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 "What Is Cover in Concrete?"

 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 = 2Ï€r = Ï€d (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 = 400mm x 450mm

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  = 400mm x 400mm

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 90 + 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