Bond & Development Length Study Notes for Civil Engineering

By Deepanshu Rastogi|Updated : May 28th, 2021

The article contains fundamental notes on the "Bond and Development length"  topic of the "RCC & Prestressed Concrete" subject.                                                                                                                                                                                                                                                                                            


Bond, Anchorage and Development Length

Bond stress image001



Where V = Shear force at any section

d = Effective depth of the section

∑ p = Sum of all perimeter of reinforcement


n = Number of reinforcement

image005 diameter of reinforcement

Permissible bond stress

As per IS 456 : 2000


  • These value of bond stress is for plain bar in tension.
  • For deformed bar the above value should be increased by 60%.
  • For bar in compression the above value should be increased by 25%.

Development Length (Ld)



Shear stress

Shear stress

(a) For Homogeneous beam




q = shear stress at any section

V = shear force at any section

image011 Moment of area of section above the point of consideration

I = Moment of inertia of section


(b) For Reinforced concrete beam


(i) Shear stress above NA


(ii) Shear stress below NA 


Nominal shear stress, image016

Design shear strength of concrete image017 without shear reinforcement as per IS 456: 2000 image018 depends on

(i) Grade of concrete

(ii) Percentage of steel,



Ast = Area of steel

b = Width of the Beam

d = Effective depth of the beam


Maximum shear stress image021 with shear reinforcement is



Minimum shear reinforcement (As per IS 456 : 2000)


This is valid for both WSM and LSM



ASV = Area of shear reinforcement

SV = Spacing for shear reinforcement

Spacing of shear reinforcement

Maximum spacing is minimum of (i), (ii) and (iii)

(i) image026

(ii) 300 mm

(iii) 0.75 → For vertical stirrups

d → For inclined stirrups

where, d = effective depth of the section


(a) Critical section X-X at d from the face of the support


(b) Critical section X-X at the face of the support

The above provisions are applicable for beams generally carrying uniformly distributed load or where the principal load is located beyond 2d from the face of the support.

Vertical stirrups:


Shear force VS will be

Resisted by shear Reinforcement provided in 'd' length of the beam,


where, ASV = Cross-sectional area of stirrups

SV = Centre to centre spacing of stirrups


Inclined stirrups: or a series of bars bent-up at different cross-section:


Bent up Bars:

  • Single or a group of bent up bars are provided at distance image034 from support.

Generally bar should not be bent up beyond a distance l/4 from the support. Where l = length of span.


You can follow the detailed study plan for ESE technical 

Achiever's Study Plan for ESE Non-Tech 2021: Click Here

If you are preparing for ESE/ GATE or other PSU Exams (Civil Engineering), then avail Gradeup Super for ESE and GATE CE:

Gradeup Super for ESE/GATE CE(20+ Courses and 180+ Mock Tests)

You can avail of Gradeup Green Card specially designed for all Civil Engineering Exams:

Gradeup Green Card ESE/GATE CE (180+ Mock Tests)


Sahi Prep Hai To Life Set Hai

Download gradeup, Best GATE exam app for Preparation" 

Posted by:

Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
cracked GATE DTU AIR 1130-GATE
Share this article   |


write a comment
venkatesh venkat
For , q=V/bjd what is "j"
Shubham G Meshram
Sir please give a video lecture also to understand better.............👍👍
duddu dhilipkumar
Can you please make a notes on stairs, footings
Civil Jungle

Civil JungleJan 19, 2021

Amazing post, thank you for sharing this knowledgeable post, really this is very helpful. Development Length
Jitendra Tiwari
Amazing post, thank you for sharing this knowledgeable post, really this is very helpful. Development Length

Follow us for latest updates