Bond & Development Length
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Through Champion Study Plan for GATE Civil Engineering (CE) 2022, we are providing Bond & Development Length study notes and other important materials on every topic of each subject.
These topic-wise study notes are useful for the preparation of various upcoming exams like GATE Civil/ IES/ BARC/ ISRO/ SSC-JE/ State Engineering Services examinations and other important upcoming competitive exams.
The article contains fundamental notes on the “Bond & Development Length” topic of the “Design of Concrete Structures” subject.
Table of content
Bond, Anchorage and Development Length
Bond stress 
Where V = Shear force at any section
d = Effective depth of the section
∑ p = Sum of all perimeter of reinforcement
n = Number of reinforcement
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
where,
q = shear stress at any section
V = shear force at any section
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
j=Lever arm constant
Nominal shear stress, 
Design shear strength of concrete 
without shear reinforcement as per IS 456: 2000 
depends on
(i) Grade of concrete
(ii) Percentage of steel,
Where,
Ast = Area of steel
b = Width of the Beam
d = Effective depth of the beam
Maximum shear stress 
with shear reinforcement is
Minimum shear reinforcement (As per IS 456 : 2000)
This is valid for both WSM and LSM
where,
ASV = Area of shear reinforcement
SV = Spacing for shear reinforcement
Spacing of shear reinforcement
Maximum spacing is minimum of (i), (ii) and (iii)
(i) 
(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
from support.
Generally bar should not be bent up beyond a distance l/4 from the support. Where l = length of span.
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