# How to Calculate Cutting Length of Stirrups in Column? – Different Shapes

According to the need for stress and load actions,  we need different types and shapes of columns consisting n number of bars.

In this post, we are going to see “How to calculate cutting length of Stirrups in Column?” for different shapes

## 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

# Cutting Length of Stirrups

Before going to the actual calculations. please be familiar with the below assumptions

Assumptions

• Hook Length = 10d or 75 mm
• 45° Bend = 1d
• 90° Bend = 2d
• 135° Bend = 3d

## Cutting Length of Rectangular Stirrups

From the Diagram,

Clear Cover – 25 mm

Column Size = 200mm X 600mm

Stirrups – 8mm

Formula,

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 of Square Stirrups

From the Diagram,

Clear Cover – 25 mm

Column Size = 300mm X 300mm

Stirrups – 8mm

Formula,

Cutting Length of Rectangular Stirrup = 4a + 2 numbers of hooks – 3 numbers of 90° bends – 2 numbers of 135° bends

a = 300 – 2 x Clear Cover = 300 – (2 x 25) = 250

Cutting Length of Rectangular Stirrup = 4a + 2 numbers of hooks – 3 numbers of 90° bends – 2 numbers of 135° bends

= 2 x 250 + (2 x10d) – (3 x 2d) – (2 x 3d) = 500 + (2 x 10 x 8) – (3 x 2×8) – (2 x 3 x 8)

Cutting Length of Rectangular Stirrup = 564 mm or 0.56 m

## 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 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 of Triangle Stirrups

From the Diagram,

Clear Cover – 25mm

Diameter of Stirrups – 8mm

Column Size – 300mm x 400mm

Cutting Length of Stirrup = (2 x H) + a + 2 numbers of hooks –  4 numbers of 135° bends

Cutting Length of Stirrup = (2 x H) + a + (2 x 10d) – (4 x 3d)

Where a = 300 – 2 x Clear Cover = 300 – (2 x 25) = 250

b = 400 – 2 x Clear Cover= 400 – (2×25) = 350

H = √((b2) + (a/2)2) = √(3502)+(250/2)2) = 371.65 mm or 372 mm

Note: Since it is a rectangular column we are taking H = √((b2) + (a/2)2) if it is a square column then the shape of the triangle becomes a symmetrical triangle and the formula will totally differ which we will discuss on upcoming post.

Back to our Formula,

Cutting Length of Stirrup = (2 x H)+a+(2 x 10d)-(4 x 3d) = (2 x 372)+ 250 +(2 x 10 x 8) – (4 x 3 x 8)

Cutting Length of Stirrup = 1058 mm or 1.06 m

## Cutting Length of Diamond Stirrups

From the Diagram,

Clear Cover – 25mm

Column Size = 400mm X 300mm

Stirrups – 8mm

Cutting Length of Stirrup = (4 x H) + (2 x number of hook length) – (3 x number of 90° bends) – (2 x number of 135° bends)

Where H = √((b/2)2 + (a/2)2)

a = 400 – 2 x Clear Cover = 400 – (2 x 25) = 350

b = 300 – 2 x Clear Cover= 300 – (2×25) = 250

Therefore, H = √((b/2)2 + (a/2)2) = √((250/2)2 + (350/2)2) = √(1252 + 1752) = 215 mm

Cutting Length of Stirrup = (4 x H)+(2x10d)-(3x2d)-(2 x 3d) = (4×215)+(2x10x8)-(3x2x8)-(2x3x8) = 924mm

Cutting Length of Stirrup = 924mm

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