How To Calculate The Cutting Length Of Stirrups In Columns
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:
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 beams also.
Let’s calculate the cutting length for a…
Rectangular Stirrup
The following is an example of a rectangular stirrup in a 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 arm's 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.
Originally published at https://www.acivilengineer.com on August 11, 2019.
