How to calculate the cutting length of Trapezium shaped stirrups?/Calculating the cutting length of trapezoidal stirrups in columns.

 Let us now calculate the cutting length of the trapezium-shaped stirrup as shown below.

Given data:

Column width = 750mm,

Column depth = 450mm.

Clear cover = 40mm.

Main bar dia. = 20mm.

The diameter of trapezium stirrup bar = d = 8mm. 

The cutting length formula for trapezium stirrup

= [(a + 2b + c ) +(2nos × hook length) - {(4nos. × bend > 90°) + (1no.× bend < 90° )}]

I have given a trapezium stirrup drawing showing h, a, b, & c., where blue colored line is the centerline of the trapezium stirrup.

First, we will calculate the value of c,a, & b.

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

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

   = [750mm - { 80mm - 8mm}]

  = [ 750mm - 88mm]

c = 662mm.

a = [x + {(2nos.×1/2 × dia.of main bar) + (2nos. ×1/2 ×dia. of stirrup.)}]

Here, 

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

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

   = [ 600mm - { 80mm + 8mm + 20mm }] ÷ 3

  = [ 600mm - 108mm ] ÷ 3

  = 492mm ÷ 3

 x = 162mm.

a =  [x + {(2nos.×1/2 × dia.of main bar) + (2nos. ×1/2 ×dia. of stirrup.)}]

  = [ 162mm +{( 2nos.× 1/2 × 20mm ) + ( 2nos. × 1/2 × 8mm )}]

  = [ 162mm + { 20mm + 8mm }]

  =[ 162mm + 28mm]

a = 190mm.

I have drawn the triangle part of the trapezium stirrup, for your clear understanding. 

b =√( y )2 +( h )2

[ b is a hypotenuse of a triangle ]

Here,

 y =[ x+ (1/2 × dia. of stirrup)]

   = [162mm + (1/2 × 8mm.)]

y = 166mm.

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

  =[450mm - {( 2nos.× 40mm ) + ( 2nos. ×1/2 × 8mm )}]

  = [ 450mm - { 80mm + 8mm }]

  =  [ 450mm - 88mm ]

 h= 362mm.

b =√( y )2 +( h )2

   =√( 166 )2 +( 362 )2

  = √27556 +131044

=√158,600

= 398.246mm.

The cutting length of trapezium stirrup

= [(a + 2b + c ) +(2nos × hook length) - {(4nos. × bend > 90°) + (1no.× bend < 90° )}]

= [ { 190mm + (2 × 398.246mm) + 662mm } + ( 2nos.× 10d ) - {(4nos. × 3d) + (1no.× 2d )}]

{Here, 10d is taken as hook length, 3d for the bend > 90°, 2d for bend < 90° & d is stirrup bar dia.}

=  [ {190mm + 796.49mm + 662mm } + ( 2nos.× 10×8mm ) - {(4nos. × 3×8mm) + (1no.×2×8mm )}]

= [ 1648.49mm + 160mm - { 96mm + 16mm }]

= [ 1808.49mm - 112mm]

= 1696.49mm.

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