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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 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 image001

image002

image003

Where V = Shear force at any section

d = Effective depth of the section

∑ p = Sum of all perimeter of reinforcement

image004

n = Number of reinforcement

image005 diameter of reinforcement

Permissible bond stress

As per IS 456 : 2000

image006

  • 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)

image008

image007

Shear stress

Shear stress

(a) For Homogeneous beam

image009

image010

where,

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

 image012

(b) For Reinforced concrete beam

image013

(i) Shear stress above NA

image014

(ii) Shear stress below NA 

image015

      j=Lever arm constant

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,

image019

Where,

Ast = Area of steel

b = Width of the Beam

d = Effective depth of the beam

image020

Maximum shear stress image021 with shear reinforcement is

image022

image023

Minimum shear reinforcement (As per IS 456 : 2000)

image024 

This is valid for both WSM and LSM

image025 

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) image026

(ii) 300 mm

(iii) 0.75 → For vertical stirrups

d → For inclined stirrups

where, d = effective depth of the section

image028

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

image029

(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:

image030

Shear force VS will be

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

image031

where, ASV = Cross-sectional area of stirrups

SV = Centre to centre spacing of stirrups

image032

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

image033

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.

 

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