How We Calculate the Cutting Length of Stirrups in Civil Engineering

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What Is the Stirrup Meaning?

A Stirrup is essentially a closed loop of steel reinforcement bar (rebar) that is bent into various shapes, most commonly rectangular or square, but also circular, triangular, or even more complex multi-legged forms. It encircles the main longitudinal (straight) reinforcement bars within the concrete element.

While often referred to as "ties" in columns, their function remains largely similar across both elements:

  • Shear Resistance: This is their primary function. Concrete is strong in compression but weak in tension. Beams and columns are subjected to shear forces, which can cause diagonal tension cracks. Stirrups, positioned perpendicular to these potential cracks, effectively resist these forces, preventing shear failure.
  • Confinement of Concrete: In columns, stirrups (or ties) confine the concrete core, significantly increasing its compressive strength and ductility. This is particularly crucial during seismic events, preventing premature concrete crushing and buckling of longitudinal bars.
  • Holding Longitudinal Bars in Position: During concreting, stirrups ensure that the main longitudinal reinforcement bars remain accurately spaced and aligned according to the structural design. This prevents them from shifting, ensuring the effective transfer of forces.
  • Preventing Buckling of Main Bars: For compression members like columns, stirrups provide lateral support to the main longitudinal bars, preventing them from buckling outwards under compressive loads.

Without accurately cut and placed stirrups, the shear capacity of beams and columns would be severely compromised, leading to potential structural failure and safety hazards.

Why we need to calculate the Cutting Length?

The goal is to cut a straight piece of steel bar that, when bent into the desired stirrup shape, will perfectly fit within the concrete element while providing adequate anchorage.

The General Formula to Calculate the Cutting Length

A Stirrup is essentially a closed loop of steel reinforcement bar (rebar) that is bent into various shapes, most commonly rectangular or square, but also circular, triangular, or even more complex multi-legged forms. It encircles the main longitudinal (straight) reinforcement bars within the concrete element. While often referred to as "ties" in columns, their function remains largely similar across both elements:
Stirrups

Main Formula: 

Cutting Length= Perimeter of Stirrup Shape + Total Hook Length - Total Bend Length

Standard Used For Hooks Length and Bends Length

  1. Standard Hook Length (Lh): While specific values can vary slightly by code (e.g., IS 456, ACI 318, Eurocode 2), a commonly accepted value is 9d or 10d (9 or 10 times the stirrup bar diameter), or a minimum of 75mm, whichever is greater.
  2. Standard Bend Length: 
  • 45° bend length=1d (It means 1times of stirrups bar diameter)
  • 90° bend length=2d (It means 2times of stirrups bar diameter)
  • 135° bend length=3d (It means 3times of stirrups bar diameter)
  • 180° bend length=4d (It means 4times of stirrups bar diameter).

In this post, we will calculate the cutting length in 3 Shape of Columns (or Beams):

  • Rectangular Shape
  • Square Shape
  • Circular Shape

Cutting Length of Stirrups in Rectangular Shape

Given:

  • Size of Rectangular Shape=200mmx300mm
  • Diameter of Stirrup, D=8mm
  • Concrete Cover, C=25mm

A Stirrup is essentially a closed loop of steel reinforcement bar (rebar) that is bent into various shapes, most commonly rectangular or square, but also circular, triangular, or even more complex multi-legged forms. It encircles the main longitudinal (straight) reinforcement bars within the concrete element. While often referred to as "ties" in columns, their function remains largely similar across both elements:
Rectangular Shape

  • X=200-(2 x Cover)-Diameter of Stirrup=200mm-(2*25mm)-8mm=158mm
  • Y=300-(2 x Cover)-Diameter of Stirrup=300mm-(2x25mm)-8mm=258mm

  • Hook Length=10D=10x8mm=80mm

  • Total Hook Length (There are 2 Hooks Length which mean):

  • So, Total Hook Length= 2 x (Hook Length)=2 x 80mm=160mm

  • Total Bend Length=3 x (bends length @90°) +2 x (bends length @135°)

                                          =3 x (2D) + 2 x (3D) =6 x 8mm + 6 x 8mm= 96mm

The Cutting Length of Rectangular Stirrup= 2X + 2Y + Total Hook Length - Total Bends  Length

= 2 x 158mm + 2 x 258mm + 160mm - 96mm

= 896mm

Therefore, The Cutting Length of Rectangular Stirrup = 896mm=0.896m

Cutting Length of Stirrups in Square Shape

Given:

  • Size of Square Shape=200mm x 200mm

  • Diameter of Stirrup, D=8mm

  • Concrete Cover, C=25mm

A Stirrup is essentially a closed loop of steel reinforcement bar (rebar) that is bent into various shapes, most commonly rectangular or square, but also circular, triangular, or even more complex multi-legged forms. It encircles the main longitudinal (straight) reinforcement bars within the concrete element. While often referred to as "ties" in columns, their function remains largely similar across both elements:

Square Shape

  • X=200-(2 x Cover)-Diameter of Stirrup

             =200mm-(2 x 25mm)-8mm=158mm
  • Y=300-(2 x Cover)-Diameter of Stirrup
             =200mm-(2 x 25mm)-8mm=158mm
  • Hook Length=10D=10 x 8mm=80mm

  • Total Hook Length (There are 2 Hooks Length):
  • So, Total Hook Length= 2 x (Hook Length)=2 x 80mm=160mm
  • Total Bend Legnth = 3 x (bends length @90°) +2 x (bends length @135°)

                                           = 3 x (2D) + 2 x (3D) =6 x 8mm + 6 x 8mm= 96mm

The Cutting Length of Square Stirrup= 2X + 2Y + Total Hook Length - Total Bends  Length

= 2 x 158mm + 2 x 158mm + 160mm - 96mm

= 696mm=0.696m

Therefore, The Cutting Length of Square Stirrup is 0.696m

Cutting Length of Stirrups in Circular Shape

Given:

  • Diameter of Circular Column , D=2000mm
  • Concrete Cover, C=25mm
  • Diameter of Stirrup used, d=8mm

A Stirrup is essentially a closed loop of steel reinforcement bar (rebar) that is bent into various shapes, most commonly rectangular or square, but also circular, triangular, or even more complex multi-legged forms. It encircles the main longitudinal (straight) reinforcement bars within the concrete element. While often referred to as "ties" in columns, their function remains largely similar across both elements:
Circular Shape

  • Circumference Length of Column= Ï€ x (D-2cover-2diameter of stirrup)

                                                                    =Ï€ x (2000mm-2 x 25mm - 2 x 8mm)=6075.84mm

  • Hook Length=10D=10x8mm=80mm

  • Total Hook Length (There are 2 Hooks Length):

  • So, Total Hook Length= 2 x (Hook Length)=2 x 80mm=160mm

  • Total Bend Legnth=2 x (bends length @135°)

                                =2 x (3D) = 6 x 8mm= 48mm

The Cutting Length of Circular Stirrup= Circumference Length of Column + Total Hook Length - Total Bends  Length

= 6075.84mm+ 160mm - 48mm

= 5867.84mm = 5.868m

Therefore, The cutting length of circular stirrup =  5.868m



Click Here to Understanding the Types of Concrete Cracking in Construction




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