How to calculate Cutting length of Stirrups in Beam and column ?

How to calculate Cutting length of Stirrups in Beam and column ?

To cater the stresses and loads in RCC, Bars are bent to different shapes in the bar bending schedule.

Different shapes of bars have different cutting length. In this post, we are going to explain you about “How to calculate or find the cutting length of Stirrups for different shapes”.

Remember,

The transverse reinforcement provided in Column is called Ties and the transverse reinforcement provided in Beam is called Stirrups. But on-site, we usually call both transverse reinforcements as Stirrups.

The prime reason for providing the stirrups in the beam is for shear requirements and to keep the longitudinal bars in position. If you wanted to know more about the why stirrups & ties provided in the beam and column you can refer here

Deducting the concrete cover is most important in Bar bending, if you dont know how to deduct the concrete cover then refer this - 

Concrete Cover deductions in Beams, Columns, Slab, Footings

Steps involved in finding the cutting length of stirrups:-

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

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 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)

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.

Considering the below Rectangular column size 230mm x 450mm for calculation purpose

rectangular column details

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

cutting length of rectangular stirrup

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 900 and two bends are bent at an angle of 1350

Total bend length = 3 x 900 Bend length + 2 x 1350 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

square stirrup details

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)

Square stirrup deductions

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 900 and one is bent at an angle of 1350.

Total bend length = 3 x 900 Bend length + 2 x 1350 Bend length = 3 x 2d + 2 x 3d = 12d = 12 x 8 = 96mm

square stirrup details

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

Circular Stirrups details

Deducting the concrete cover from diameter of column

D = 1000-25-25 = 950mm

circular stirrup with hooks and bends

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 1350

Total bend length = 2 x 1350 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

traingular stirrup details

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,

Hypotenuse2=(Opposite)2 + (Adjacent)2 

finding hypotnuse in triangular stirrup

look at 2nd triangle in above image

H2=(x/2)2 + y2

H2=1802 + 4102 => = √(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

Triangular stirrup Hooks and Bend Lengths

Total length of Bends:

There are 4 bends which are bent at an angle of 1350

Total bend length =4 x 1350 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

diamond stirrup details

Adopting Dia of Bar used for stirrups is d = 8mm

Deducting the concrete cover 25mm from all sides

x = 400-20-20 = 360mm

y = 400-20-20 =360mm

diamond stirrups hook length and bend length

From Pythagorean theorem,

Hypotenuse2=(Opposite)2 + (Adjacent)2 

H2=(x/2)2 +( y/2)2

H2=1802 + 1802 => = √(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 900 + 2 bends which are bent at an angle of 1350

Total bend length = 3 x 900 Bend length + 2 x 1350 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