The usual practice of bending
of a bar near a support is at an angle of 450. The angle of bend may
also be 300 in shallow beams where effective depth is less than 1.5
times its breadth. The purpose of bend near a support is two fold, firstly to
resist negative bending moment which occurs at the region of the support and
secondly to resist shear force which is greater at the support.
Bending moment which is maximum
at the mid span diminishes towards the supports (except cantilevers) and the
number of tensile bars required to resist bending moment may thus be reduced
near the ends providing sufficient bond length. The bending moment and shear
force along the span of a beam depends on the loading and end fixation
conditions of a beam.
However, when the position of
bent up bars are not shown in the drawing but it is required to prepare a bar
bending schedule then the position of crank may be considered as 1/4th
to 1/5th of the effective span of a beam.
Denoting effective depth of a
member by d and L = span.
For 450 bends length
of crank = d/sin 450 = d/0.707 = 1.42d Length covered by crank = d.
Therefore, Extra length
required for one bend = 1.42d – d = 0.42d.
Thus if a bar is cranked at
both ends at 450 then total length of the bar = L + 2 x 0.42d.
Thus for 300 bends –
Length of crank = d /sin 300
= 2d, Length covered by crank = d/tan 300 = 1.73 d.
Therefore, Extra length
required for only one bend = 2d – 1.73d = 0.27d.
Thus if a bar is cranked at
both ends at 300 then total length of bar = L + 2 x 0.27 d.
Table showing the number of
bars available for bending and the position at which bars in bottom of beams
can be bent up or stopped giving sufficient bond for different end conditions.
This is applicable for Beams carrying uniformly distributed load only.
L =
Effective span
No. of
bars at mid span
|
For
freely supported
|
End
Span
|
Interior
span (Fixed)
|
|||||||||||||
Free
|
Fixed
|
|||||||||||||||
1st
bent at
|
2st
bent at
|
3st
bent at
|
4st
bent at
|
1st
bent at
|
2st
bent at
|
3st
bent at
|
4st
bent at
|
1st
bent at
|
2st
bent at
|
3st
bent at
|
4st
bent at
|
1st
bent at
|
2st
bent at
|
3st
bent at
|
4st
bent at
|
|
2
|
0.15L
|
-
|
-
|
-
|
0.13L
|
-
|
-
|
-
|
0.11L
|
-
|
-
|
-
|
0.21L
|
0.09L
|
-
|
-
|
3
|
0.21L
|
0.09L
|
-
|
-
|
0.18L
|
0.08L
|
-
|
-
|
0.30L
|
0.19L
|
0.11L
|
-
|
0.27L
|
0.16L
|
0.09L
|
-
|
4
|
0.25L
|
0.15L
|
0.07L
|
-
|
0.22L
|
0.13L
|
0.05L
|
-
|
0.33L
|
0.24L
|
0.17L
|
0.11L
|
0.30L
|
0.2L
|
0.15L
|
0.09L
|
5
|
0.27L
|
0.19L
|
0.12L
|
0.05L
|
0.24L
|
0.15L
|
0.09L
|
0.04L
|
0.35L
|
0.28L
|
0.21L
|
0.16L
|
0.31L
|
024L
|
0.18L
|
0.13L
|
6
|
0.30L
|
0.21L
|
0.15L
|
0.09L
|
0.25L
|
0.18L
|
0.13L
|
0.08L
|
0.36L
|
0.30L
|
0.24L
|
0.19L
|
0.33L
|
027L
|
0.21L
|
0.16L
|
