Development Length Calculation as per Indian Code

Development length is the extra length of bar provided beyond the required section in order to ensure the following;

• To develop a safe bond between the bar surface & the concrete so that no failure due to slippage of bar occurs during the ultimate load conditions.
• Also, the extra length of the bar provided as development length is responsible for transferring the stresses developed in any section to the adjoining sections (such as at column beam junction the extra length of bars provided from beam to column).

Importance: Provision of appropriate development is an important aspect of safe construction practices, proper development length in reinf. bars shall be provided as per the steel grade considered in design otherwise in scenarios where less development length against the required is provided the structures will be prone to encounter  failure due to slippage of joints, bonds, anchors & Laps, in such cases the bars will not yield first but the failure will happen at joints & laps prior to yielding of reinforcement bars.

Calculation of Development length:

As per the Indian Standard – IS 456: 2000, clause 26.2.1 the development length Ld is given the following expression;

 Where,             Ø            = nominal dia of reinforcement bar

 σ_s               = Stress in bar at the section considered at design load

 τ_bd           = Design bond stress

The above given formula is used to calculate the required development length in mm for any given dia of bar, same formula is used for limit state method as well as working stress method. The only change in calculation in both methods is due to the different value of design bond stress; the values of design bond for Limit State & working stress are as follows;

Design Bond Stress in Limit State Method
Concrete Grade	M20	M25	M30	M35	M40 & Above
Design Bond Stress (τbd, N/mm2)	1.2	1.4	1.5	1.7	1.9	For Plain Bars in Tension
	1.92	2.24	2.4	2.72	3.04	For deformed bars in tension

**Note: For bars in compression 1.25 times the above-given values shall be used.
              

Design Bond Stress in Working Stress Method
Concrete Grade	M20	M25	M30	M35	M40	M45	M50
Design Bond Stress (τbd, N/mm2)	0.8	0.9	1.0	1.1	1.2	1.3	1.4	For Plain Bars in tension
	1.28	1.44	1.6	1.76	1.92	2.08	2.24	For deformed bars in tension

**Note: For bars in compression 1.25 times the above given values shall be used.
            

Generally, in practice, the development length requirement is expressed as ‘41 times Ø’ or ‘41 Ø’ where 41 is the factor calculated using the above formula & Ø is the dia of the bar.

Example: In the following images, calculation for development length in limit state method (Fig.1), as well as working stress method (Fig.2) for M25 concrete grade & 415 steel grade, are illustrated;

Fig-1 (For Limit State Method)

Fig-2 (For Working Stress Method)

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