Week 5 Challenge
1 Basic design data
1.1 Span and cross-section data Left span Right span
C/C of expansion gap 13.3 13.3
C/C of bearing 12.3 12.3
Distance of bearing to expansion gap 0.5 m 0.5 m
Girder overhang beyond bearing 0.35 1.35
Total Width 12m 12m
Carriage way width 9m 9m
Footpath Width (Left side) 1.5m 0
Crash Barrier Width (Left side) 0.5m 0.5m
Width of median 0.5m 0.5m
2 Superstructural details Left Right
Number of girders 4 5
spacing of girders 3m 3m
Cantilever on both sides 1.5m 1.5m
Depth of superstructures 1.32m 1.32m
C.G of superstructure 0.88m 0.88m
Wearing coat thickness 0.065m 0.065m
Distance of FRL from bearing of least height 10.9m 10.9m
Bearing Thickness 0.07m 0.07m
Pedestal thickness 0.25m 0.25m
Superelevation 2.50% 2.50%
3 Levels
Height of Substructures 10m assume
HFL 227.105
Bed Level 224.178
Pier cap top 228.143
Pier top 227.393
Footing top level 217.262
Footing bottom level 216.262
Clear cover for foundation 75mm
Water Current Data
Max. mean velocity 0.98 m/s
Constant "k" for the pier in the transverse direction 0.66
Constant "k" for the pier in the longitudinal direction 1.5
% of uplift considered 100%
Material Used
Grade of concrete fck M35
Design of concrete fcd 15.63 Mpa
Grade of steel fyk Fe500
The design strength of steel fyd 434.8 Mpa
The density of RC Concrete 2.5 t/m3
The density of wearing a coat 2.2 t/m3
Coef. Of thermal expansion of steel 1.2 E-05/ºc
Shrinkage strain of concrete 2.00E-04
Modulus of elasticity of steel Es 20000000 Mpa
Modulus of elasticity of concrete Ecm for M35 32000 Mpa
Mean axial tensile strength of concrete fctm 2.8 Mpa
Soil parameters
The density of dry backfill 2 t/m3
The density of submerged backfill 1 t/m3
Net SBC 25 t/m3
Gross SBC (LWL) 33.92 t/m3
Gross SBC (HFL) 27 t/m3
Type of soil medium soil
Load on super structure
Left Right
Total wt of super structure 199 t 199t
Dead load reaction of span 99.5 99.5
total reation on pier 199 t
Unbalanced long moment 0 0
Transverse ecc of DL from pier C/L 0 0
Transverse moment due to unbalanced DL 0 0
SIDL (Except WC)
Weight of crash barrier 1 t/m
weight of crash barrier 26.6 t
weight of median 13.3 t
weight of footpath 19.96 t
total reaction on pier 54.86 t
total long moment 0 tm
Transverse ecc of CB 0 m
Transverse ecc of median 3.75 m
transverse moment of median 49.88 tm
Transverse ecc of foothpath 4.75 m
Transverse moment of FP 71.07 tm
Total Trans. Moment 120.95 tm
SIDL (WC)
Load Intensity due to WC 0.22 t/m2
Weight of WC 26.33 t/m2
Intensity of FPLL 500 kg/m2
FPLL 0.5 t/m2
FPLL 9.98 t
Unbalanced long Moment 0 tm
Trans Moment due to unbalanced WC 52.67 tm
Substructure
Pier cap (Rectangular Part)
Length (T-T) 10.1 m
Length (L-L) 2.2 m
Height 0.25 m
Volume 5.555 m3
Weight 13.89 t
Pier cap (Trapezoidal Part)
Top length (T-T) 10.1 m
Bottom Length (T-T) 8.5 m
Width at the top 2.2 m
Width at the bottom 0.6 m
Height 0.5 m
Volume 6.33 m3
Weight 15.82 t
Total weight of pier cap 29.71 t
Pier shaft
Dimension along with traffic 0.7 m
Dimension perpendicular to traffic 8.5 m
Area of recantangular part 5.95 m2
Height 10.13 m
Volume 60.28 m3
Area-Semicircular 0.19 m2
Height 10.13 m
Volume 3.9 m3
Weight 160.44 t
Total Weight of substructure 190.15 t
Foundation
Type of foundation Open
Width of footing(Long dir) 6.5 m
Width of footing(Tran dir) 9.4 m
The thickness of footing at the top 1 m
The thickness of footing at the end 0.3 m
Volume rectangular 18.33 m3
Volume trapezoidal 20.09 m3
The total volume of footing 38.42 m3
Total weight of footing 96.05 t
Weight of soil on the footing
Low water level case
Bed level 224.178 m
Footing bottom level 216.262 m
Width 6.5 m
Length 9.4 m
Height 7.92 m
Total volume 483.912 m3
Volume of soil 445.25 m3
Total weight of soil above the footing 890.5 t
HFL Case
Volume of soil 445.25 m3
Total weight of soil above the footing 445.25 t
Force and moment due to water current
Velocity through the vent 0.98 m/sec
HFL 227.105 m
Source level 218.262 m
Pier bottom Level 217.262
Founding Level 216.262
Length fo Pier 13.55 m
Width of pier 0.8 m
Constant 'K'in transverse direction 0.66
Constant 'K'in longitudinal direction 1.5
The intensity of water current pressure = 52 k V2 kg / m2 149.8224 kg / m2
Velocity in Transverse direction = V max x cos 20 (Assuming 20-degree variation in water current direction)
Velocity in Longitudinal direction = V max x sin 20
Where Vmax = 2 x V
Mean velocity of flow = 0.980 m / s
Therefore, Vmax = 1.386 m / s
Water current forces
Submerged height of pier 8.843 m
Intensity of pressure at pier bottom level 0
Dia of pier 0.7 m
Force on pier in transverse direction 24.26968 kg / m2 0.242697 t
Transverse moment at bottomm of pier 1.430698 tm
Cross current forces
As per the Clause 210.5 of IRC:6-2014, a deviationn of 20 degree to the direction of flow is assumed
Resolving the forces along and across the direction of flow
Force on the pier in Transverse direction 0.2 t
Transverse moment at the bottom of pier 1.2 tm Velocity in Transverse direction = V max x cos 20 0.39992
Dia of pier 0.7 m Velocity in Longitudnal direction = V max x sin 20 1.265278
Force on the pier in Longitudinal direction 0.1 t
Longitudinal Direction at the base of pier 0.4 tm Where, Vmax = 2 x V
Mean velocity of flow = 0.980 m / s
Therefore, Vmax = 1.386 m / s
Intensity of water current pressure = 52 k V2 kg / m2
Transverse 5.489015 kg / m2
Longitudinal 124.8723 kg / m2
Force summary due to water(@ pier top)
Load case Load P Load (Min) ML MT HL HT
t t tm tm t t
Water current 0 degree 0 0 0 1.4 0 0.2
Water current 20 degree 0 0 0.4 1.2 0.1 0.2
Force summary due to water(@ Footing bottom)
Load case Load P Load (Min) ML MT HL HT
t t tm tm t t
Water current 0 degree 0 0 0 1.6 0 0.2
Water current 20 degree 0 0 0.4 1.2 0.1 0.2
Carriageway Live Load Reactions and Moments:
Maximum Reaction Case
Left Side Span (C/C of Exp. Gap) = 13.30 m
Right Side Span (C/C of Exp. Gap) = 13.30 m
Left Side Dist. Between Exp Gap & Bearing = 0.50 m
Right Side Dist. Between Exp Gap & Bearing = 0.50 m
Left Side Span (C/C of Bearing) = 12.30 m
Right Side Span (C/C of Bearing) = 12.30 m
The train of loads are placed in such a way that CG of the load system is at the center line of pier to get the max reaction.
R1 = 490 x { 12.3 - ( 2.658 + 0.666 - 0.5 ) } / ( 12.3 ) = 377.50 KN
R3 = 490 - 377.5 = 112.50 KN
R2 = 510 x { 12.3 - ( 1.93 + 0.704 - 0.5 ) } / ( 12.3 ) = 421.52 KN
R4 = 510 - 421.52 = 88.48 KN
Total Reaction on pier = 377.5 + 421.52 1.50 = 799.02 KN
1.20
Longitudinal Moment = (421.52 - 377.5 ) * 0.5 1.00 = 22.01 KNm
Braking Force for LHS = 0.2 * 490 = 98.00 KN
Braking Force for RHS = 0.2 * 510 = 102.00 KN
R1 = 272 x { 12.3 - ( 4.5 + 0.708 - 0.5 ) } / ( 12.3 ) = 167.89 KN
R3 = 272 - 167.89 = 104.11 KN
R2 = 282 x { 12.3 - ( 1.432 + 3.592 - 0.5 ) } / ( 12.3 ) = 178.28 KN
R4 = 282 - 178.28 = 103.72 KN
Total Reaction on pier = 167.89 + 178.28 = 346.17 KN
Longitudinal Moment = (178.28 - 167.89 ) * 0.5 = 5.20 KNm
Braking Force for LHS = 0.2 * 272 = 54.40 KN
Braking Force for RHS = 0.2 * 282 = 56.40 KN
2 Lane Class A:
For Class A 2 Lane the loads & the moments shall be multiplied by 2 times that of Class A 1 Lane.
R1 = 2 x 167.89 = 335.78 KN
R3 = 2 x 104.11 = 208.22 KN
R2 = 2 x 178.28 = 356.56 KN
R4 = 2 x 103.72 = 207.44 KN
Total Reaction on pier = 335.78 + 356.56 = 692.34 KN
Longitudinal Moment = (356.56 - 335.78 ) * 0.5 10.39 KNm
Braking Force for LHS = 0.2 * 272 = 54.40 KN
Braking Force for RHS = 0.2 * 282 = 56.40 KN
Wind Load
Height of crash barrier 0.5 m
Width of super structure 12 m
h=clear height of pier 10.13 m
Overall depth of super structure 1.32 m
Transverse wind load
Wind velocities & Pressures: (Refer Table 4: of IRC:6)
PZ 1064.5
VZ 42.1
Basic Wind speed 50 m/s
Type of terrain plain terrain
Wind load on DL+SIDL
Gust factor,G 2
CD 1.3
Exposed solid area 29.526 m2
Transverse Wind force
Transverse Wind force 8.17 t
Wind force FDL=25% of transverse wind force FTD 2.04 T
Projected area in plan producing obstruction 159.6 m2
Lift coefficient,CL 0.75
Total upward wind force on superstructure -25.48 t
Wind load on live load as per clause 209.4 of IRC:6
Basic wind speed is restricted to 36m/s as for the above speeds, it is considered that deck is not carrying any live load on it. (Cl.209.3.7,IRC6:2014)
Distance of railing top from OGL 5.937 m
Type of terrain Plain terrain
Wind speed 42.1 m/s
Wind load on substructure as per CL.209.4 of IRC6:2014
Pier cap:
Area of pier cap exposed to wind above GL in m2 1.25 m2
Avg height of pier cap from top of GL 3.66 m2
Raitio of thickness to breadth,t/b 4.498
Ratio of height to breadth,h/b 0.33
Drag coefficient for the piercap from Table-6 CD 1.2
Transverse wind force, FT
Transverse wind force, FT 0.319 t
Force at pier bottom level
HL wind Ftxsin(theta) 0
HT wind Ft x cos(theta) 1
ML 0
MT 10.4
Force at footing bottom level
HL wind Ftxsin(theta) 0
HT wind Ft x cos(theta) 1
ML 0
MT 11.4
Pier
Area of pier exposed to wind above GL in m2 6.4 m2
Avg height of pier from top of GL 9.13 m2
Raitio of thickness to breadth,t/b 12.14
Ratio of height to breadth,h/b 13.04
Drag coefficient for the piercap from Table-6 CD 1.2
Wind load on substructure as per CL.209.4 of IRC6:2014
PZ 1064.5 N/m2
VZ 50 m/s
Transverse wind force, FT
Transverse wind force, FT 1.635 t
Force at pier bottom level
HL wind Ftxsin(theta) 0
HT wind Ft x cos(theta) 6.1
ML 0
MT 69.9
Force at footing bottom level
HL wind Ftxsin(theta) 0
HT wind Ft x cos(theta) 6.1
ML 0
Forces at pier bottom level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
Wind -25.48 -25.48 22.9 171.8 2.04 8.17
Base pressure check
Area of footing, A=LxB 61.1 m2
Section modulus about trans. Axis ,ZLL =(L x B2)/6 = 66.19 m3
Section modulus about long. Axis ,ZTT =(B x L2)/6 = 95.72 m3
Gross SBC (lwl) 32.92 t/m3
Both span present
Load Pmax Pmin ML MT HL HT
DL 199 199 0 0 0 0
SDL 54.86 54.86 0 120.95 0 0
Wearing Coat 26.33 26.33 0 53 0 0
LL 94.22 94.22 91 179.49 9.42
FPLL 9.98 9.98 0 0 0 0
Weight of substructure 190.15 190.15 0 0 0 0
Weight of footing 96.05 96.05 0 0 0 0
Weight of soil above footing 890.5 890.5 0 0 0 0
Wind load -25.48 -25.48 22.9 171.8 2.04 8.17
Water current (0) 0 0 0 1.6 0 0.2
Water current (20) 0 0 0.4 1.4 0 0.2
Total 1535.6 1535.6 114.3 527.9 11.56 8.57
Combination for base pressure
p1= (P/A)+[(ML/ZL)+(MT/ZT) 32.3742
p2= (P/A)+[(ML/ZL)-(MT/ZT) 21.3445
p3= (P/A)-[(ML/ZL)-(MT/ZT) 17.8909
p4= (P/A)-[(ML/ZL)+(MT/ZT) 28.9206
Summary
Force @ bearing level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 199 199 0 0 0 0
SIDL 54.86 54.86 0 120.95 0 0
SIDL (WL) 26.33 26.33 0 53 0 0
Force @ pier bottom level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 199 199 0 0 0 0
SIDL 54.86 54.86 0 120.95 0 0
SIDL (WL) 26.33 26.33 0 53 0 0
Force @ piercap bottom level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 199 199 0 0 0 0
SIDL 54.86 54.86 0 120.95 0 0
SIDL (WL) 26.33 26.33 0 53 0 0
One span dislodged condition
DL of superstructure 99.5 t
Long moment 49.75 tm
SIDL (wo WC)
Load on pier 27.43 t
Long. Moment 13.72 tm
Trans. Moment 0
SIDL (WC)
Load on pier 13..17 t
Long moment 6.58 tm
Trans. Moment 0
Forces at bearing level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 99.5 99.5 49.75 0 0 0
SIDL 27.43 27.43 13.72 0 0 0
SIDL (WL) 13.17 13.17 6.58 0 0 0
Force at pier top level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 99.5 99.5 49.75 0 0 0
SIDL 27.43 27.43 13.72 0 0 0
SIDL (WL) 13.17 13.17 6.58 0 0 0
Force at piercap level
Load case Load (max) Load (min) ML MT HL HT
t t tm tm tm tm
DL 99.5 99.5 49.75 0 0 0
SIDL 27.43 27.43 13.72 0 0 0
SIDL (WL) 13.17 13.17 6.58 0 0 0
Combination of loads for design of foundation
Footing bootom level
Both span present
Loads Factors Unfactored Factored
Pmax Pmin ML MT HL HT Pmax Pmin ML MT HL HT
DL 1.35 199 199 0 0 0 0 268.65 268.65 0 0 0 0
SDL 1.35 54.86 54.86 0 0 0 0 74.061 74.061 0 0 0 0
Wearing coat 1.75 26.33 26.33 0 0 0 0 46.0775 46.0775 0 0 0 0
LL-Leading 1.5 94.22 94.22 91 179.49 9.42 0 141.33 141.33 136.5 269.235 14.13 0
LL-Accompaning 1.15 75.03 75.03 72.47 142.93 7.5 0 86.2845 86.2845 83.3405 164.3695 8.625 0
FPLL 1.15 9.98 9.98 0 0 0 0 11.477 11.477 0 0 0 0
Weight of substructure 1.35 190.15 190.15 0 0 0 0 256.7025 256.7025 0 0 0 0
Footing Weight 1.35 96.05 96.05 0 0 0 0 129.6675 129.6675 0 0 0 0
Weight of soil above footing 1.35 890.5 890.5 0 0 0 0 1202.175 1202.175 0 0 0 0
Wind leading 1.5 -25.48 -25.48 22.9 171.8 2.04 8.17 -38.22 -38.22 34.35 257.7 3.06 12.255
Wind accompanying 0.9 -25.48 -25.48 22.9 171.8 2.04 8.17 -22.932 -22.932 20.61 154.62 1.836 7.353
LL -Leading Total 2068.97 2068.97 191.46 681.55 19.04 19.61
LL-accompanying Total 2013.93 2013.93 138.3 576.69 13.53 19.61
Rare combination of loads
Footing bottom level
Both span present
Loads Factors Unfactored Factored
Pmax Pmin ML MT HL HT Pmax Pmin ML MT HL HT
DL 1 199 199 0 0 0 0 199 199 0 0 0 0
SDL 1 54.86 54.86 0 0 0 0 54.86 54.86 0 0 0 0
Wearing coat 1.2 26.33 26.33 0 0 0 0 31.596 31.596 0 0 0 0
LL-Leading 1 94.22 94.22 91 179.49 9.42 0 94.22 94.22 91 179.49 9.42 0
LL-Accompaning 0.75 75.03 75.03 72.47 142.93 7.5 0 56.2725 56.2725 54.3525 107.1975 5.625 0
FPLL 0.75 9.98 9.98 0 0 0 0 7.485 7.485 0 0 0 0
Weight of substructure 1 190.15 190.15 0 0 0 0 190.15 190.15 0 0 0 0
Footing Weight 1 96.05 96.05 0 0 0 0 96.05 96.05 0 0 0 0
Weight of soil above footing 1 890.5 890.5 0 0 0 0 890.5 890.5 0 0 0 0
Wind leading 1 -25.48 -25.48 22.9 171.8 2.04 8.17 -25.48 -25.48 22.9 171.8 2.04 8.17
Wind accompanying 0.6 -25.48 -25.48 22.9 171.8 2.04 8.17 -15.288 -15.288 13.74 103.08 1.224 4.902
LL -Leading Total 1523.08 1523.08 127.64 454.37 12.69 13.08
LL-accompanying Total 1485.13 1485.13 90.99 382.08 8.9 13.08
Base pressure for foting design
Area of footing A= L x B 61..10 m2
Section modulus about trans axis, ZLL= (L x B2)/6 66.19 m3
Section modulus about Loong axis, ZTT= (Bx L2)/6 95.72 m3
Gross SBC (LWL) 32.92 t/m2
Both span Present
Factored loads for base pressure
Pmax Pmin ML MT HL HT
LL -Leading 2068.97 2068.97 191.46 681.55 19.04 19.61
LL-accompanying 2013.93 2013.93 138.3 576.69 13.53 19.61
Combination for base pressure
LL-Leading
p1= (P/A)+[(ML/ZL)+(MT/ZT) 43.87 t/m2
p2= (P/A)+[(ML/ZL)-(MT/ZT) 29.63 t/m2
p3= (P/A)-[(ML/ZL)-(MT/ZT) 23.85 t/m2
p4= (P/A)-[(ML/ZL)+(MT/ZT) 38.09 t/m2
LL-Accompanying
p1= (P/A)+[(ML/ZL)+(MT/ZT) 41.08 t/m2
p2= (P/A)+[(ML/ZL)-(MT/ZT) 29.03 t/m2
p3= (P/A)-[(ML/ZL)-(MT/ZT) 24.85 t/m2
p4= (P/A)-[(ML/ZL)+(MT/ZT) 36.9 t/m2
Design of footing slab-Transverse Direction
Grade of concrete M35
Design strength of concrete 15.63
Grade of steel Fe500
Design strength of steel 434.8
Modulus of elasticity of steel 200000 Mpa
Modulus elasticity of concrete 32000 Mpa
Cu 0.8095*fcd*b*xu
Tu (fy/1.15)*Ast
xu,lim/d 0.617
Rlim= Mu,lim/bd2 0.8095fcd*(xu/d)*(1-0.416*xu/d)
5.8
Overall depth of the section 1 m
Critical section for moment is at the face of column
Critical case for design
Gross pressure(t/m2)
p1 p2 p3 p4
43.87 29.63 23.85 38.09
Net pressure(t/m2)
p1 p2 p3 p4
27.8 13 7.7 22.5
Overhang h= 0.45 m
A1 p1+p4*l/2 236.41 t/m
A2 p1+p2*l/2 187.06 t/m
volume (A1+A2+sqrt(A1A2))*h/3 95.06 t
lever arm h/4*(A1+2*sqrt(A1*A2)+3*A2)/(A1+sqrt(A1*A2)+A2)
0.22m
Design Moment,Mu Volume*lever arm 20.91 tm
Equivalent width of rectangular section, b b+1/8*(B-bt) 1.425 m
R 0.17
Effective depth required sqrt(Mu/R*b) 293.82 mm
Effective depth available 917 mm
Area of steel required 513 mm2
Dia of main reinforcement 16 mm
Provide 16 mm dia @ 125mm c/c
Area of steel provided 1607.68 mm2 ok
Top reinforcement
Min % of steel 0.146
Area os steel required at top 673 mm2
Provide 12 mm dia @150 mm c/c
Checked for minimum and maximum reinforcement as per IRC 112
Base pressure for rare combination
Base pressure for foting design
Area of footing A= L x B 61..10 m2
Section modulus about trans axis, ZLL= (L x B2)/6 66.19 m3
Section modulus about Loong axis, ZTT= (Bx L2)/6 95.72 m3
Gross SBC (LWL) 32.92 t/m2
Both span Present
Factored loads for base pressure
Pmax Pmin ML MT HL HT
LL -Leading 1523.08 1523.08 127.64 454.37 12.69 13.08
LL-accompanying 1485.13 1485.13 90.99 382.08 8.9 13.08
Combination for base pressure
LL-Leading
p1= (P/A)+[(ML/ZL)+(MT/ZT) 31.6 t/m2
p2= (P/A)+[(ML/ZL)-(MT/ZT) 22.11 t/m2
p3= (P/A)-[(ML/ZL)-(MT/ZT) 18.25 t/m2
p4= (P/A)-[(ML/ZL)+(MT/ZT) 27.75 t/m2
LL-Accompanying
p1= (P/A)+[(ML/ZL)+(MT/ZT) 29.67 t/m2
p2= (P/A)+[(ML/ZL)-(MT/ZT) 21.69 t/m2
p3= (P/A)-[(ML/ZL)-(MT/ZT) 18.94 t/m2
p4= (P/A)-[(ML/ZL)+(MT/ZT) 26.92 t/m2
Design of footing for SLS
Overall depth of section
Critical case for design
Gross pressure(t/m2)
p1 p2 p3 p4
31.6 22.11 18.25 27.75
Net pressure(t/m2)
p1 p2 p3 p4
15.4 5.6 2.1 11.9
Overhang,h 0.45 m
A1 p1+p4*l/2 128.6 t/m
A2 p1+p2*l/2 126.3 t/m
Volume (A1+A2+sqrt(A1+A2))*h/3 57.35 t
Lever arm h/4*(A1+2*sqrt(A1*A2)+3*A2)/(A1+sqrt(A1*A2)+A2)
Design moment,Mu Volume*leverarm 12.62 tm
Equivalent width of rectangular section,b 1.425 m
Calculation of stress in concrete
Permissible stress in concrete 0.48fck 16.8 Mpa
Permissible stress on raft 0.8fyk 400 Mpa
Design moment per unit width 1.98 tm/m
Modular ratio 6.25
width 1 m
Ast Provided 1607.68 mm2/m
Eff Depth 917 mm
NA depth 126.6 mm
Eff moment of inertia 7.08*10^9 mm4
Section modulus of concrete 5.59*10^7 mm3
Section modulus of reinforcement 8.87*10^6 mm3
Stress in concrete 0.35 Mpa ok
Stress in reinforcement 13.94 Mpa ok
Design of footing slab -Longitudinal Direction
Grade of concrete M35
Design strength of concrete 15.63
Grade of steel Fe500
Design strength of steel 434.8
Modulus of elasticity of steel 200000 Mpa
Modulus of elasticity of conctrete 32000 Mpa
Ovelall depth of section 1 m
Critical section for moment is at the face of column
Gross pressure(t/m2)
p1 p2 p3 p4
43.87 29.63 23.85 38.09
Net pressure(t/m2)
p1 p2 p3 p4
27.8 13 7.7 22.5
Overhang,h 0.45 m
A1 p1+p4*l/2 191.6 t/m
A2 p1+p2*l/2 169.5 t/m
Volume (A1+A2+sqrt(A1+A2))*h/3 523.2 t
Lever arm h/4*(A1+2*sqrt(A1*A2)+3*A2)/(A1+sqrt(A1*A2)+A2) 1.42 m
Design moment,Mu Volume*leverarm 742.94 tm
Equivalent width of rectangular section,b 8.6125 m
Effective depth required sqrt(Mu/R*b) 292.25mm
Effective depth available 917 mm ok
Area of steel required 19132.83 mm2
Area of steel required per meter width 2221.52 mm2/m
Dia of main reinforcement 25 mm
Provide 25mm dia @ 125mm c/c
Area of steel provided 3925 mm2/m ok
Top reinforcement
Min % of steel 0.146
Area os steel required at top 673 mm2
Provide 12 mm dia @150 mm c/c
Checked for minimum and maximum reinforcement as per IRC 112
Design of footing slab -SLS
Longitudinal Direction
Overall depth of the section 1 m
Critical case for design
Gross pressure(t/m2)
p1 p2 p3 p4
31.6 22.11 18.25 27.75
Net pressure(t/m2)
p1 p2 p3 p4
15.4 5.6 2.1 11.9
Overhang,h 2.9m
A1 p1+p4*l/2 68.3 t/m
A2 p1+p2*l/2 58.1 t/m
Volume (A1+A2+sqrt(A1+A2))*h/3 183.2 t
Lever arm h/4*(A1+2*sqrt(A1*A2)+3*A2)/(A1+sqrt(A1*A2)+A2) 1.41 m
Design moment,Mu Volume*leverarm 258.31 tm
Equivalent width of rectangular section,b 8.6125m
Calculation of stress in concrete
Permissible stress in concrete 0.48fck 16.8 Mpa
Permissible stress on raft 0.8fyk 400 Mpa
Design moment per unit width27.5 tm/m
Modular ratio 6.25
width 1 m
Ast Provided 3925 mm2/m
Eff Depth 917 mm
NA depth 189.95 mm
Eff moment of inertia 1.55*10^10 mm4
Section modulus of concrete 8.18*10^7 mm3
Section modulus of reinforcement 2.11*10^7 mm3
Stress in concrete 3.36 Mpa ok
Stress in reinforcement 81.26 Mpa ok
2.Difference between free pier and fixed pier
The pier which supports a free bearing is called free pier. In case of free pier transfer of axial forces only happens and movement in longitudinal direction is allowed and hence there is no longitudinal reactions. Hence horizontal force such as braking load, surcharge, seismic load, water pressure are not considered in free pier. Because of less horizontal force, the size of the foundation is considerably less to the fixed pier.
The pier which supports a fixed bearing is called fixed pier. In fixed pier, rotation and lateral movements are resisted and hence large amount of transverse and longitudinal moments occur. All the horizontal and vertical force are considered in fixed pier. The size of the foundation of the fixed pier is large comparatively to accommodate the heavy forces.
Longitudinal force due to friction (CL.211.5.1 IRC 6)
For simply supported span with fixed bearing on stiff support, horizontal force at the bearing level in longitudinal direction shall be greater of the two values given below: -
Fh= Applied horizontal forces
Rg= Reaction at the free end due to dead load
Rq= Reaction at free end due to live load
μ= Co-efficient of friction at movable bearing
One span loaded condition
Horizontal force = μ(Rh+Rq) Left span Right span
Rg 140.1 t 140.10 t
Rq 0 41.8 t
μ 0.03 0.05
Horizontal force dead load, μRg 4.20 t 7.00 t
Horizontal force live load, μRq 0 2.09 t
Applied horizontal force Fh 14.58 t
Fixed End
Total horizontal force= Maximum of the following two cases
Fh-μ(Rg+Rq) 10.38 t
Fh/2+μ(Rh+Rq) 11.49 t HL 11.49 t
Free End
Total Horizontal force
μ(Rg+Rq) 4.20 t HL 4.20 t
Two span loaded condition
Horizontal force = μ(Rh+Rq) Left span Right span
Rg 140.1 t 140.10 t
Rq 34.8 41.8 t
μ 0.03 0.05
Horizontal force dead load, μRg 4.20 t 7.00 t
Horizontal force live load, μRq 1.0 t 2.09 t
Applied horizontal force Fh 21.87 t
Fixed End
Total horizontal force= Maximum of the following two cases
Fh-μ(Rg+Rq) 16.62 t
Fh/2+μ(Rh+Rq) 16.18 t HL 16.62 t
Free End
Total Horizontal force
μ(Rg+Rq) 5.25 t HL 5.25 t
3. RCC detailings.
4. RCC design checks to be done in the ultimate & serviceability state
ULS
This limit state includes static equilibrium and failure of structure when acted by ultimate design load.
Limit state of strength
Limit state of equilibrium.
SLS
These limit state specifically deals with the condition of the structure subjected to the influence of serviceability design loads.
Limit state of internal stress (Rare combination),” Stress in concrete can be controlled”.
Limit state of crack control (Quasi permanent combination),” Crack control shall be considered. The allowable crack width is 0.3mm.
Limit state of deformation.
Limit state of vibration.
Limit state of fatigue.