Effective width method
Sheets Reference
SS-1 axle IRC:112-2011, "Concrete Road Bridges"
SS-2 axle IRC:112-2011, "Concrete Road Bridges"
SS-4 axle IRC:112-2011, "Concrete Road Bridges"
Girder slab IRC:112-2011, "Concrete Road Bridges"
C-1 axle IRC:112-2011, "Concrete Road Bridges"
C-2 axle IRC:112-2011, "Concrete Road Bridges"
C-4 axle IRC:112-2011, "Concrete Road Bridges"
Table IRC:112-2011, "Concrete Road Bridges"
Group members
Adhitya Chauhan MT19STR001
Akarsh K R MT19STR002
Shriram Asthakar MT19STR004
Faisal Khan MT19STR015
Apeksha Khandelwal MT19STR018
Effective width method-Simply supported slab with 1 axle
Assumptions and limitations
1. Slab is simply supported between bearings
2. Slab is spanning in one direction
3. Width of slab is supported completely (no cantilever)
4. Only longitudnal Bending moment can be calculated. No transverse and torsional moments.
Start
α,x, L,bw
𝒃_𝒆𝒇𝒇=𝜶 𝑿 (𝟏−𝑿/𝑳)+𝒃_𝒘
M=(P/beff)xL/2
End
Input
Span L 10 m
Carriageway B' 7.25 m
Foothpath+kerb 0.375 m
Edge distance c 1.125 m
Width of wheel
parallel to
support w 0.86 m
Wearing coat 0.075 m
1
1
200
1 kN
1
1
1
Longitudnal section
5 5
a b c
100 100
Transverse section
d e f g
ef 1.93 m
de 1.93 m
fg 3.765 m
B/l 0.8
α 2.24 (From Table sheet)
Effective width of one wheel beff=αX(1-X/L)+bw b eff 6.61 m
Note:
If its overlapping refer 1 (Axle load to be divided with this beff)
If its not overlapping refer 2 (Wheel load to be divided with this beff)
Present case Overlapping
1.Overlapping beff b ef* 7.17 m
2. Not overlapping beff b ef* 5.24 m
Bending moment M 70 kN-m/m
Effective width method-Simply supported slab with 2 axle
Assumptions and limitations
1. Slab is simply supported between bearings
2. Slab is spanning in one direction
3. Width of slab is supported completely (no cantilever)
4. Only longitudnal Bending moment can be calculated. No transverse and torsional moments.
Start
α,x, L,bw
𝒃_𝒆𝒇𝒇=𝜶 𝑿 (𝟏−𝑿/𝑳)+𝒃_𝒘
End
Input
Span L 10 m
Carriageway B' 8m
Foothpath+kerb 0m
Edge distance c 1.2 m
Width of wheel
parallel to support w 0.86 m
Wearing coat 0.075 m
1 2
1 1
200
1 200
1
1 1
1 1
1 1
Longitudnal section a b c d e
1.22
bc 0.915 m
cd 0.305 m
ab 4.085 m
de 4.695 m
1 2
1 1
100 1 100 100 100
1
1 1
1 1
1 1
Transverse section
f g h i f g h i
gh 1.93 m gh 1.93 m
fg 1.63 m fg 1.63 m
hi 4.44 m hi 4.44 m
B/l 0.8 B/l 0.8
α 2.24 (From Table sheet) α 2.24 (From Table sheet)
Effective width of one wheel beff=αX(1-X/L)+bw 6.42 m b eff 6.59 m
Note:
If its overlapping refer 1 (Axle load to be divided with this beff)
If its not overlapping refer 2 (Wheel load to be divided with this beff)
Present case Overlapping Present case Overlapping
1.Overlapping beff b ef* 6.77 m b ef* 6.85 m
2. Not overlapping beff b ef* 4.84 m b ef* 4.92 m
Effective width method-Simply supported slab with 4- axle
Assumptions and limitations
1. Slab is simply supported between bearings
2. Slab is spanning in one direction
3. Width of slab is supported completely (no cantilever)
4. Only longitudnal Bending moment can be calculated. No transverse and torsional moments.
Start
α,x, L,bw
𝒃_𝒆𝒇𝒇=𝜶 𝑿 (𝟏−𝑿/𝑳)+𝒃_𝒘
End
Input
Span L 10 m
Carriageway B' 8m
Foothpath+kerb 0m
Edge distance c 1.2 m
Width of wheel
parallel to support w 0.86 m
Wearing coat 0.075 m
1 2
1 1
170
1 170
1
1 1
1 1.37 1 3.05
1 1
Longitudnal section a b c
1.3425 1.37 2.2875
C.G from 1 2.895
1 2
1 1
85 1 85 85
1
Transverse section 1 1
1 1
1 1
h i j k h i
ij 1.93 m ij
hi 1.63 m hi
jk 4.44 m jk
B/l 0.8 B/l
α 2.24 (From Table sheet) α
x 1.3425 m x
Effective width of
one wheel beff=αX(1-X/L)+bw 3.61 m b ef
Note:
If its overlapping refer 1 (Axle load to be divided with this beff)
If its not overlapping refer 2 (Wheel load to be divided with this beff)
Present case Not Overlapping Present case
1.Overlapping beff b ef* 5.37 m b ef*
2. Not overlapping beff b ef* 3.44 m b ef*
with 4- axle
3 4
1 1
170
1 170
1
1 1
3.05 1 1.37 1
1 1
d e f g
0.7625 1.37 2.8675
m
2 3
1 85 85 1 85
1 1
1 1
1 1
1 1
j k h i j k
1.93 m ij 1.93 m
1.63 m hi 1.63 m
4.44 m jk 4.44 m
0.8 B/l 0.8
2.24 (From Table sheet) α 2.24 (From Table sheet)
2.7125 m x 4.2375 m
5.44 m b ef 6.48 m
Overlapping Present case Overlapping
6.28 m b ef* 6.80 m
4.35 m b ef* 4.87 m
4
85 1 85
1
1
1
1
h i j k
ij 1.93 m
hi 1.63 m
jk 4.44 m
B/l 0.8
α 2.24 (From Table sheet)
x 2.8675 m
b ef 5.59 m
Present case Overlapping
b ef* 6.36 m
b ef* 4.43 m
Effective width method-Girder Slab
57 57
Input
Wheel Load P1 57 c s
P2 57
Cantilver span c 2 B
Internal span s 4
Span L 10
Width B 8 P1 P1
Width of wheel parallel to support b 0.25 Bef Bef
Width of wheel perpendicular to support w 0.5 a
Distance between axle a 1.2 P2 P2
Distance between wheels d 1.8 Bef Bef L
Footpath f 0.5 d
Edge distance e 0.15
Wearing coat thickness t 0.075 Trailing Leading
B/l 0.8
α 2.08 (From Table sheet)
b1 0.4
Wheels moved 100 mm from left to right
Cantilever Intermediate span
Reference x Bef-Single Case Beff* P/Beff* Reference x for leading x for Trailing Bef leading wheel Bef Trailing wheel Leading wheels Trailing wheels Beff* Leading Beff* Trailing P/Beff* leading (P/Beff*) Trailing
0.9 1.1 1.72 Overlapping 2.92 39.04 0.7 0.7 0 1.60 0.00 Overlapping Not Overlapping 2.80 0.00 40.70 #DIV/0!
1 1 1.6 Overlapping 2.8 40.71 0.8 0.8 0 1.73 0.00 Overlapping Not Overlapping 2.93 0.00 38.89 #DIV/0!
1.1 0.9 1.48 Overlapping 2.68 42.54 0.9 0.9 0 1.85 0.00 Overlapping Not Overlapping 3.05 0.00 37.37 #DIV/0!
1.2 0.8 1.36 Overlapping 2.56 44.53 1 1 0 1.96 0.00 Overlapping Not Overlapping 3.16 0.00 36.08 #DIV/0!
1.3 0.7 1.24 Overlapping 2.44 46.72 1.1 1.1 0 2.06 0.00 Overlapping Not Overlapping 3.26 0.00 34.98 #DIV/0!
1.4 0.6 1.12 Not overlapping 1.12 50.89 1.2 1.2 0 2.15 0.00 Overlapping Not Overlapping 3.35 0.00 34.06 #DIV/0!
1.5 0.5 1 Not overlapping 1 57.00 1.3 1.3 0 2.23 0.00 Overlapping Not Overlapping 3.43 0.00 33.28 #DIV/0!
1.6 0.4 0.88 Not overlapping 0.88 64.77 1.4 1.4 0 2.29 0.00 Overlapping Not Overlapping 3.49 0.00 32.64 #DIV/0!
1.7 0.3 0.76 Not overlapping 0.76 75.00 1.5 1.5 0 2.35 0.00 Overlapping Not Overlapping 3.55 0.00 32.11 #DIV/0!
1.8 0.2 0.64 Not overlapping 0.64 89.06 1.6 1.6 0 2.40 0.00 Overlapping Not Overlapping 3.60 0.00 31.69 #DIV/0!
1.9 0.1 0.52 Not overlapping 0.52 109.62 1.7 1.7 0 2.43 0.00 Overlapping Not Overlapping 3.63 0.00 31.38 #DIV/0!
2 0 1.8 1.8 0 2.46 0.00 Overlapping Not Overlapping 3.66 0.00 31.15 #DIV/0!
1.9 1.9 0.1 2.47 0.60 Overlapping Not Overlapping 3.67 0.60 31.02 94.56
2 2 0.2 2.48 0.80 Overlapping Not Overlapping 3.68 0.80 30.98 71.68
2.1 2.1 0.3 2.47 0.98 Overlapping Not Overlapping 3.67 0.98 31.02 58.33
2.2 2.2 0.4 2.46 1.15 Overlapping Not Overlapping 3.66 1.15 31.15 49.62
2.3 2.3 0.5 2.43 1.31 Overlapping Not Overlapping 3.63 1.31 31.38 43.51
2.4 2.4 0.6 2.40 1.46 Overlapping Not Overlapping 3.60 1.46 31.69 39.02
2.5 2.5 0.7 2.35 1.60 Overlapping Not Overlapping 3.55 1.60 32.11 35.60
2.6 2.6 0.8 2.29 1.73 Overlapping Not Overlapping 3.49 1.73 32.64 32.93
2.7 2.7 0.9 2.23 1.85 Overlapping Not Overlapping 3.43 1.85 33.28 30.80
2.8 2.8 1 2.15 1.96 Overlapping Not Overlapping 3.35 1.96 34.06 29.08
2.9 2.9 1.1 2.06 2.06 Overlapping Overlapping 3.26 3.26 34.98 34.98
3 3 1.2 1.96 2.15 Overlapping Overlapping 3.16 3.35 36.08 34.06
3.1 3.1 1.3 1.85 2.23 Overlapping Overlapping 3.05 3.43 37.37 33.28
3.2 3.2 1.4 1.73 2.29 Overlapping Overlapping 2.93 3.49 38.89 32.64
3.3 3.3 1.5 1.60 2.35 Overlapping Overlapping 2.80 3.55 40.70 32.11
3.4 3.4 1.6 1.46 2.40 Overlapping Overlapping 2.66 3.60 42.84 31.69
3.5 3.5 1.7 1.31 2.43 Overlapping Overlapping 2.51 3.63 45.42 31.38
3.6 3.6 1.8 1.15 2.46 Not Overlapping Overlapping 1.15 3.66 49.62 31.15
3.7 3.7 1.9 0.98 2.47 Not Overlapping Overlapping 0.98 3.67 58.33 31.02
3.8 3.8 2 0.80 2.48 Not Overlapping Overlapping 0.80 3.68 71.68 30.98
3.9 3.9 2.1 0.60 2.47 Not Overlapping Overlapping 0.60 3.67 94.56 31.02
Effective Width Method- Cantilever Slab
Start
57 kN
x, w, t
x
bw= w + 2*t
beff = 1.2*x + bw
0.25
beff
M = (P/beff)*x
x
End
INPUT
Distance of the Wheel from Cantilever Support, x 1.4 m
Width of the wheel Parallel to the support w 0.25 m
Wearing Coat
thickness t 0.08 m
Load of Wheels P
due to different class loading 57 kN
bw 0.41 m
Effective width of one wheel beff=1.2X+bw 2.09 m
Live Load Moment M=(P/beff)*x 38 kN-m/m
Effective Width Method- Cantilever Slab
2 Axels - 2 Wheels
Start 57 kN 57 kN
d1= 1.2
x, w, t
a
bw= w + 2*t
x 0.25 0.25
beff = 1.2*x + bw 1 2
M = (P/beff)*x
beff beff
End
INPUT
Distance of the Wheel from Cantilever Support x 1.4 m
Width of the wheel Parallel to the support w 0.25 m
Wearing Coat
thickness t 0.08 m
P1 57 kN
Load of Wheels P2
due to different class loading 57 kN
d1 1.2 m
Distance between Axle 1 and Axle 2
bw=w+2t bw 0.41 m
Effective width of one wheel beff=1.2x+bw beff 2.09 m
Note:
If its overlapping, refer 1 (Two Wheel load to be divided with this b eff* for moment)
If its not overlapping refer 2 (Wheel load to be divided with this b eff for moment calculation)
Present Case Overlapping
1. Overlapping beff beff* 3.29 m
2. Non-Overlapping beff beff 2.09 m
Live Load Moment M=(P/beff)*x M 49 kN-m/m
Effective Width Method- Cantilever Slab
4 Axel - 4 Wheels
P1 P2 P3 P4
13.5 kN 13.5 kN 57 kN 57 kN
Start
d1 d2 d3
x, w, t 1.1 3.2 1.2
bw= w + 2*t
x
0.25 0.25 0.25 0.25
beff = 1.2*x + bw
1 2 3 4
beff1 beff3
M = (P/beff)*x
beff2 beff4
End
INPUT
Distance of the Wheel from Cantilever Support x 1.4 m
Width of the wheel Parallel to the support w 0.25 m
Wearing Coat thickness t 0.08 m
P1 13.5 kN
P2 13.5 kN
Load of Wheels due to different class loading
P3 57 kN
P4 57 kN
Distance between Axle 1 and Axle 2 d1 1.1 m
Distance between Axle 2 and Axle 3 d2 3.2 m
Distance between Axle 3 and Axle 4 d3 1.2 m
bw=w+2t bw 0.41 m
Effective width of one wheel beff=1.2x+bw beff 2.09 m
For Axle 1 and 2 : If beff > d1, then its overlapping, else its not overlapping
Present Case Overlapping
beff* 3.19 m
For Axle 2 and 3 : If beff > d2, then its overlapping, else its not overlapping
Present Case Not Overlapping
beff* 2.09 m
For Axle 3 and 4 : If beff > d3, then its overlapping, else its not overlapping
Present Case Overlapping
beff* 3.29 m
Final Effective width considering Overlapping
conditions beff' 2.09 m
Live Load Moment M=(P/beff')*x M 6 kN-m/m
B/L K (SSS) K (Continous)
0.1 0.4 0.4
0.2 0.8 0.8
0.3 1.16 1.16
0.4 1.48 1.44
0.5 1.72 1.68
0.6 1.96 1.84
0.7 2.12 1.96
0.8 2.24 2.08
0.9 2.36 2.16
1 2.48 2.24
1.1 2.6 2.28
1.2 2.64 2.36
1.3 2.72 2.4
1.4 2.8 2.48
1.5 2.84 2.48
1.6 2.88 2.52
1.7 2.92 2.56
1.8 2.96 2.6
1.9 3 2.6
2 3 2.6
2.1 3 2.6
2.2 3 2.6
2.3 3 2.6
2.4 3 2.6
2.5 3 2.6
2.6 3 2.6
