**Cutting Length of Stirrups in Column or Beam | Cutting Length Formula for Reinforcement | Stirrups Length Calculation**

In this Article today we will talk about the **Cutting Length of Stirrups in Column or Beam | Cutting Length Formula for Reinforcement | Stirrups Length Calculation | Hook Length Formula for Stirrups | Number of Stirrups in Column**** |** **BBS of Stirrups**

**What is Stirrup:**

A stirrup is basically a shear **reinforcement** wrapped around the longitudinal bars in columns and beams. **Cutting Length Formula for Reinforcement**

**Purpose of Stirrups in Reinforcement:**

In order to achieve the required stress resistance, we have to place required number of bars in respective positions. We have already discussed the load acting on a column in types of column failure where we have explained about the load actions such as compressive and buckling stress. Each load acting on a column will raise some sort of displacement, cracks, and tension in the reinforcement. So the main purpose of stirrups are

- 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

**Method for Calculating Cutting Length of Stirrup:**

- Look at the size of column or beam from drawings
- Adopt Dia of the bar (generally 8mm Dia is used for stirrups)
- Deduct the concrete cover or clear cover
- Find the total outer length of stirrup after deducting concrete cover.
- Add the length of the hook to the length of the stirrup
- Deduct the length of bends.
**Stirrups Length Calculation** - Use below formula to find the total cutting length of stirrups

Formula:Cutting Length of Stirrups = Perimeter of Shape + Total hook length – Total Bend Length

**Important Basic Stirrups Length Calculation 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)
**Number of Stirrups in Column**

**Typical Diagram of Stirrup:**

Refer the below image of the typical diagram of stirrup for clear understanding about x & y length, bends, hooks and concrete cover.

In the above image, there are 5 bends at 4 corners, 2 hooks and concrete cover around the stirrup.

x = length of the stirrup in the x-direction after deducting concrete cover &

y = length of the stirrup in the y-direction after deducting concrete cover.

**Important standards used in Bends & Hooks:**

The below standards are most important in calculating the hook length and bend lengths at corners while finding cutting length of stirrups.

- 1 Hook length = 9d or 75mm
- 45° Bend length = 1d
- 90° Bend length = 2d
- 135° Bend length = 3d

Remember, **d = Diameter of Bar**

**Cutting length for Rectangular Stirrups:**

Rectangular column or rectangular beam is the most commonly used shape of the column in any construction. In this shape of beam or column, a rectangular stirrup is usually adopted. **Number of Stirrups in Column**

- Considering the below Rectangular column size 230mm x 450mm for calculation purpose
- Adopting Dia of Bar used for stirrups is 8mm
- Deducting the concrete cover 20mm from all sides x = 230 – 20-20 = 190mm y = 450-20-20 = 410mm
**Total Length of the hooks:**From fig, There are two hooks which means 9d+9d = 18d**Total Length of Bends:**From above fig, There are 3 bends which are bent at an angle of 90^{0}and two bends are bent at an angle of 135^{0}

Total bend length = 3 x 90^{0} Bend length + 2 x 135^{0} Bend length = 3 x 2d + 2 x 3d = 12d = 12 x 8 = 96mm

**Total Cutting length of Rectangular Stirrup** = Perimeter of Rectangle + Total Hook length – Total Bend Length

*= 2 (x+y) +18d – 12d = 2(190 + 410) + 18 x 8 – 12 x 8 = 1248mm = 1.248m*

**Cutting length for Square Stirrups:**

- Considered the column size as 450mm x 450mm
- Adopting Dia of Bar used for stirrups is 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 90^{0}and one is bent at an angle of 135^{0}. Total bend length = 3 x 90^{0}Bend length + 2 x 135^{0}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 for Circular Stirrup:**

- Considered the column dia as D = 1000mm
- Adopting Dia of Bar used for stirrups is d =8mm
- Deducting the concrete cover from diameter of column D = 1000-25-25 = 950mm
- Circumference length of Ring = πD = 950 x 3.14 = 2983mm
**Total Length of the hook:**There are two hooks which means 9d+9d= 18d**Total Length of Bends:**There are 2 bends which are bent at an angle of 135^{0}Total bend length = 2 x 135^{0}Bend length = 2 x 3d = 6d= 6 x 8 = 48mm

**Total Cutting length of Circular Stirrup or Ring** = Circumference of Circle + Total Hook length – Total Bend Length

*= 2983 +18d – 6d =3079mm = 3.07m*

**Cutting Length for Triangular Stirrups:**

- Considered the Column size 400mm x 450mm
- Adopting Dia of Bar used for stirrups is d = 8mm
- Deducting the concrete cover 25mm from all sides x = 400-20-20 = 360mm y = 450-20-20 = 410mm From Pythagorean theorem,
**Hypotenuse**look at 2nd triangle in above image H^{2}=(Opposite)^{2}+ (Adjacent)^{2}^{2}=(x/2)^{2}+ y^{2}H^{2}=180^{2}+ 410^{2}=> = √(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 135^{0}Total bend length =4 x 135^{0}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 for Diamond Stirrups:**

- Considered the Column size 400mm x 400mm
- Adopting Dia of Bar used for stirrups is d = 8mm.
**Hook Length Formula for Stirrups** - Deducting the concrete cover 25mm from all sides x = 400-20-20 = 360mm y = 400-20-20 =360mm From Pythagorean theorem,
**Hypotenuse**H^{2}=(Opposite)^{2}+ (Adjacent)^{2}^{2}=(x/2)^{2}+( y/2)^{2}H^{2}=180^{2}+ 180^{2}=> = √(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^{0 }+ 2 bends which are bent at an angle of 135^{0}Total bend length = 3 x 90^{0}Bend length + 2 x 135^{0}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*

**Cutting Length for Helical Stirrups:**

A spiral stirrup is similar to circular stirrup except for hook:

**I hope now you have enough knowledge on how to calculate the cutting length of stirrups for different shapes. Number of Stirrups in Column**

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**Conclusion:**

Full article on **Cutting Length of Stirrups in Column or Beam | Cutting Length Formula for Reinforcement | Stirrups Length Calculation | Hook Length Formula for Stirrups | Number of Stirrups in Column**** |** **BBS of Stirrups****.** Thank you for the full reading of this article in “**The Civil Engineering**” platform in English. If you find this post helpful, then help others by sharing it on social media. **If any formula of BBS is missing from this article please tell me in comments.**

It’s good

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Quite educative ,well done

But why the provision for hook length not for all the vertical rebar ?

please explain your question i did not understand properly

Excellent GURU.

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