Week 5 Challenge
Aim:- To design manually the open pier foundation using IRC-6 & IRC-112.
| Basic design details | |||
| 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 | |||||||||
 |
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| 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 | |||||||||
|
 |
||||||||||
| 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 | ||||||||||
|
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 | 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.