How to calculate the cutting length of 6 - legged stirrups?/ Calculating the cutting length of 6-legged lateral ties.

 Let us calculate the cutting length of 6-legged stirrups as shown below.

Given data :

Column width = 750mm.

Column depth = 600mm.

Corner bar 20T - 4nos.

Mid bar 16T - 8nos.

No. of stirrups - 3nos.

Dia. of all 3 stirrups = d = 8mm.

Clear cover = 40mm.

For your understanding, I have given different colors for all these 3 types of stirrups. 

1.   Stirrup -1:

Cutting length formula for stirrup-1

= [(2nos × a1) + (2nos. × b1) + (2nos. × hook length) - {(3nos. × 90° bend )+ (2nos. × 135° bend)}]

First, we will calculate the value of  a1 & b1

a1 = [(column width ) - {(2nos. × clear cover) + (2nos.× 1/2 dia. of stirrup-1 bar)}]

     = [ ( 750mm ) - { ( 2nos. × 40mm ) + ( 2nos. × 1/2 × 8mm )}]

     = [ 750mm - { 80mm + 8mm }]

     = [ 750mm - 88mm ]

     = 662mm.

b1 = [ x + ( 2nos.× 1/2 dia. of  mid bar.) + ( 2nos. × 1/2 dia of stirrup-1 bar )]

First, we will find out the value of x

x = [column depth -{(2nos.×cover )+( 2nos.× dia. of stirrup-3)+ (2nos.× 1/2 dia. of outer bar)}] ÷ 3

   = [ 600mm - {( 2nos. × 40mm ) + ( 2nos. × 8mm ) + ( 2nos.× 1/2 × 20mm )}] ÷ 3

   = [ 600mm - { 80mm + 16mm + 20mm }] ÷ 3

  = [ 600mm - 116mm ] ÷ 3

  = 484mm ÷ 3

 x = 161.33mm.

b1 = [ x + ( 2nos.× 1/2 dia. of  mid bar.) + ( 2nos. × 1/2 dia of stirrup-1 bar )]

    = [ 161.33mm + ( 2nos. × 1/2 × 16mm ) + ( 2nos. × 1/2 × 8mm )]

   = [ 161.33mm + 16mm + 8mm]

  = 185.33mm.

The cutting length for stirrup-1

= [(2nos × a1) + (2nos. × b1) + (2nos. × hook length) - {(3nos. × 90° bend )+ (2nos. × 135° bend)}]

= [ (2nos.× 662mm) + ( 2nos. × 185.33mm ) + (2nos. × 10d ) - {( 3nos.×  2d ) + ( 2nos. × 3d )}]

Note:

1. Here,10d is taken for hook length.

2. We have deducted 2d for 90° bend -3nos., & 3d for 135° bend -2nos. as similar to the above drawing in all the 3 types of stirrups.

  =[ 1324mm + 370.66mm + ( 2nos. × 10 × 8mm ) - {( 3nos.×  2× 8mm) + ( 2nos. × 3 × 8mm)}]

  = [1694.66mm + 160mm - { 48mm + 48mm }]

 = [1854.66mm - 96mm ]

= 1758.66mm.

2.    Stirrup-2:

Cutting length formula for stirrup-2

= [(2nos × b2) + (2nos. × a2) + (2nos. × hook length) - { (3nos. × 90° bend )+ (2nos. × 135° bend)}]

First, we will calculate the value of  b2 & a2

b2 = [(column depth ) - {(2nos. × clear cover) + (2nos.× 1/2 dia. of stirrup-2)}]

     = [ ( 600mm ) - { ( 2nos. × 40mm ) + ( 2nos. × 1/2 × 8mm )}]

     = [ 600mm - { 80mm + 8mm }]

     = [ 600mm - 88mm ]

     = 512mm.

a2 = [ y + ( 2nos.× 1/2 dia. of  mid bar.) + ( 2nos. × 1/2 dia of stirrup-2 )]

First, we will find out the value of y

y = [column width -{(2nos.×cover )+( 2nos.× dia. of stirrup-3)+ (2nos.× 1/2 dia. of outer bar)}] ÷ 3

   = [ 750mm - {( 2nos. × 40mm ) + ( 2nos. × 8mm ) + ( 2nos.× 1/2 × 20mm )}] ÷ 3

   = [ 750mm - { 80mm + 16mm + 20mm }] ÷ 3

  = [ 750mm - 116mm ] ÷ 3

  = 634mm ÷ 3

 y = 211.33mm.

a2 = [ y + ( 2nos.× 1/2 dia. of  mid bar.) + ( 2nos. × 1/2 dia of stirrup-2 )]

    = [ 211.33mm + ( 2nos. × 1/2 × 16mm ) + ( 2nos. × 1/2 × 8mm )]

   = [ 211.33mm + 16mm + 8mm]

  = 235.33mm.

The cutting length for stirrup-2

= [(2nos × a2) + (2nos. × b2) + (2nos. × hook length) - {(3nos. × 90° bend )+ (2nos. × 135° bend)}]

= [ (2nos.× 235.33mm) + ( 2nos. × 512mm ) + (2nos. × 10d ) - {( 3nos.×  2d ) + ( 2nos. × 3d )}]

=[ 470.66mm + 1024mm + ( 2nos. × 10 × 8mm ) - {( 3nos.×  2× 8mm) + ( 2nos. × 3 × 8mm)}]

= [1494.66mm + 160mm - { 48mm + 48mm }]

= [1654.66mm - 96mm ]

= 1558.66mm.

3.     Stirrup-3

Cutting length formula for stirrup-3

= [(2nos.× a3) + (2nos. × b3) + (2nos. × hook length) - {(3nos. × 90° bend )+ (2nos. × 135° bend)}]

First, we will calculate the value of  a3 & b3

a3 = [(column width ) - {(2nos. × clear cover) + (2nos.× 1/2 dia. of stirrup-3)}]

     = [ ( 750mm ) - { ( 2nos. × 40mm ) + ( 2nos. × 1/2 × 8mm )}]

     = [ 750mm - { 80mm + 8mm }]

     = [ 750mm - 88mm ]

     = 662mm.

b3 = [(column depth ) - {(2nos. × clear cover) + (2nos.× 1/2 dia. of stirrup-3)}]

     = [ ( 600mm ) - { ( 2nos. × 40mm ) + ( 2nos. × 1/2 × 8mm )}]

     = [ 600mm - { 80mm + 8mm }]

     = [ 600mm - 88mm ]

     = 512mm.

The Cutting length of stirrup-3

= [(2nos.× a3) + (2nos. × b3) + (2nos. × hook length) - {(3nos. × 90° bend )+ (2nos. × 135° bend)}]

= [ (2nos.× 662mm) + ( 2nos. × 512mm ) + (2nos. × 10d ) - {( 3nos.× 2d ) + ( 2nos. × 3d )}]

=[ 1324mm + 1024mm + ( 2nos. × 10 × 8mm ) - {( 3nos.×  2× 8mm) + ( 2nos. × 3 × 8mm)}]

= [2348mm + 160mm - { 48mm + 48mm }]

= [2508mm - 96mm ]

= 2412mm.

For you 👇

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