Cutting Length of Stirrups – Theory and Formula

What are Stirrups?
Stirrups are closed-loop reinforcements used in beams and columns to hold the main reinforcement bars together and provide lateral support. They prevent buckling of the main bars and resist shear forces.

📐 Cutting Length of Stirrups

The cutting length of a stirrup is the total length of the bar required to form the stirrup, including bends and hooks.

1. Basic Formula for Cutting Length of Stirrups

Cutting Length = Perimeter of the Stirrup + Hook Length – Bend Deductions

📊 2. Components Explained:

1. Perimeter of the Stirrup:

   • For rectangular stirrups: Perimeter=2(Length+Width)\text{Perimeter} = 2 (Length + Width)

2. Hook Length:

   • Hooks are provided at both ends to anchor the stirrup properly.
   • Standard hook length: 9d to 10d, where d is the bar diameter.
   • For both hooks: Hook Length=2×10d\text{Hook Length} = 2 \times 10d

3. Bend Deductions:

   • Bends consume some length of the bar, which must be deducted.
   • Standard bend angles and their length deductions:
     • 45° bend: 0.42d
     • 90° bend: 0.57d
     • 135° bend: 0.90d

4. Clear Cover:

   • Reduce the cover from the length and width of the stirrup to get the internal dimensions.

   Lengthin=Length−2×Cover\text{Length}_{in} = \text{Length} – 2 \times \text{Cover} Widthin=Width−2×Cover\text{Width}_{in} = \text{Width} – 2 \times \text{Cover}

🧮 3. General Formula for Rectangular Stirrups:

Cutting Length=2(L+W)+2×10d−(4×0.57d)\text{Cutting Length} = 2 (L + W) + 2 \times 10d – (4 \times 0.57d)

🧩 4. Example Calculation:

• Stirrup Size: 300 mm × 500 mm
• Bar Diameter (d): 8 mm
• Cover: 25 mm

Step 1: Find internal dimensions:

Lin=300−2(25)=250 mmL_{in} = 300 – 2(25) = 250 \, mm Win=500−2(25)=450 mmW_{in} = 500 – 2(25) = 450 \, mm

Step 2: Perimeter:

P=2(250+450)=1400 mmP = 2 (250 + 450) = 1400 \, mm

Step 3: Hooks (10d on each end):

Hook Length=2×10×8=160 mm\text{Hook Length} = 2 \times 10 \times 8 = 160 \, mm

Step 4: Bend Deductions (Assuming 4 bends of 90°):

Bend Deduction=4×0.57×8=18.24 mm\text{Bend Deduction} = 4 \times 0.57 \times 8 = 18.24 \, mm

Step 5: Cutting Length:

Cutting Length=P+Hook Length−Bend Deduction\text{Cutting Length} = P + \text{Hook Length} – \text{Bend Deduction} =1400+160−18.24= 1400 + 160 – 18.24 =1541.76 mm (or 1.542 m)= 1541.76 \, mm \, (\text{or} \, 1.542 \, m)

📝 5. Important Notes:

• Add extra length for bends if using a standard bend formula for stirrups with more than 4 corners.
• Always refer to local standards such as IS 2502 (Indian Standard), ACI, or BS codes.
• Cutting length should be slightly increased if hooks are longer than 10d as per the design.