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Thursday, 3 June 2021

How to calculate Effective Span of Beam & Slab As per IS 456 2000 in 2021

 Here we will learn with some simple examples how to calculate Effective Span of Beam & Slab of various type As per IS 456 2000 Clause 22.2.

Effective span: It is that length of Beam or Slab using which we can calculate the moment acting on it & it is further help us to design & analyze the members. (Show in Fig:1) [IS 456 2000 Clause 22.2]

Clear span: It is the clear distance between two supports over which the member (Beam or Slab) resting. (Shown in Fig :1)


Effective span & clear span of a simply supported Beam & Slab

Fig:1 Simply supported Beam & Slab

Effective depth: It is the distance between top most compression fiber of the concrete member (Beam or Slab) to the center of the tension reinforcement. (Shown in Fig:3) [All Beam & Slab here have same dimension profile shown below]

Cross section of Beam with effective depth, clear cover,overall depth,reinforcement details etc.
Fig:2 X-ray view of section of Beam
Cross section of slab with effective depth,clear cover,overall depth,reinforcement detals
Fig:2.1 Cross Sectional view of Slab

Effective span is an important parameter for design & analysis of a structure parts like Beams & Slabs also its necessary for calculating “MOR” (Moment of resistance:the moment which can be safely withstand by a structure or parts of structure’s without showing any considerable deformation), but the effective span depends on lots of other factors, because of that we divided effective span into Four main categories:-

a) Simply supported Beam & Slab

b) Continuous Beam & Slab

c) Cantilever Beam & Slab

d) Frames

a) Simply supported Beam & Slab: The effective span of a member that is not built integrally (monolithic-ally) with its supports shall be taken as lesser than of these two: -

Clause (i): Clear Span (L) + effective depth (d) (shown in fig:2 &2.1)

Or

Clause (ii): Clear Span (L) + support/2 +support/2 (Center to Center distance b/w support)

Effective span of Simply supported beam with Smaller support width
Fig:3 Simply supported beam with 200 mm wide support

              Example 1: (as shown in fig 1; where span length= 3000 mm & width of support= 300 mm)

                 Clause i)

                   Effective span of the Beam = Clear Span (L) + effective depth (d) 

                                                                   = 3000 mm + 252 mm 

                                                                    = 3252 mm

                 Cause ii)

                  Effective span of the Beam = Clear Span (L) + support/2 +support/2 (Center to Center distance b/w support) 

                                                                  =3000 mm+300 mm/2+300 mm/2

                                                                  =3300 mm

                   “here the Clause(i) is the deciding clause of the effective length (L)= 3252 mm < 3300 mm (Clause ii)”

              

                 Example 2: (as shown in fig 2; where span length= 3000 mm & width of support= 200 mm)

                 Clause i)

                  Effective span of the Beam = Clear Span (L) + effective depth (d) 

                                                                  = 3000 mm + 252 mm 

                                                                   = 3252 mm

                Cause ii)

                 Effective span of the Beam = Clear Span (L) + support/2 +support/2 (Center to Center distance b/w support)

                                                                =3000 mm+300 mm/2+200 mm/2 

                                                                 = 3200 mm

                     “here the Clause(ii) is the deciding clause of the effective length (L)= 3200 mm < 3252 mm (Clause i)”


b) Continuous Beam or Slab: If the member (Beam or Slab) continuous over more than two support then it’s called continuous Slab or Beam.

if the width of the support is less than 1/12 of the clear span, the effective span of a continuous Beam or Slab is calculated as per clause (a) explain above. (As shown in Fig:4)

width of support < 1/12 of clear span

or

12 x width of support < clear span (we can write this expression mathematically)

The clear span length should be greater than twelve times of width

 

If the supports are wider than 1/12 of the clear span or 600 mm whichever is less, the effective span shall be taken by following below mentioned criteria’s

Width of support > 1/12 of clear span

Or

12 x width of support > clear span (we can write this expression mathematically)

The clear span should be less than twelve times of support width

 1) For end span with one end fixed and the other continuous or for intermediate spans. the effective span shall be the clear span between supports.

Effective span = Clear span

Effective span of continuous beam with one end Fixed

Fig 4: Continuous Beam with one end of the span ‘fixed’
                Example:  As shown in fig 4;
                  For span 1: effective span= clear span= 3500 mm
                  For Span 2: effective spa = clear span = 3400 mm (This is the intermediate span)
                  For Span 3: effective span= clear span = 3200 mm

                                       [All span is less than twelve times of the width which is 3600 mm]

2) For end span with one end free & other continuous the effective span shall be equal to lesser of these TWO

Clause (i) Clear span + effective depth (d)/2

Or

Clause (ii) Clear span + width of support/2

Effective span of Continuous Beam with one end Free

Fig 5: Continuous Beam or Slab with one end of the span ‘free’

Example 1: (as shown in fig 5; where span 1; clear span= 3500 mm; support width= 300 mm; effective depth=252 mm)

Clause (i) Clear span + effective depth (d)/2 = 3500 + 252/2 = 3626 mm

or

Clause (ii) Clear span + width of support /2 = 3500 + 300/2 = 3650 mm

                                      Here clause (i) is the deciding clause for the effective length =3626 mm

Example 2(as shown in fig 5; where span 3; clear span= 3850 mm; support width= 200 mm; effective depth=252 mm)

Clause (i) Clear span + effective depth (d)/2 = 2300 + 252/2 = 2426 mm

or

Clause (ii) Clear span + width of support /2 = 2300 + 200/2 = 2400 mm

                                     Here clause (ii) is the deciding clause for the effective length = 2400 mm

                                  [All span is less than twelve times of the width which is 3600 mm & 2400 mm]

            3) For Roller or Rocket bearing

                         Effective span = Center to center distance between support

                                                   = clear span + roller dia/2 + roller dia/2

                                                    = clear span +roller radius +roller radius

                                                     = clear span + dia of roller

Effective span of roller supported Beam & Slab

Fig: 6 Continuous roller supported Beam or Slab

Example: as show in fig 6; clear span =3400 mm; roller dia=250 mm

Effective span = clear span + dia of roller

= 3400 + 250

= 3650 mm

                                             [All span is less than twelve times of the width which is 3600 mm]

c) Cantilever Beam & Slab: The cantilever beam or slab are categorized into two types for calculating their effective length there are:

  • Fixed at the end (not continuous over support): For these cantilever bear or slab effective length consider as the clear length from the face of the support plus effective depth. (as shown in fig:7)

Effective length = length from face of the support + effective depth(d)

Effective Span of fixed end cantilever Beam & slab

Fig:7 Cantilever Beam or Slab fixed at end

Example: as show in fig 7; clear length =1350 mm; effective depth (d) = 252 mm

Effective length= 1350 mm + 252 mm

= 1602 mm

  • Continuous over support: The cantilever which is continuous over support to form a cantilever, the effective length of that cantilever should be taken as length from face of the support plus half the width of the support.

Effective length = length from face of the support + support width/2

Effective span of Cantilever Beam continuous over support

                                     Fig:8 Cantilever Beam or Slab continuous over support

Example: as show in fig 8; clear length =1410 mm; support width = 300 mm;

Effective length= 1410 mm + 300/2

= 1410 mm + 150 mm

= 1560 mm

d) Frame: For analysis of continuous frame center to center distance shall be consider for effective length.

Effective length= Center to center

                                                       = Clear span + width of support/2

Effective Span of Frame , Frame structure

Fig:9 Frame structure of Beam & Slab

Example: as show in fig 9; Frame 1; clear span =3600 mm; support width = 300 mm;

Effective length= 3600 mm + 300/2

= 3750 mm


 

 

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