Updated August 14th, 2019

When it comes to the length of a stirrup bar, you’ll find two types of length.

One is the ACTUAL LENGTH of a stirrup bar and another is the CUTTING LENGTH.

Cutting length is always smaller than the actual length.

When you go to make stirrups, you’ll need to cut bars based on the cutting length. Otherwise, you won’t get the required size of stirrups.

In this post, I’ll show you how to calculate the cutting length of stirrups.

Before that let’s learn a little about stirrups.

## What Is A Stirrup?

A stirrup is basically a shear reinforcement wrapped around the longitudinal bars in columns and beams.

Different shapes of stirrups are used in civil construction.

A stirrup has different parts.

See the image below to get familiar with that.

As you’re now familiar with the stirrup, let’s calculate…

## The Actual Length Of A Stirrup

For example, we have a rectangular column.

And the cross-sectional dimension of the column is as the image below:

From the image:

The long side of the column = 550 mm

The short side of the column = 450 mm

Clear cover = 40 mm

So **the long side of the stirrup** is,

= Long side of the column – (2 × clear covers)

= 550 – (2 × 40)

= **470 mm**

The **short side of the stirrup** is,

= short side of the column – (2 × clear cover)

= 450 – (2 × 40)

= **370 mm**

The hook length of the stirrup is (as per code),

= 6d ≧ 75mm

[ d = diameter of the stirrup’s bar]

= 6 × 10 mm

=60 mm

But, the **hook length shouldn’t be less than 75mm**.

So, the hook length of our example stirrup is 75mm.

**The actual length of the stirrup** is,

= (2 × long sides of the stirrup) + (2 × short sides of the stirrup) + (2 × hook length)

= (2 × 470) + (2 × 370) + (2 × 75)

= **1830 mm**

But if you cut this length of a bar for making the stirrup, it’ll be bigger than the required size.

If you want to get the stirrup’s size as you require, you need to calculate the cutting length of a stirrup.

But…

## What Is The Cutting Length Of A Stirrup?

For making a stirrup, we need to bend a steel bar.

When we bend a steel bar it increases in length due to elongation.

So, if you cut a bar as the length of the actual stirrup, you won’t get the desired size of the stirrup.

Because you bend the bar several times to get the stirrup’s shape.

To get the cutting length of a stirrup’s bar, you need to deduct the increased length for bending.

So **the cutting length of a stirrup **will be,

= Actual length of stirrups – increased length due to bending

But **how much should be deducted for a bend?**

As per code, the bend deduction for a:

- 45° bend = 1d

- 90° bend = 2d

- 135° bend = 3d, and

- 180° bend = 4d

Where, d = Diameter of the bar.

So if the stirrup’s bar size is 10mm, the bend deduction will be for-

45° bend = 1d = 1 × 10 = 10 mm

90° bend = 2d = 2 × 10 = 20 mm

135° bend = 3d = 3 × 10 = 30 mm

180° bend = 4d = 4 × 10 = 40 mm

To help you remember this thing, just deduct the 1d length for every 45° bend.

I think you’ve got the point.

Then let’s see…

## How To Calculate The Cutting Length Of Stirrups In Columns

As I discussed above, different shapes of stirrup are used in columns.

I’ll show you how to calculate the cutting length of different shaped stirrups.

Applying this method, you can calculate the cutting length of stirrups in beam also.

Let’s calculate the cutting length for a…

### Rectangular Stirrup

The following is an example of a rectangular stirrup in column:

The formula for calculating the cutting length of a rectangular stirrup is,

=** (2 × long side of stirrup) + (2 × short side of stirrup) + (2 × hook length) – (3 × 90° bend) – (2 × 135° bend)**

In our example stirrup,

The long side = 470 mm

The short side = 370 mm

The hook length = 75 mm

90° bend = 2d = 2 × 10 mm = 20 mm

135° bend = 3d = 3 × 10mm = 30 mm

Now put this value in the formula,

= (2 × 470) + (2 × 370) + (2 × 75) – (3 × 20) – (2 × 30)

=** 1710 mm**

This is the cutting length of our example rectangular stirrup.

### The Cutting Length A Square Stirrup

The formula for calculating the cutting length of a square stirrup is the same as the rectangular stirrup.

The only difference is, the rectangular stirrup has both long side and short side. But the square stirrup has only one type of side.

However, the formula is,

= **(4 × one arm length of the stirrup) + (2 × hook length) – (3 × 90° bend) – (2 × 135° bend)**

= (4 × 370) + (2 × 75) – (3 × 20) – (2 × 30)

= **1510 mm**

### How To Calculate The Cutting Length Of Circular Stirrups

This is our column:

The formula for calculating the cutting length of the circular stirrup is,

= **Circumference of the stirrup + (2 × hook length) – (2 × 135° bend)**

The circumference of the stirrup is,

= **π × Diameter of the stirrup**

The diameter of the stirrup is,

= **Diameter of the column – (2 × clear cover)**

= 600 mm – (2 × 40mm)

= **520 mm**.

So the circumference of the stirrup is,

= π × 520 mm (π = 3.14)

= **1632.80 mm**.

And the cutting length of the circular stirrup is,

= Circumference of the stirrup + (2 × hook length) – (2 × 135° bend)

= 1632.80 + (2 × 75) – (2 × 30)

= **1722.80 mm**.

### Calculating The Cutting Length Of Spiral Stirrups

The formula for calculating the cutting length of spiral stirrups is,

Number of turns is,

= **length of the column ÷ spacing of stirrups**

= 10000 ÷ 200

= **50 numbers**.

Circumference of the stirrup is,

=** π × Dia of the stirrup**

Dia of the stirrup is,

= **Dia of the column – (2×clear cover)**

= 600 – (2×50)

= **500 mm**

So, the circumference of the stirrup is,

= π × 500

= **1570 mm**

Let’s put these values into the formula.

The cutting length of spiral stirrups is,

= 50 × √{(1570)2 + (200)2}

= **1582.68 mm**.

### The Cutting Length Of A Triangle Stirrup

We have two stirrups in our example column above.

We’ll learn to calculate the cutting length of the triangular one.

That’ll look like:

Formula:

The cutting length of a triangular stirrup is,

= (all arms length of the stirrup) + (2 × hook length) – (4 × 135° bend)

Calculating the arm length of the triangle is a little bit tricky.

You need to apply a geometrical formula.

Don’t worry. I’ll make the thing as simple as possible.

See the image below:

The length of the “**A**” marked arm of the triangle is,

= length of a side of the column – (2 × clear covers)

= 300 – (2 × 40)

= **220 mm**

To get the length of “B” or “C” arm, you need to apply Pythagoras formula.

See the image below:

B = √(a2 + d2)

a = A ÷2

= 220 ÷ 2

=**110 mm**

d = Length of a side of the column – (2×clear cover)

= 300 – (2×40)

= **220 mm**

So, B = √{(110)2 + (220)2}

= **245.96 mm**

In our example stirrup, B = C.

That means the length of the “B” arm is equal to the length of “C” arm of the stirrup.

So far, we’ve got all three arms’ length of the stirrup.

The hook length is,

= (6 × the diameter of the stirrup bar) ≧ 75 mm

= (6×10) ≧ 75 mm

= 60 mm ≧ 75 mm

So, the hook length is **75mm**.

There are 4 numbers of 135° bend.

We have now all the values to calculate the cutting length of the triangle stirrup.

Let’s put these values into the formula.

The formula is,

= (all arms length of the triangular stirrup) + (2 × hook length) – (4 × 135° bend)

= (220 + 245.96 + 245.96) + (2 × 75) – (4 × 30)

= **741.92 mm**.

This is the cutting length of the triangular stirrup.

### How To Calculate The Cutting Length Of Diamond Stirrups

The cutting length of a diamond stirrup is,

= **(4 × arm length) + (2 × hook length) – bend deduction**

Getting the arm length of a diamond stirrup is a little bit tricky.

We need to apply the Pythagoras theorem.

**A**, **B**, **C**, **D**, – these are the arms of the stirrup and they are equal in our example diagram.

Let’s get the length of the arm “**A**“.

To calculate the length of the “**A**” arm, we need to know the length of “**x**” and “**y**“.

**x** = {long side of the column – (2 × clear cover)} ÷ 2

= {600 – (2 × 40)} ÷ 2

= **260 mm**

y = {short side of the column – (2 × clear cover)} ÷ 2

= {300 – (2 × 40)} ÷ 2

= **110 mm**

Now A = √(x2 + y2)

= √{(260)2 + (110)2}

= **282.31 mm**.

Now let’s calculate the bend deduction.

In our example diamond stirrup, we have **four **numbers of **135°** bend and **one 45°** bend.

So the bend deduction will be,

= (4 × 135° bend) + (1 × 45° bend)

= (4 × 3d) + (1 × 1d)

= (4 × 3 × 10) + (1 × 1 × 10)

= **130 mm.**

Now we have everything to calculate the cutting length of our example diamond stirrup.

And the formula is,

= (4 × arm length) + (2 × hook length) – bend deduction.

= (4 × 282.31) + (2 × 75) – 130

= **1149.24 mm**

And this is the cutting length of our example diamond stirrup.

I think you can calculate the cutting length of all types of stirrups in columns.

Applying these formulas you’ll also be able to calculate the cutting length of stirrups in beam also.

But there is…

## A Disputing Thing Of Calculating The Cutting Length Of Stirrups

Someone may suggest calculating the cutting length of a stirrup based on its centerline.

Let’s take our rectangular stirrup for this example.

The diagram of the rectangular stirrup we discussed above:

And the formula for calculating the cutting length of a rectangular stirrup is,

= (2 × long side of stirrup) + (2 × short side of stirrup) + (2 × hook length) – (3 × 90° bend) – (2 × 135° bend)

**Considering centreline of the stirrup bar:**

The **long side of the stirrup** is,

= long side of the column – (2 × clear covers) – (2 × half dia of stirrup’s bar)

= 550 – (2 × 40) – (2 × 5)

= **460 mm**

And, the **short side of the stirrup** is,

= short side of the column – (2 × clear cover) – (2 × half dia of stirrup’s bar)

= 450 – (2 × 40) – (2 × 5)

= **360 mm**

Now put these values into the formula,

= (2 × 460) + (2 × 360) + (2 × 75) – (3 × 20) – (2 × 30)

= **1670 mm**.

You’ve noticed that I deducted the dia of a bar when calculating the arm length of the stirrup in this calculation.

**Which one is the correct method – this one or the above discussed one? Do we need to consider the dia of the stirrup bar? **

**Have you experimented these in your construction project?**

*If you haven’t, experiment these in your project and let me know which one is the correct method in the comments below…*

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