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

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

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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Posted by:

Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
cracked GATE DTU AIR 1130-GATE
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Comments

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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

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