The
transverse reinforcement provided in Column is called Ties and the transverse reinforcement provided in Beam is
called Stirrups. But on-site, we usually
call both transverse reinforcements as Stirrups.
The
prime reason for providing the stirrups in the beam is for shear requirements
and to keep the longitudinal bars in position. If you wanted to know more about
the why stirrups & ties provided in the beam and column
Each load acting on a column will raise some sort of
displacement, cracks, and tension in the reinforcement. So the main purpose of
stirrups is
·
To keep the reinforcement in place
·
To resist the flexural shear stress developed in the
reinforcement.
·
To resist the diagonal tension crack propagation though it is
limited
Deducting the concrete cover is most important in Bar
bending, if you don’t know how to deduct the concrete cover then refer this post "
Steps involved in finding the
cutting length of stirrups:-
1.
Look at the size of column or beam from drawings
2.
Adopt Dia of the bar (generally 8mm Dia is used for stirrups)
3.
Deduct the concrete cover or clear cover
4.
Find the total outer length of stirrup after deducting concrete
cover.
5.
Add the length of the hook to the length of the stirrup
6.
Deduct the length of bends
Use below formula to find the total cutting length of stirrups
Cutting Length of Stirrups = Perimeter of Shape + Total
hook length – Total Bend Length
Assumptions
·
Hook
Length = 10d or 75 mm
·
45°
Bend = 1d
· 90° Bend = 2d
· 135° Bend = 3d
Important Basic formulas:
Perimeter
of Rectangle = 2 ( length + breadth)
Perimeter
of Square = 4 x side length
Perimeter
of circle or Circumference of Circle = 2πr = πd (r= radius, d= Diameter of
Circle)
Cutting Length of
Rectangular Stirrups
From the Diagram,
Clear
Cover – 25 mm
Column
Size = 200mm X 600mm
Stirrups
– 8mm
Cutting Length of Stirrup = 2(a+b) + 2 numbers
of hooks – 3 numbers of 90° bends – 2 numbers of 135° bends
a =
600 – 2 x Clear Cover = 600 – (2×25) = 550
b =
200 – 2 x Clear Cover= 200 – (2×25) = 150
Cutting
Length of Stirrup = 2(a+b) + 2 numbers of hooks – 3 numbers of 90° bends – 2
numbers of 135° bends
=
2(550+150) + (2 x10d) – (3 x 2d) – (2 x 3d) = 1400 + (2x10x8) – (3x2x8) -(2
x3x8)
Cutting
Length of Rectangular Stirrup = 1464 mm or 1.46 m
Cutting
length for Square Stirrups:-
From the Diagram,
Clear Cover – 25 mm
Column Size = 400mm X 400mm
Stirrups – 8mm
Deducting the concrete cover 25mm from all sides (in square all sides are equal)
x = 450- 20-20 = 410mm
y = 450-20-20 = 410mm, Hence x = y (in square all sides are equal)
Total Length of the hook:
There are two hooks which mean 9d+9d = 18d
Total length of Bends:
There are 3 bends which are bent at an angle of 900 and one is bent at an
angle of 1350.
Total bend length = 3 x 900 Bend length + 2 x 1350 Bend length = 3 x
2d + 2 x 3d = 12d = 12 x 8 = 96mm
Total Cutting length of Square Stirrup =
Perimeter of Square + Total Hook length – Total Bend Length
= 4 x
410 +18d – 12d = 1648mm = 1.64m
Cutting Length of
Circular Stirrups
From the Diagram,
Clear
Cover – 40mm
Column
Diameter (D) = 900 mm
Stirrups
– 8mm
Formula,
Length of Circular ring = Circumference of Ring + 2 numbers of hooks – 2
numbers of 135° bends
Where
Circumference of ring = 2丌r (where r – Radius), We know (r) radius of
circle = d/2 (half of the diameter)
Diameter
of Ring (d) = Diameter of Column (D) – Clear Cover = 900 – 40 = 860mm
Radius
of Ring r = d/2 = 860/2 = 430mm
So,
Length of Circular ring formula = 2丌r + (2 x 10d) – (2 x 3d)
Length
of Circular ring = (2 x 3.14 x 430) + (2 x 10 x 8) – (2 x 3 x 8) = 2812.4 mm or
2.81 m
Cutting
Length for Triangular Stirrups:
From the Diagram,
Clear Cover – 25mm
Column size = 4
Stirrups – 8mm
Deducting the concrete cover 25mm from all sides
x = 400-20-20 = 360mm
y = 450-20-20 = 410mm
From Pythagorean theorem,
Hypotenuse2=(Opposite)2 + (Adjacent)2
look at 2nd triangle in above image
H2=(x/2)2 + y2
H2=1802 + 4102 => =
√(447)2 = 447mm
The total length of stirrup till now = 2 x H + 360 = 2 x 447 + 360 = 1254mm
Total Length of the hooks:
There are two hooks which means 9d+9d= 18d
Total length of Bends:
There are 4 bends which are bent at an angle of 1350
Total bend length =4 x 1350 Bend length= 4 x 3d = 12d= 12 x 8 = 96mm
Total Cutting length of
Triangular Stirrup = Perimeter of Triangle + Total Hook length – Total Bend
Length
= 1254+18d – 12d = 1302mm
= 1.3m
Cutting Length of Helical Stirrups
From
the Diagram,
Clear
Cover – 75mm
Column
Diameter (D) = 600 mm
Diameter
of helical Stirrups – 8mm
Column
Length – 20000 mm or 20m
Spacing
of stirrups – 200mm
Circular
and helical are almost same except the hooks provided. For Circular we have to
calculate the number of rings. In helical we have to calculate the required
length of stirrups for the entire length of a column. Please read the BBS for
Pile post for details.
to
find the length of the helical outer ring we have to find the circumference of
the ring
·
Length
of Inner spacer ring = Circumference of Inner Ring = 2丌r (where R – Radius)
We
already know the diameter of the pile(600mm) so it is easy to find the diameter
of inner ring and the radius
Diameter
of outer spiral ring = Diameter of Pile – Clear Cover = 600mm – 75mm =
525mm
Therefore
Radius of spiral ring (R) = D/2 Therefore radius of Inner ring = 525mm/2 =
262.5 or 263 mm
Length
of One spiral ring = Circumference of Inner Ring = 2丌r (where R – Radius) = 2 x 3.14 X 263mm
Length
of one spiral ring = 1652 mm or 1.65 m
Cutting
Length for Diamond Stirrups:
From the Diagram,
Clear Cover – 25mm
Column Size =
Diameter of helical Stirrups – 8mm
Deducting the concrete cover 25mm from all sides
x = 400-20-20 = 360mm
y = 400-20-20 =360mm
From Pythagorean theorem Hypotenuse2=(Opposite)2 +
(Adjacent)2
H2=(x/2)2 +( y/2)2
H2=1802 + 1802 => =
√(254)2 = 254mm
The total length of stirrup = 4 x H =4 x 254 = 1016mm
Total Length of the hook:
There are two hooks which means 9d+9d= 18d
Total length of Bends:
There are 3 bends which are bent at an angle of 900 + 2 bends which are bent at an angle of 1350
Total bend length = 3 x 900 Bend length + 2 x 1350 Bend length= 3 x 2d + 2 x 3d = 12d = 12 x 8 = 96mm
Total Cutting length of
Diamond Stirrup = Perimeter of Diamond shape + Total Hook length – Total
Bend Length
= 1016+144-96 = 1064mm = 1.064mm
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