What is 0.42D in a crank bar (bent-up bar) cutting length formula? - its derivation.

 While calculating the cutting length of the crank bar, you might have observed that 0.42D is included in the formula to derive the answer.

My question to you is, What is the length of the 45° bent-up bar part? Is it 0.42D or 1.42D? 

If your answer is 0.42D, THEN THIS ARTICLE IS FOR YOU😃

Now, we will understand the theory behind 0.42D by 2 different methods.

As you can observe in the diagram given below, the crank bar is bent at a 45° angle (by theory) in slab reinforcement, & now we will derive the length of that bent-up part.

Let us draw a triangle in a crank bar by naming the 3 corners as a,b, & c with sides ab, bc, & ca as shown below. Here, the bent-up part of the crank bar is named "side ac".

Calculating the length of side ac:

Angle a = 180° - (angle b+ angle c )

 ∠a = 180° - ( 90° +45°)

       = 45°

As it is an isosceles right-angle triangle, 

                 side ab = side bc = D

    By Pythagoras theorem

Hypotenuse ac2 = ab2+bc2

ac2 = D2+D2

ac2 = 2D2   

                            ac =   √ 2D2   

                       ac = 1.414D

                 say ac = 1.42D

 Derivation of 0.42D:

The cutting length formula for the crank bar, for the above-given drawing, is given by

= {clear span +( 2nos. × development length ) + (2nos × extra crank length) - [2nos.× 90° bend + 4nos.× 45° bend]}

When we add a clear span in the calculation, we already include the length of side bc and side cb in it and we have to take an extra remaining length of the side ac by deducting side bc from it.

 Extra crank length 

      = side ac - side bc

       = 1.42D - 1D

        = 0.42D

So, that is what 0.42D stands for in the cutting length formula.

The alternate method for confirmation.

Known data:

side ab = D, 

sin45°= 1/√2  (trigonometry table )

By trigonometry,

sin45° = opposite / hypotenuse

sin45° = side ab/side ac

( By the above-given triangle drawing.)

 1/√2 = D / side ac

By cross multiplication,

side ac × 1  = √2 D

side ac = 1.414 D

SAY length of side ac = 1.42D

  

Extra crank length = side ac - side bc or side cb

                              = 1.42D - 1D

                              = 0.42D

To go through the articles on Estimation & calculation in civil engineering, click here.

Thank you for going through this article❤. Have a good day😄

Share: