# Bond & Development Length

By Deepanshu Rastogi|Updated : December 2nd, 2021

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 CivilIESBARCISROSSC-JEState 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.

## 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%.

### 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

(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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