In this article, we find out how to calculate the cutting length of stirrups. Before that, we learned some basic information about stirrups and the types of stirrups.
What is Stirrups
Stirrups, also known as shear links, hoop iron, or ties, are critical in reinforcing concrete structures. They play a key role in preventing shear failure, a common structural issue. Stirrups are designed to withstand lateral forces and are particularly important in earthquake-prone regions.
Stirrups are essential in reinforcing structures, such as beams and columns. Cutting the length of stirrups is a critical skill for builders and contractors. In this comprehensive guide, we’ll explore the importance of stirrups, the different types, and the methods to cut their length effectively.
The above image has 5 bends at 4 corners, 2 hooks and a 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.
The procedure of calculating the cutting length of stirrups
- Observe the column and beam in the structural diagram
- Find the diameter of the stirrups, Minimum of 8mm dia is used
- Deduct the concrete cover in the drawing
- Find the total outer length of stirrups after deducting the concrete cover
- Add the length of the hooks to the length of the stirrups
- Deduct the length of the bends
- Use the formula to find out the cutting length of stirrups
Main Formula ;
Cutting Length of Stirrups = Perimeter of Shape + Total hook length – Total Bend Length
The perimeter of the Square = 4 x side length
Perimeter of Rectangle = 2 ( length + breadth)
Perimeter of circle or Circumference of Circle = 2πr = πd (r= radius, d= Diameter of Circle)
Standards used in bends and hooks
- 1 Hook length = 9d or 75mm
- 45° Bend length = 1d
- 90° Bend length = 2d
- 135° Bend length = 3d
Where D is the Diameter of the steel. Concrete cover is most important for all structures,
Types of stirrups
- Square Stirrups
- Rectangular Stirrups
- Triangular Stirrups
- Circular Stirrups
- Diamond Stirrups
- Spiral or Helical Stirrups
Calculating the Cutting length of stirrups
Here we calculate the cutting length of stirrups in all types.
Cutting length of Square Stirrups
- column size is 500 mm x 500 mm
- Dia of the steel used for stirrups is 8mm
- Concrete cover 25mm
Deducting the concrete cover 25mm from all sides (in square all sides are equal)
x = 500 – 25 -25 = 450 mm
y = 500 -25 – 25 = 450 mm, Hence x = y (in square all sides are equal)
The total length of the hook. There are two hooks which means 9d+9d = 18d
Total length of the bend. There are 3 bends bent at an angle of 90 and one bent at an angle of 135.
Total bend length = 3 x 90 Bend length + 2 x 135 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
Cutting length of stirrups = 4 x 450 + 18d – 12d = 1848 mm = 1.84 m
Cutting length of Rectangular Stirrups
- The beam size is 250 mm x 500 mm
- Dia of the steel used for stirrups is 8mm
- Concrete cover 25mm
Deducting the concrete cover 25mm from all sides
x = 250 – 25 -25 = 200 mm
y = 500 -25 – 25 = 450 mm
The total length of the hook. There are two hooks which means 9d+9d = 18d
Total length of the bend. There are 3 bends bent at an angle of 90 and one bent at an angle of 135.
Total bend length = 3 x 90 Bend length + 2 x 135 Bend length = 3 x 2d + 2 x 3d = 12d = 12 x 8 = 96mm
Total cutting length of rectangular stirrups = Perimeter of Rectangle + Total Hook length – Total Bend Length
= 2 (x+y) +18d – 12d = 2 ( 200 + 450 ) + ( 18 x 8 ) – ( 12 x 8 )
= 1348 mm = 1.348 m
Cutting length of circular stirrups
- Column diameter is 1500mm
- Dia of the steel used for stirrups is 8mm
- Concrete cover 25mm
Deducting the concrete cover from the diameter of the column
D = 1500-25-25 = 1450mm
Circumference length of Ring = πD = 1450 x 3.14 = 4553 mm
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
Total bend length = 2 x 135 Bend length = 2 x 3d = 6d= 6 x 8 = 48mm
Total Cutting length of Circular Stirrup or Ring = Circumference of the ring + Total Hook length – Total Bend Length
= 4553 + 18d – 6d = 4664 mm =4.649 m
Cutting Length of triangular stirrups
- column size is 500 mm x 500 mm
- Dia of the steel used for stirrups is 8mm
- Concrete cover 25mm
Deducting the concrete cover 25mm from all sides
x = 500 – 25 -25 = 450 mm
y = 500 -25 – 25 = 450 mm
From Pythagorean theorem, Hypotenuse² = (Opposite)² + (Adjacent)²
Refer to the second triangle in the above image
H² = (x/2)² + y²
H²= 225² + 450². H = 503 mm
The total length of stirrup from now = 2 x H + X = 2 x 503 + 450 = 1456 mm
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 Total bend length = 4 x 135 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
= 1456 +18d – 12d = 1504 mm = 1.5 m
Cutting Length of diamond stirrups
- column size is 500 mm x 250 mm
- Dia of the steel used for stirrups is 8mm
- Concrete cover 25mm
Deducting the concrete cover 25mm from all sides
x = 500 – 25 -25 = 450 mm
y = 250 -25 – 25 = 200 mm
From Pythagorean theorem, Hypotenuse² = (Opposite)² + (Adjacent)²
H² = (x/2)² + (y/2)²
H²= 225² + 100². H = 246 mm
The total length of stirrup from now = 4 x H = 4 x 246 = 984 mm
Total Length of the hooks. There are two hooks which means 9d+9d= 18d
Total length of Bends. There are 5 bends which are bent at an angle of 135
Total bend length = 5 x 135 Bend length = 5 x 3d = 15d = 15 x 8 = 120 mm
Total Cutting length of Diamond Stirrup = Perimeter of Diamond shape + Total Hook length – Total Bend Length
= 984+144-120 = 1008 mm = 1.008 m
Cutting length of Spiral or helical Stirrups
- depth of pile = 14 m.
- Diameter of pile = 800mm = 0.8 m
- Clear cover = 50mm =0.05m
- Pitch = 150 mm. = 0.15m
- The diameter of the helical stirrup bar = 8mm.= 0.008m
The cutting length of the spiral stirrup is given by the formula = n√C² + P²
Here, n = number of turns of the helical stirrup ( no. of the pitch in total pile length )
C = circumference of the helical stirrup.
P = pitch of the helical stirrup.
Number of turns (n) = [( length of pile / pitch ) + no. of closure rings]
[ (14/0.15) +2 = 96 Nos
Circumference of the helical stirrup ( C ) = C = πD or 2πr
Here, r = [(diameter of pile ) – ( 2 nos. × clear cover ) – (2 × 1/2 × diameter of the spiral stirrup bar )] / 2
r = [ (800) – (2×50) – (2 x 0.5 x 8) ] / 2 = 346 mm
r = 0.346 m
Circumference of the helical stirrup = C = 2πr
= [2 × 3.142 × 0.346 m] = 2.174 m
The cutting length of the spiral stirrup is given by the formula = n√C² + P²
= 96 × √2.174² + 0.15²
= 209 m
to get the exact cutting length of the spiral stirrup bars, we have to add lap length, as the length of an individual bar is limited to 12m.
Let us provide a lap length of 50d, where d = diameter of the helical bar.
Number of lapping required = [Calculated length of the helical bar/length of a single bar]
= [ 209 / 12 ] = 17.42 says, 18 Nos
The total length of the helical stirrup bar required in a pile
= [ calculated cutting length of the bar + ( no. of lapping × lap length )]
= [ 209 m + ( 18 nos × 50d ) ]
= [ 209 m + ( 18 × 50 × 0.008m ) ]
= [209 m + 7.20 m]
= 216.2 says, 216 m
Hope you get a clear solution for calculating the cutting length of stirrups. If any further assistance message us on Instagram or WhatsApp. Have a happy day.
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