Cover plates
used to vary flange area, as in the case of the
cover plate add to the flange of a rolled section
to increase its moment capacity, must extend
beyond the theoretical cut-off a sufficient
distance to develop the capacity of the plate
i.e., the allowable weld strength beyond the
cut-off must equal to the allowable axial force
in the plate.
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Strength of cover plate Ac??t 2?s?a?Fw Fw
0.23 Fy,
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1. length of flange plate for girders carrying
uniformly distributed load. Moment of resistance
(Mr) varies as the effective flange area
A1(bf1?tf1 Aw/6). Let Ln be the theoretical
length of plate at which a smaller flange plate
may be used. B.M. diagram will be parabola, M1
K.A1, A1(bf1?tf1 Aw/6) (Af1 Aw/6) M2
K.A2, A2(bf2?tf2 Aw/6) (Af2 Aw/6) Mn
K.An, An(bfn?tfn Aw/6) (Afn Aw/6)
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1.      Graphical method We can compute the
maximum moment at several points and construct
the curve of maximum moment. If the plate girder
supports moving loads, as in the case of highway
and roadway bridges, the envelope of maximum
moments is needed. Since the maximum moment at
each point results from a different position of
the moving live load, the envelope is not the
same thing as the actual moment diagram. However,
a satisfactory approximate method which avoids
the construction of the envelope has been
developed. It is a straight line through the
point of maximum moment, extending 0.05 L on each
side of the mid point of the span flanked by
parabolas tangent at its ends and passing through
the ends of the span. Since each parabolic
segment has a base 0.45 L in length, cover plate
lengths can be determined by adding 0.1 L to the
value of Ln from the equation-
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provided L in that equation is replaced with
(0.9L), i.e., for plate girder supports moving
loads
this method is to assume that the curve of
maximum moment may be represented by a parabola
drawn on a base of 0.9 L, cut at the center and
the two sides separated by a distance 0.1 L.
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Effective flange area comprises one-six of web
area and area of flange plate. the flange area is
drawn to scale on the vertical line such that the
total effective flange area is equal ordinate of
maximum bending moment, then the theoretical
curtailment of plates can be obtained as shown in
Fig..
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1.                  Accurate method of
curtailment In this method, the moment of
resistance of the section with modified flange
plate is calculated and the point at which the
envelope of maximum bending moment will be equal
to this moment of resistance, will be the
theoretical point at which the plate may be
modified. Since the maximum moment at each point
results from a different position of the moving
live load, the envelope is not the same thing as
a moment diagram. For uniformly loaded simply
supported beam, B.M. diagram will be a parabola
if M is the maximum B.M and Mn is the moment of
resistance of the section after modifying the
flange plate and Ln the length of plate, hence
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as before for plate girder supports moving load