RCC : Design of Beam & Design of slabs

By Saurabh Kumar|Updated : August 30th, 2021

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Design of Beam

Design stress-strain curve at ultimate state

image001

Design value of strength

For concrete

image002

where,

image003 Partial factor of safety for concrete = 1.5

fd = design value of strength

For steel

image004

Singly Reinforced Beam

image005

  1. Limiting depth of the neutral axis (xu, lim)
    image006

 

image007

Here d = effective depth of beam

  1. Actual depth of neutral axis (Xu)
    image008
  2. Lever arm = d – 0.42 Xu
  3. Ultimate moment of resistance
    image009

Some special cases

  1. When Xu < Xu,lim
    It is an under-reinforced section
    image009
  2. When Xu = Xu,lim
    It is balanced section
    image010
  3. When Xu > Xu,lim
    It is over reinforced section. In this case, keep Xu limited to Xu,lim and moment of resistance of the section shall be limited to limiting moment of resistance, (Mu,lim)

Doubly Reinforced Section

image011

  1. Limiting depth of neutral axis
    image012
  2. For actual depth of neutral axis (Xu)


image013

  1. Ultimate moment of resistance


image014


where fSC = stress in compression steel and it is calculated by strain at the location of compression steel (fSC)

T-Beam

  1. Effective width of flange
    Discussed in WSM
  2. Limiting depth of neutral axis
    image012

Singly reinforced T-Beam

Case-1: When NA is in flange area

i.e., Xu < Df

image015

(a) for Xu

image016

(b) Ultimate moment of resistance

image017

Case-2: When NA is in web area (Xu > Df)

image018

Case (a) when Xu > Df and

 image019

i.e., depth of flange in less than the depth of the rectangular portion of stress diagram.

  1. For actual depth of neutral ais


image020

  1. Ultimate moment of resistance

image021

image022

Special Case (2): When Xu > Df and

 image023

i.e., depth of flange is more than depth of rectangular portion of stress diagram.

image024

As per IS 456 : 2000

(bf – bw) Df portion of flange is converted into (bf – bw)yf section for which stress is taken constant throughout the section is 0.45 fck.

As per IS 456 : 2000

image025

  1. For actual depth of neutral axis

image026

image027

image028

image029

image030

DESIGN OF SLAB

One way slab

(i) Ly/Lx ratio is less than 2

 where, ly = length of longer span

lx = length of shorter span

(ii) Slab is supported only on two edges.

Design of One way slab

image026

Two way slab

(i)  Ly/Lx ratio is more than 2

(ii) Slab is supported on all edges.

Design of two way slab

  1. Grasoff Ranking method
    It is used for corners not held down position.
    It is purely simply supported case.

image028

(i) image029

(ii) Moment in x-direction image030

Moment in y-direction image031

(iii) Shear force

image032

At shorter edge (VX)

image033

At longer edge (Vy)

image034

  1. Design of slab with corner held down position

(a) Pigeauds method: image035

where, the values of image036 are read from table

(b) I.S. code method

image037

The values of image038 read from table (page 91, IS : 456-2000)

 

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Posted by:

Saurabh KumarSaurabh KumarMember since Jun 2020
Associate Community Civil Engineering - GATE/ESE
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Comments

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Sanjeev Kumar
good information
Biya

BiyaSep 17, 2021

For two way slab, lx/ly < 2
One way slab  lx/ly > 2

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