CoverDESIGN OF SKEW BRIDGEName of the work:-Construction of High Level Bridge on the R/F Yaganamilli to Komatilanka

Design PhilosophyDesign Philosophy:-The design of 5V-- 6.37m right span skew bridge with skew angle of 230 is carried asper the procedure out lined below:-Step1:-The design discharge was fixed after arriving discharge based on the following methods:-a.The Catchment area is plotted from the Topo sheet.Ryve's formula is used to arriveat the discharge duly taking the coefficient as 8.5.b.By Area-Velocity method using Manning's equation for arriving at the flow velocityand area by considering actual cross-section of the stream.Step2:-a.Hydraulic particulars like HFL,OFL are fixed as per the local enquiry.b.Bottom of deck level was fixed based on HFL and road formation levels on both sides.The vertical clearence and afflux are also verified.c.Ventway calculations are done for fixation of ventway.d.Normal scour depth with reference to HFL was calculated using Lacey's equationse.After arriving at the Maximum scour depth,bottom level of the foundation was fixedbelow the maximum scour depthStep3:-After arriving at bottom of deck level,bottom of foundation level and requiredventway,the dimensions of the bridge are finalised.The structural components are desined in the following manner:-a.As per the recommendations of IRC 6:2010,two lanes of IRC class A live load orone lane of IRC Class AA tracked or wheel loads,whichever produces severe effectis considered.b.Other loads and Load combinations are selected as per IRC 6:2010c.Based on the soil test reports,type of foundation was selected.d.The structural components like Abutments,piers,RCC Wing walls,raft foundation aredesigned as per the guide lines given in relevent IRC codes.e.The deck slab is proposed as per the MOST drawing Nos.BD 12-74&BD 13-74f.The dirt wall is proposed as per the drawings given in Plate No.7.25 ofIRC:SP20-2002(Rural roads manual)g.The pier cap is proposed as per the drawings given in Plate No.7.25 ofIRC:SP20-2002(Rural roads manual)

Structural Design_AbutDesign of Abutments for skew bridgeI)Design Parameters:-Clear Right Span=6.00mDeck slab length=7.322mWidth of the carriage way=7.50mLength of abutment=8.15mThickness of deck slab as per MOST Dg.BD 12-74=0.540mThickness of wearing coat=0.075mHeight of hand rail(Vertical)=0.845mSectional area of hand rail (vertical)=0.220sqmNo.of hand rails per span(Verticals)=10NosLength of hand rail(Horizontal)1.354mSectional area of hand rail (Horizontal)=0.020sqmNo.of hand rails per span(Horizontal)=16NosThickness of dirt wall=0.30mSectional area of dirt wall=0.370sqmSectional area of kerb=0.130sqmThickness of raft=0.60mHeight of abutments=3.202m(As per hydralic calculations)Top width of abutments=0.700mBottom width of abutments=2.40mSectional area of abutment section=4.963sqmBank side batter of abutment=0.000mStream side batter of abutment=1.700mWidth of 1st footing=3.00mThickness of 1st footing=0.50mCanal side offset of 1st footing wrt abutment=0.30mBank side offset of 1st footing wrt abutment=0.30mWidth of 2nd footing=3.30mThickness of 2nd footing=0.50mCanal side offset of 2nd footing wrt abutment=0.60mBank side offset of 2nd footing wrt abutment=0.30mWidth of 3rd footing=3.60mThickness of 3rd footing=0.50mCanal side offset of 3rd footing wrt abutment=0.90mBank side offset of 3rd footing wrt abutment=0.30mThickness of VRCC raft footing=0.60mOffset of top footing along width=0.00mOffset of 2nd footing along width=0.00mOffset of 3rd footing along width=0.00mType of bearings=No bearings proposedUnit weight of RCC (yrc)=25KN/cumUnit weight of PCC (ypc)=24KN/cumDensity of back fill soil behind abutments (y)=18KN/CumUnit weight of water (yw)=10KN/CumAngle of shearing resistance of back fill material(Q)=30Angle of face of wall supporting earth with horizontal(In degrees)(in clock wise direction)(a)=90Slope of back fill (b)=0Angle of wall friction (q)=15Height of surcharge considered (h3)=1.20mRoad crest level (RTL)=9.280mLow bed level (LBL)=5.62mHigh flood Level (HFL)=7.950mBottom of foundation level (BFL)=3.30mSafe Bearing Capacity of the soil (SBC)=15.00t/sqmCompressive strength of concrete for RCC Strip footing (fck)=25.00N/sqmmYield strength of steel (fy)=415.00N/sqmmCover to reinforcement=50.00mmII)General loading pattern:-As per IRC:6---2010,the following loadings are to be considered on the bridge or slabculvert:-1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Earth pressure9.Seismic force10.Water pressure forceAs per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.III)Loading on the slab culvert for design of abutments:-1.Dead Load:-i)Self wieght of the deck slab =402.80KNii)Self wieght of dirtwall over abutment =75.39KNiii)Self weight of wearing coat =55.95KNiv)Self weight of kerb =23.80KNv)Self weight of hand rails(verticals) =23.24KNvi)Self weight of hand rails(horizontals) =5.42KN586.59KNThere is no need to consider snow load as per the climatic conditionsSelf wieght of the abutments upto bottom most footing based on the preliminarysection assumed:-iv)Self wieght of the abutment section =970.76KNv)Self wieght of top footing =293.40KNvi)Self wieght of 2nd footing =322.74KNvii)Self wieght of 3rd footing =352.08KNviii)Self wieght of 4th footing =0.00KN1938.98KNix)Calculation of eccentricity of self weight of abutment w.r.t base of abutmentS.NoDescriptionLoad in KNDistance of centroid of load from toe of abutmentMoment1Back batter(W1)02.402Centre portion(W2)438.417842.05898.763Front batter(W3)532.364521.133603.17970.782361501.93Location of resultant from toe of abutment =1.55mEccentricity wrt centre of base of abutment =0.350mx)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 1st footingMoment1Back batter02.702Centre portion438.417842.351030.283Front batter532.364521.433762.8841st footing293.41.5440.11264.182362233.26Location of resultant from toe of abutment =1.77mEccentricity wrt centre of 1st footing=0.270mxi)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 2nd footingMoment1Back batter0302Centre portion438.417842.651161.813Front batter532.364521.733922.5941st footing293.41.80528.1252nd footing322.741.65532.521586.922363145.04Location of resultant from toe of abutment =1.98mEccentricity =0.330mxii)Calculation of eccentricity of self weight of abutment w.r.t bottom of 3rd footingS.NoDescriptionLoad in KNDistance from toe of 3rd footingMoment1Back batter03.302Centre portion438.417842.951293.333Front batter532.364522.0331082.341st footing293.42.1616.1452nd footing322.741.95629.3463rd footing352.08KN1.8633.741939.002364254.85Location of resultant from toe of abutment =2.19mEccentricity =0.39mxii)Calculation of eccentricity of self weight of abutment,1st,2nd & 3rd footings w.r.t bottom of 3rd footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 3rd footingMoment1Back batter0302Centre portion438.417842.651161.813Front batter532.364521.733922.5941st footing293.41.80528.1252nd footing322.741.65532.5263rd footing352.081.80633.741939.002363778.78Location of resultant from toe of abutment =1.95mEccentricity =0.150m2.Live Load:-As per clause 204.3 of IRC:6--2010,the bridges of carriage way width 7.5m shall be designed for IRCloadings of one lane of 70R or two lanes of Class A.GENERAL IRC Class-AA tracked vehicle loading PatternGENERAL IRC Class-AA wheeled vehicle loading PatternGENERAL IRC Class-A loading PatternThe IRC Class AA Tracked loading as per the drawing is consideredResultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment13501.63m568.75KNm23503.68m1286.25KNm700.0001855.00KNmDistance of centroid of forces from y-axis=2.650mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment13503.54m1239.00KNm23503.54m1239.00KNm7002478.00KNDistance of centroid of forces from x-axis=3.540mLocation of Resultant is as shown in the figure:-Reaction on the abutment =469.44KNThe IRC Class AA wheeled loading as per the drawing is consideredResultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment137.51.20m45.00KNm237.51.20m45.00KNm362.51.95m121.88KNm462.51.95m121.88KNm562.52.95m184.38KNm662.52.95m184.38KNm737.53.55m133.13KNm837.53.55m133.13KNm400.000968.75KNmDistance of centroid of forces from y-axis=2.422mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment137.52.921m109.54KNm262.52.921m182.56KNm362.52.921m182.56KNm437.52.921m109.54KNm537.51.721m64.54KNm662.51.721m107.56KNm762.51.721m107.56KNm837.51.721m64.54KNm400928.40KNDistance of centroid of forces from x-axis=2.321mLocation of Resultant is as shown in the figure:-Reaction on the abutment =329.38KNThe details of wheel loads for IRC Class A live load ,each axle wise are asgiven below:-Axle loadGround Contact Area(Tonnes)B(mm)W(mm)11.42505006.82003802.7150200Placement of two lanes of IRC Class A loading as shown below:-Resultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment1570.835m47.60KNm2570.835m47.60KNm3340.835m28.39KNm4572.625m149.63KNm5572.625m149.63KNm6342.625m89.25KNm7574.325m246.53KNm8574.325m246.53KNm9576.125m349.13KNm10576.125m349.13KNm524.0001703.38KNmDistance of centroid of forces from y-axis=3.251mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment1576.947m395.98KNm2576.947m395.98KNm3576.947m395.98KNm4576.947m395.98KNm5575.747m327.58KNm6575.747m327.58KNm7575.747m327.58KNm8575.747m327.58KNm9341.447m49.20KNm10341.447m49.20KNm5242992.63KNDistance of centroid of forces from x-axis=5.711mLocation of Resultant is as shown in the figure:-Calculation of reactions on abutments:-As per PCI bridge design code,apply correction factor for skew angle of bridge,as given below:-The reaction at the obtuse corner of skew slab is to be multiplied with correctionfactor1.0+{[Ld/12]0.5 +(Tan/6S)}for 600Where L =Effective spand =Depth of slabS =Width of slabHence correction factor =1.585112003Reaction due to loads Ra =310.20KNReaction due to loads = Rb =213.80KNThe critical reaction from the above loading patterns is469.44KNHence,the critical reaction is Ra =469.4KNThe corrected reaction at obtuse corner =744.11KNAssuming that the live load reaction acts at the centre of the contact area on the abutment,The eccentricty of the line of action of live load on top of 1st footing =0.685m-----do------ on top of 2nd footing =0.835m-----do------ on top of 3rd footing =0.985m-----do------ on top of raft =0.985mThe eccentricity in the other direction need not be considered due to high section modulus in transversedirection.3.Impact of vehicles:-As per Clause 208.3(a) of IRC:6--2010,impact allowance for the spans designed for class AA tracked vehicles,is increment of live load by a percent of5+2.5*(25-10)/4 =1437.500%Hence,the factor is0.14375Further as per clause 208.7(a),(b)&(c) of IRC:6--2010,the above impact factor shall be only50% for calculation of pressure on piers and abutments just below the level of bed block.Thereis no need to increase the live load below 3m depth.As such,the impact allowance for the top 3m of abutments will be0.071875For the remaining portion,impact need not be considered.4.Wind load:-Data:-Bredth of the Bridge cross section 'b' =8.15mDepth of the Bridge cross section 'd' =0.54mb/d ratio =15.0925925926Gust Factor 'G' =2Length of the bridge =6.74mHeight of the bridge in elevation =3.66mBasic wind speed =50.00m/s(From basic wind speed map of India)1)CALCULATION OF WIND FORCES ON SUPER STRUCTURE:-A)Transverse Wind force:-The drag coefficient for the deck slab bridges with b/d 10 is=1.10Hence,drag Coefficient for the bridge 'CD' ==1.10Area exposed to the wind A1 = Length of the bridgex(Ht.including ralings-Perforations)Area of perforations =3.22sqmNet exposed area 'A1' =21.45sqmHourly mean wind pressure ' Pz' for height upto 10m =1064.5N/sqm(Table 4 of IRC 6:2010)The transverse wind force FT = PzXA1XGXCD =50.23KNB)Longitudinal Wind force:-As per the clause 209.3.4. of IRC 6:2010,the longitudinal wind force FL shall be taken as 25% of thetransverse wind force,henceFL =12.56KNC)Upward/Downward Wind force:-The upward or downward windforce FV = PzxA3XGXCLA3 is plan area of the bridge =56.95sqmCL is lift coefficient =0.75Hence FV =90.94KN2)CALCULATION OF WIND FORCES ON LIVE LOAD OVER THE ROAD SURFACE:-As per the clause 209.3.2 of IRC 6:2010,the shall not be considered to be carryingany live load when the wind speed at deck level exceeds 36m/s.Hence,it is not necessary to consider the effect of wind on live load.3)CALCULATION OF WIND FORCES ON SUBSTRUCTURE:-The ratio of l/b =3.3958333333The ratio of h/b =1.3341666667Exposed area =4.963sqmThe drag coefficient for abutment CD from the0.8table 5 of IRC 6:2010 =The transverse wind force acting on the abutment only =8.45KNThe location of this force from top of raft =3.63mTranverse wind force transmitted to abutment from super structure =50.23KNThe location of this force from top of raft =6.24mTaking moments of the above forces about top of raft,the locationof resultant from the top of raft =5.86mHence,the final transverse wind force FT =58.68KNThe location of the wind force from the top of RCC raft footing =5.86m5.Water current force:-Water pressure considered on square ended abutments as per clause 210.2 ofIRC:6---2010 isP = 52KV2 =3.51Kg/m2.(where the value of 'K' is 1.5 for square ended abutments)Hence,the water current force =0.11KNPoint of action of water current force from the top of RCC raft footing =2.70m6.Tractive,braking effort of vehicles&frictional resistance of bearings:-The breaking effect of vehicles shall be 20% of live load acting in longitudinaldirection at 1.2m above road surface as per the clause 211.2 of IRC:6--2010.As no bearings are assumed in the present case,50% of the above longitudinalforce can be assumed to be transmitted to the supports of simply supported spans resting onstiff foundation with no bearings as per clause 211.5.1.2 of IRC:6---2010Hence,the longitudinal force due to braking,tractive or frictional resistance ofbearings transferred to abutments is74.41KNThe location of the tractive force from the top of RCC raft footing =6.82m7.Buoyancy :-As per clause 213.4 of IRC:6---2010,for abutments or piers of shallow depth,thedead weight of the abutment shall be reduced by wieght of equal volume of water upto HFL.The above reduction in self wieght will be considered assuming that the back fillbehind the abutment is scoured.For the preliminary section assumed,the volume of abutment section isi)Volume of abutment section =40.45Cumii)Volume of top footing =12.23Cumiii)Volume of 2nd footing =13.45Cumiv)Volume of 3rd footing =14.67Cumv)Volume of 4th footing =0.00Cum80.79CumReduction in self wieght =807.91KN8.Earth pressure :-As per clause 214.1 of IRC:6---2010,the abutments are to be designed for asurcharge equivalent to a back fill of hieght 1.20m behind the abutment.The coefficient of active earth pressure exerted by the cohesion less back fill onthe abutment as per the Coulomb's theory is given by'2Ka =Sin(a+Q)sina sin(a-q)sin(Q+q)sin(Q-b)sin(a+b)Sin(a+Q) =SIN[3.14*(76.06+30)/180] =0.961Sin(a-q) =SIN[3.14*(76.06-15)/180] =0.875Sina =SIN[3.14*(76.06)/180] =0.97Sin(Q+q) =SIN[3.14*(30+15)/180] =0.707Sin(Q-b) =SIN[3.14*(30-0)/180] =0.5Sin(a+b) =SIN[3.14*(76.06+0)/180] =0.97From the above expression,Ka =0.3The hieght of abutment above GL,as per the preliminary section assumed =3.202mHence,maximum pressure at the base of the wallPa =17.29KN/sqmThe pressure distribution along the height of the wall is as given below:-Surcharge load =6.48KN/sqm6.483.20217.296.48Area of the rectangular portion =20.75Area of the triangular portion =27.6848.43Taking moments of the areas about the toe of the wallS.NoDescriptionAreaLever armMoment1Rectangular20.751.60133.220752Triangular27.681.067333333329.543786666748.4362.7645366667Height from the bottom of the wall =1.30mThe active Earth pressure acts on the abutment as shown below:-0.70153.202m1.30m902.400Total earth pressure acting on the abutment P =394.71KNHorizontal component of the earth pressure Ph =381.27KNVertical component of the earth pressure Pv =102.11KNEccentricity of vertical component of earth pressure =1.20m9.Siesmic force :-As per clause 219.1.1(a) of IRC:6---2010 in all siesmic zones,the bridges and culverts of spans upto 10m neednot be designed for siesmic forces.As the span of the bridge is only 6.37m,it need not be designed for siesmic forces.10.Water pressure force:-The water pressure distribution on the abutment is as given below:-HFL7.95m4.65BFL3.30m46.50kn/sqmTotal horizontal water pressure force =881.12KNThe above pressure acts at height of H/3 =1.55mIV)Check for stresses for abutments&footings:-a)Load Envelope-I:-(The Canal is dry,back fill scoured with live load on span)i)On top of RCC raft footingThe following co-ordinates are assumed:-a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehiclesVertical forces acting on the abutment (P) composes of the following componentsS.NoType of loadIntensity in KNEccentricty about x-axis(m)Eccentricty about y-axis(m)1Reaction due to dead load from super structure586.59KN0.000.002Self wieght of abutment&footings1939.00KN0.1500.0003Reaction due to live load with impact factor---(Wheel loads)851.08KN-0.9850.0004Upward wind load-90.940.000.003285.73Horizontal forces acting/transferred on the abutment (H) composes of the following componentsS.NoType of loadIntensity in KNDirection x or yLocation(Ht.from the section considered).(m)1Wind load58.68KNx-Direction5.862Tractive,Braking&Frictional resistance of bearings74.41KNy-Direction6.82Check for stresses:-About x-axis:-Breadth of 3rd footing b =8.15mDepth of 3rd footing d =3.60mArea of the footing = A =29.34m2Section modulus of bottom footing(1/6)bd2 =17.60m3about x-axis --Zx =For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2i.e,4000KN/sqmFor M15 grade of concrete permissible tensile stress in bending tension is -2N/mm2i.e,-2000KN/sqmS.NoType of loadIntensity in KN (P)Eccentricity/Lever armStress at heelP/A(1+6e/d)Vertical loads:-(Stress = P/A(1+6e/d)1Reaction due to dead load from super structure586.59KN0.0019.992Self wieght of abutment&footings1939.00KN0.1582.613Reaction due to live load with impact factor851.08KN-0.985-18.614Upward wind load-90.94KN0.00-3.10Horizontal loads:- (Stress = M/Z)5Tractive,Braking&Frictional resistance of bearings74.41KN6.82-28.8352.06S.NoType of loadIntensity in KN (P)EccentricityStress at toeP/A(1+6e/d)Vertical loads:-(Stress = P/A(1+6e/d)1Reaction due to dead load from super structure586.59KN0.0019.992Self wieght of abutment&footings1939.00KN-0.1558.793Reaction due to live load with impact factor851.08KN0.98550.044Upward wind load-90.94KN0.00-3.1Horizontal loads:- (Stress = M/Z)5Tractive,Braking&Frictional resistance of bearings74.41KN6.8228.83154.55Stress at heel =P/A(1+6e/d)+M/Z =52.06KN/Sqm>-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =154.55KN/Sqm-2000KN/sqm.edge =Hence safe.Stress at down stream sideP/A(1+6e/d)+M/Z =120.62KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =162.14KN/Sqm-2000KN/sqm.edge =Hence safe.Stress at down stream sideP/A(1+6e/d)+M/Z =117.68KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =182.86KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =115.37KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =200.16KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =128.11KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/b)+M/Z =25.3KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =67.56KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =24.35KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =65.27KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =44.66KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =63.21KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =84.67KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge of abutment =P/A(1+6e/d)+M/Z =77.89KN/Sqm 2.0Hence safe(As per clause 706.3.4 of IRC:78-2000)Check for stability against sliding:-Total vertical load acting on the base of the abutment Vb =2419.59KNTotal sliding force,ie,horizontal load on the abutment Hb =514.37KNCoefficient of friction between concrete surfaces =0.80Factor of safety against sliding Fs =3.7632286461> 1.5Hence safe(As per clause 706.3.4 of IRC:78-2000)b)Load Envelope-II:-(The Canal is running upto HFL with no live load on span)The following co-ordinates are assumed:-a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehiclesVertical load acting on the abutment (P) composes of the following componentsS.NoType of loadIntensity in KNEccentricty about x-axis(m)Eccentricty about y-axis(m)1Reaction due to dead load from super structure586.59KN0.000.00Self wieght of abutments970.76KNReduction in self weight due to buoyancy-404.50KN2Net self wieght566.26KN0.3500.0003Vertical component of Active Earth pressure102.111.2000.005Upward wind force-90.94KN0.000.00Horizontal load acting/transferred on the abutment (H) composes of the following componentsS.NoType of loadIntensity in KNDirection x or yLocation(Ht.from the section considered).(m)1Wind load58.68KNx-Direction4.362Tractive,Braking&Frictional resistance of bearings0.00KNy-Direction0.003Active Earth pressure force381.27KNy-Direction1.304Force due to water pressure881.12KNy-Direction0.05Check for stability against over turning:-Taking moments of all the overturning forces about toe of the abutment wrt x-axis,Moment due to tractive,braking&frictional resistance of bearings =0.00Kn-mMoment due to active earth pressure force =494.12Kn-mTotal overturning moment =494.12Kn-mTaking moments of all the restoring forces about toe of the abutment wrt x-axis,Moment due to self weight of abutment =877.70Kn-mMoment due to water pressure force on the abutment =44.06Kn-mMoment due to vertical component of active earth pressure =245.06Kn-mTotal Restoring moment =1166.82Kn-mFactor of safety =2.361402637> 2.0Hence safe(As per clause 706.3.4 of IRC:78-2000)Check for stability against sliding:-Total vertical load acting on the base of the abutment Vb =1458.54KNTotal sliding force,ie,horizontal load on the abutment Hb =381.27KNCoefficient of friction between concrete surfaces =0.80Factor of safety against sliding Fs =3.0603591321> 1.5Hence safe(As per clause 706.3.4 of IRC:78-2000)

Pier_DesignDesign of pier for skew bridgeI)Design Parameters:-Clear Right Span=6.00mDeck slab length=7.387mWidth of the carriage way=7.50mLength of pier=8.15mThickness of deck slab as per MOST Dg.BD 12-74=0.540mThickness of wearing coat=0.075mHeight of hand rail(Vertical)=0.845mSectional area of hand rail (vertical)=0.220sqmNo.of hand rails per span(Verticals)=10NosLength of hand rail(Horizontal)1.354mSectional area of hand rail (Horizontal)=0.020sqmNo.of hand rails per span(Horizontal)=16NosThickness of dirt wall=0.30mSectional area of dirt wall=0.240sqmSectional area of kerb=0.130sqmThickness of raft=0.60mHeight of piers=3.202m(As per hydralic calculations)Top width of pier=0.800mBottom width of pier=1.20mSectional area of pier section=3.202sqmOne side batter of pier=0.200mOther side batter of pier=0.200mWidth of 1st footing=1.80mThickness of 1st footing=0.50mOne side offset of 1st footing wrt pier=0.30mOther side offset of 1st footing wrt pier=0.30mWidth of 2nd footing=2.40mThickness of 2nd footing=0.50mOne side offset of 2nd footing wrt pier=0.60mOther side offset of 2nd footing wrt pier=0.60mWidth of 3rd footing=3.00mThickness of 3rd footing=0.50mOne side offset of 3rd footing wrt pier=0.90mOther side offset of 3rd footing wrt pier=0.90mThickness of VRCC raft footing=0.60mOffset of top footing along width=0.00mOffset of 2nd footing along width=0.00mOffset of 3rd footing along width=0.00mType of bearings=No bearings proposedUnit weight of RCC (yrc)=25KN/cumUnit weight of PCC (ypc)=24KN/cumUnit weight of water (yw)=10KN/CumRoad crest level (RTL)=9.280mLow bed level (LBL)=5.62mHigh flood Level (HFL)=7.950mBottom of foundation level (BFL)=3.30mSafe Bearing Capacity of the soil (SBC)=15.00t/sqmCompressive strength of concrete for VRCC raft footing (fck)=25.00N/sqmmYield strength of steel (fy)=415.00N/sqmmCover to reinforcement=50.00mmII)General loading pattern:-As per IRC:6---2010,the following loadings are to be considered on the bridge or slabculvert:-1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Seismic force9.Water pressure forceAs per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.III)Loading on the slab culvert for design of piers:-1.Dead Load:-i)Self wieght of the deck slab =812.75KNii)Self wieght of pier cap over pier =48.90KNiii)Self weight of wearing coat =112.88KNiv)Self weight of kerb =48.02KNv)Self weight of hand rails(verticals) =46.48KNvi)Self weight of hand rails(horizontals) =10.83KN1079.86KNThere is no need to consider snow load as per the climatic conditionsSelf wieght of the piers upto bottom most footing based on the preliminarysection assumed:-iv)Self wieght of the pier section =626.31KNv)Self wieght of top footing =176.04KNvi)Self wieght of 2nd footing =234.72KNvii)Self wieght of 3rd footing =293.40KNviii)Self wieght of 4th footing =0.00KN1330.47KNix)Calculation of eccentricity of self weight of pier w.r.t base of pierS.NoDescriptionLoad in KNDistance of centroid of load from toe of pierMoment1Back batter(W1)62.631121.06766.832Centre portion(W2)501.048960.6300.633Front batter(W3)62.631120.1338.33626.3112375.79Location of resultant from toe of pier =0.60mEccentricity wrt centre of base of pier =0.000mx)Calculation of eccentricity of self weight of pier&1st footing w.r.t bottom of 1st footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 1st footingMoment1Back batter62.631121.36785.622Centre portion501.048960.9450.943Front batter62.631120.43327.1241st footing176.040.9158.44802.3512722.12Location of resultant from toe of pier =0.90mEccentricity wrt centre of 1st footing=0.000mxi)Calculation of eccentricity of self weight of pier,1st&2nd footings w.r.t bottom of 2nd footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 2nd footingMoment1Back batter62.631121.667104.412Centre portion501.048961.2601.263Front batter62.631120.73345.9141st footing176.041.20211.2552nd footing234.721.20281.661037.07121244.49Location of resultant from toe of pier =1.20mEccentricity =0.000mxii)Calculation of eccentricity of self weight of abutment w.r.t bottom of 3rd footingS.NoDescriptionLoad in KNDistance from toe of 3rd footingMoment1Back batter62.631121.967123.22Centre portion501.048961.5751.573Front batter62.631121.03364.741st footing176.041.5264.0652nd footing234.721.5352.0863rd footing293.40KN1.5440.11330.47121995.71Location of resultant from toe of abutment =1.50mEccentricity =0.00mxii)Calculation of eccentricity of self weight of pier,1st,2nd & 3rd footings w.r.t bottom of 3rd footingS.NoDescriptionLoad in KNDistance of centroid of load from toe of 3rd footingMoment1Back batter62.631121.967123.22Centre portion501.048961.5751.573Front batter62.631121.03364.741st footing176.041.50264.0652nd footing234.721.50352.0863rd footing293.41.50440.11330.47121995.71Location of resultant from toe of pier =1.50mEccentricity =0.000m2.Live Load:-As per clause 204.3 of IRC:6--2010,the bridges of carriage way width 7.5m shall be designed for IRCloadings of one lane of 70R or two lanes of Class A.GENERAL IRC Class-AA tracked vehicle loading PatternGENERAL IRC Class-AA wheeled vehicle loading PatternGENERAL IRC Class-A loading PatternThe IRC Class AA Tracked loading as per the drawing is consideredResultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment13501.625m568.75KNm23503.675m1286.25KNm700.0001855.00KNmDistance of centroid of forces from y-axis=2.650mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment13504.198m1469.30KNm23504.198m1469.30KNm7002938.60KNDistance of centroid of forces from x-axis=4.198mLocation of Resultant is as shown in the figure:-Reaction on the abutment =640.70KNThe IRC Class AA wheeled loading as per the drawing is consideredResultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment137.51.20m45.00KNm237.51.20m45.00KNm362.51.95m121.88KNm462.51.95m121.88KNm562.52.95m184.38KNm662.52.95m184.38KNm737.53.55m133.13KNm837.53.55m133.13KNm400.000968.75KNmDistance of centroid of forces from y-axis=2.422mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment137.55.310m199.13KNm262.55.310m331.88KNm362.55.310m331.88KNm437.55.310m199.13KNm537.54.110m154.13KNm662.54.110m256.88KNm762.54.110m256.88KNm837.54.110m154.13KNm4001884.00KNDistance of centroid of forces from x-axis=4.710mLocation of Resultant is as shown in the figure:-Reaction on the abutment =400.00KNThe details of wheel loads for IRC Class A live load ,each axle wise are asgiven below:-Axle loadGround Contact Area(Tonnes)B(mm)W(mm)11.42505006.82003802.7150200Placement of two lanes of IRC Class A loading as shown below:-Resultant live load:-Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)Taking moments of all the forces w.r.t y-axisS.NoWheel Load/UDL in KNDistance from Y-axisMoment1570.835m47.60KNm2570.835m47.60KNm3340.835m28.39KNm4572.625m149.63KNm5572.625m149.63KNm6342.625m89.25KNm7574.325m246.53KNm8574.325m246.53KNm9576.125m349.13KNm10576.125m349.13KNm524.0001703.38KNmDistance of centroid of forces from y-axis=3.251mEccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)Taking moments of all the forces w.r.t x-axisS.NoLoad in KNDistance from X-axisMoment1576.947m395.98KNm2576.947m395.98KNm3576.947m395.98KNm4576.947m395.98KNm5575.747m327.58KNm6575.747m327.58KNm7575.747m327.58KNm8575.747m327.58KNm9341.447m49.20KNm10341.447m49.20KNm5242992.63KNDistance of centroid of forces from x-axis=5.711mLocation of Resultant is as shown in the figure:-Calculation of reactions on abutments:-As per PCI bridge design code,apply correction factor for skew angle of bridge,as given below:-The reaction at the obtuse corner of skew slab is to be multiplied with correctionfactor1.0+{[Ld/12]0.5 +(Tan/6S)}for 600Where L =Effective spand =Depth of slabS =Width of slabHence correction factor =1.5876542287Reaction due to loads Ra =478.36KNReaction due to loads = Rb =45.64KNThe critical reaction from the above loading patterns is640.70KNHence,the critical reaction is Ra =640.7KNThe corrected reaction at obtuse corner =1017.21KNAssuming that the live load reaction acts at the centre of the contact area on the pier,The eccentricty of the line of action of live load on top of 1st footing =0.215m-----do------ on top of 2nd footing =0.215m-----do------ on top of 3rd footing =0.215m-----do------ on top of raft =0.215mThe eccentricity in the other direction need not be considered due to high section modulus in transversedirection.3.Impact of vehicles:-As per Clause 208.3(a) of IRC:6--2010,impact allowance for the spans designed for class AA tracked vehicles,is increment of live load by a percent of5+2.5*(25-10)/4 =1437.500%Hence,the factor is0.14375Further as per clause 208.7(a),(b)&(c) of IRC:6--2010,the above impact factor shall be only50% for calculation of pressure on piers and abutments just below the level of bed block.Thereis no need to increase the live load below 3m depth.As such,the impact allowance for the top 3m of abutments will be0.071875For the remaining portion,impact need not be considered.4.Wind load:-Data:-Bredth of the Bridge cross section 'b' =8.15mDepth of the Bridge cross section 'd' =0.54mb/d ratio =15.0925925926Gust Factor 'G' =2Length of the bridge =6.74mHeight of the bridge in elevation =3.66mBasic wind speed =50.00m/s(From basic wind speed map of India)1)CALCULATION OF WIND FORCES ON SUPER STRUCTURE:-A)Transverse Wind force:-The drag coefficient for the deck slab bridges with b/d 10 is=1.10Hence,drag Coefficient for the bridge 'CD' ==1.10Area exposed to the wind A1 = Length of the bridgex(Ht.including ralings-Perforations)Area of perforations =3.22sqmNet exposed area 'A1' =21.45sqmHourly mean wind pressure ' Pz' for height upto 10m =1064.5N/sqm(Table 4 of IRC 6:2010)The transverse wind force FT = PzXA1XGXCD =50.23KNB)Longitudinal Wind force:-As per the clause 209.3.4. of IRC 6:2010,the longitudinal wind force FL shall be taken as 25% of thetransverse wind force,henceFL =12.56KNC)Upward/Downward Wind force:-The upward or downward windforce FV = PzxA3XGXCLA3 is plan area of the bridge =56.95sqmCL is lift coefficient =0.75Hence FV =90.94KN2)CALCULATION OF WIND FORCES ON LIVE LOAD OVER THE ROAD SURFACE:-As per the clause 209.3.2 of IRC 6:2010,the shall not be considered to be carryingany live load when the wind speed at deck level exceeds 36m/s.Hence,it is not necessary to consider the effect of wind on live load.3)CALCULATION OF WIND FORCES ON SUBSTRUCTURE:-The ratio of l/b =6.7916666667The ratio of h/b =2.6683333333Exposed area =3.202sqmThe drag coefficient for pier CD from the0.8table 5 of IRC 6:2010 =The tranvese wind force acting on the pier only =5.45KNThe location of this force from top of raft =3.63mTranverse wind force transmitted to pier from super structure =50.23KNThe location of this force from top of raft =6.24mTaking moments of the above forces about top of raft,the locationof resultant from the top of raft =5.98mHence,the final transverse wind force on pier FT =55.68KNThe location of the wind force from the top of RCC raft footing =5.98m5.Water current force:-Water pressure considered on square ended piers as per clause 210.2 ofIRC:6---2010 isP = 52KV2 =3.51Kg/m2.(where the value of 'K' is 1.5 for square ended piers)Hence,the water current force =0.07KNPoint of action of water current force from the top of RCC raft footing =2.70m6.Tractive,braking effort of vehicles&frictional resistance of bearings:-The breaking effect of vehicles shall be 20% of live load acting in longitudinaldirection at 1.2m above road surface as per the clause 211.2 of IRC:6--2010.As no bearings are assumed in the present case,50% of the above longitudinalforce can be assumed to be transmitted to the supports of simply supported spans resting onstiff foundation with no bearings as per clause 211.5.1.2 of IRC:6---2010Hence,the longitudinal force due to braking,tractive or frictional resistance ofbearings transferred to pier is101.72KNThe location of the tractive force from the top of RCC raft footing =6.82m7.Buoyancy :-As per clause 213.4 of IRC:6---2010,for abutments or piers of shallow depth,thedead weight of the pier shall be reduced by wieght of equal volume of water upto HFL.For the preliminary section assumed,the volume of pier section isi)Volume of abutment section =26.10Cumii)Volume of top footing =7.34Cumiii)Volume of 2nd footing =9.78Cumiv)Volume of 3rd footing =12.23Cumv)Volume of 4th footing =0.00Cum55.44CumReduction in self wieght =554.36KN9.Siesmic force :-As per clause 219.1.1(a) of IRC:6---2010 in all siesmic zones,the bridges and culverts of spans upto 10m neednot be designed for siesmic forces.As the span of the bridge is only 6.37m,it need not be designed for siesmic forces.10.Water pressure force:-The water pressure distribution on the pier is as given below:-HFL7.950m4.65BFL3.30m46.50kn/sqmAs the pier is subjected to water pressure force from both the sides simultaneously,thenet water pressure will be zero.Hence,Total horizontal water pressure force =0.00KNThe above pressure acts at height of H/3 =0.00mIV)Check for stresses for piers&footings:-a)Load Envelope-I:-(The Canal is dry,with live load on span)i)On top of RCC raft footingThe following co-ordinates are assumed:-a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehiclesVertical forces acting on the pier (P) composes of the following componentsS.NoType of loadIntensity in KNEccentricty about x-axis(m)Eccentricty about y-axis(m)1Reaction due to dead load from super structure1079.86KN0.000.002Self wieght of pier&footings1330.47KN0.0000.0003Reaction due to live load with impact factor---(Wheel loads)1163.43KN-0.2150.0004Upward wind load-90.940.000.003482.83Horizontal forces acting/transferred on the pier (H) composes of the following componentsS.NoType of loadIntensity in KNDirection x or yLocation(Ht.from the section considered).(m)1Wind load55.68KNx-Direction5.982Tractive,Braking&Frictional resistance of bearings101.72KNy-Direction6.82Check for stresses:-About x-axis:-Breadth of 3rd footing b =8.15mDepth of 3rd footing d =3.00mArea of the footing = A =24.45m2Section modulus(1/6)bd2 =12.23m3about x-axis --Zx =For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2i.e,4000KN/sqmFor M15 grade of concrete permissible tensile stress in bending tension is -2N/mm2i.e,-2000KN/sqmS.NoType of loadIntensity in KN (P)Eccentricity/Lever armStress at heelP/A(1+6e/d)Vertical loads:-(Stress = P/A(1+6e/d)1Reaction due to dead load from super structure1079.86KN0.0044.172Self wieght of pier&footings1330.47KN0.0054.423Reaction due to live load with impact factor1163.43KN-0.21527.124Upward wind load-90.94KN0.00-3.72Horizontal loads:- (Stress = M/Z)5Tractive,Braking&Frictional resistance of bearings101.72KN6.82-56.7565.24S.NoType of loadIntensity in KN (P)EccentricityStress at toeP/A(1+6e/d)Vertical loads:-(Stress = P/A(1+6e/d)1Reaction due to dead load from super structure1079.86KN0.0044.172Self wieght of pier&footings1330.47KN0.0054.423Reaction due to live load with impact factor1163.43KN0.21555.124Upward wind load-90.94KN0.00-3.72Horizontal loads:- (Stress = M/Z)5Tractive,Braking&Frictional resistance of bearings101.72KN6.8256.75206.74Stress at heel =P/A(1+6e/d)+M/Z =65.24KN/Sqm>-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =206.74KN/Sqm-2000KN/sqm.edge =Hence safe.Stress at down stream sideP/A(1+6e/d)+M/Z =152.48KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =277.2KN/Sqm-2000KN/sqm.edge =Hence safe.Stress at down stream sideP/A(1+6e/d)+M/Z =174.54KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =392.76KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =215.33KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =688.66KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =302.9KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/b)+M/Z =72.19KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =82.23KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =81.49KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =92.98KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =99.31KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge =P/A(1+6e/d)+M/Z =113.24KN/Sqm-2000KN/sqm.Hence safe.Stress at toe =P/A(1+6e/d)+M/Z =148.98KN/Sqm-2000KN/sqm.Hence safe.Stress at down stream sideedge of pier =P/A(1+6e/d)+M/Z =167.77KN/Sqm 2.0Hence safe(As per clause 706.3.4 of IRC:78-2000)Check for stability against sliding:-Total vertical load acting on the base of the pier Vb =2778.66KNTotal sliding force,ie,horizontal load on the pier Hb =157.40KNCoefficient of friction between concrete surfaces =0.80Factor of safety against sliding Fs =14.12272551> 1.5Hence safe(As per clause 706.3.4 of IRC:78-2000)b)Load Envelope-III:-(The Canal is full ,with live load on span)The following co-ordinates are assumed:-a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehiclesVertical load acting on the pier (P) composes of the following componentsS.NoType of loadIntensity in KNEccentricty about x-axis(m)Eccentricty about y-axis(m)1Reaction due to dead load from super structure1079.86KN0.000.00Self wieght of pier626.31KNReduction in self weight due to buoyancy-261.00KN2Net self wieght365.31KN0.0000.0003Reaction due to live load with impact factor1017.21KN-0.2150.0004Upward wind force-90.94KN0.000.00Horizontal load acting/transferred on the pier (H) composes of the following componentsS.NoType of loadIntensity in KNDirection x or yLocation(Ht.from the section considered).(m)1Wind load55.68KNx-Direction4.482Tractive,Braking&Frictional resistance of bearings101.72KNy-Direction5.323Force due to water pressure0.00KNy-Direction-1.50Check for stability against over turning:-Taking moments of all the overturning forces about toe of the pier wrt x-axis,Moment due to tractive,braking&frictional resistance of bearings =541.16Kn-mTotal overturning moment =541.16Kn-mTaking moments of all the restoring forces about toe of the pier wrt x-axis,Moment due to self weight of pier =219.19Kn-mMoment due to live load reaction =391.63Kn-mMoment due to dead load from super structure =647.92Kn-mTotal Restoring moment =1258.73Kn-mFactor of safety =2.3259992432> 2.0Hence safe(As per clause 706.3.4 of IRC:78-2000)Check for stability against sliding:-Total vertical load acting on the base of the pier Vb =1291.58KNTotal sliding force,ie,horizontal load on the pier Hb =101.72KNCoefficient of friction between concrete surfaces =0.80Factor of safety against sliding Fs =10.157823715> 1.5Hence safe(As per clause 706.3.4 of IRC:78-2000)

Wing wallDESIGN OF CANTILEVER WING WALLData:-Height of Retaining wall(h) =4.20mHeight of wall above G.L=4.20mHeight of wall below G.L=0.00mDensity of back fill soil&material in toe portion(y) =1800Kg/CumGrade of concrete =M20Grade of steel =Fe415Ground water Table level =Angle of shearing resistance of back fill material&material at toe portion(Q) =30Angle of face of wall supporting earth with horizontal(a)(In degrees)87.32(in clock wise direction)Slope of back fill(b) =0Angle of wall friction (q) =15Undrained Cohesion ( c) =0Kg/sqmSafe bearing capacity(SBC) =11000Kg/sqmSurcharge over the back fill(s) =0.60m(Assumed)Characteristic compressive strength =25N/sqmmTensile strength of steel =415N/sqmmUnit weight of RCC =2500Kg/CumUnit weight of PCC =2400Kg/CumCoefficient of active earth pressure by Coulomb's theory2Ka =Sin(a+Q)sina sin(a-q)sin(Q+q)sin(Q-b)sin(a+b)Sin(a+Q) =SIN[3.14*(88+30)/180] =0.887Sin(a-q) =SIN[3.14*(87.55-15)/180] =0.954Sina =SIN[3.14*(87.55)/180] =0.999Sin(Q+q) =SIN[3.14*(30+15)/180] =0.707Sin(Q-b) =SIN[3.14*(30-0)/180] =0.5Sin(a+b) =SIN[3.14*(87.55+0)/180] =0.999From the above expression,Ka =0.32Dimensions of the Cantilever wall(Assumed for preliminary design):-Thickness of base slab =0.40mWidth of the heel slab =2.00mThickness of stem at bottom =0.40mThickness of stem at top =0.20mLength of the toe =1.00m4.20mF GC1.00m2.00mEarth pressure at top including surcharge = Kays =345.6Kg/sqmEarth pressure at bottom including surcharge = Kay(s+h) =2764.8Kg/sqmPressure distribution is as shown below:-345.64.20m2764.8345.6Area of the rectangular portion =1451.52Area of the triangular portion =5806.087257.6Taking moments of the areas about the toe of the wallS.NoDescriptionAreaLever armMoment1Rectangular1451.522.13048.1922Triangular5806.081.48128.5127257.6011176.704Height from the bottom of the wall =1.54mThe active Earth pressure acts on the abutment as shown below:-0.2017.684.200m1.54m87.320.40m0.07Total earth pressure acting on the wall per 1m length P =7257.60KgHorizontal component of the earth pressure Ph =6915.15KgVertical component of the earth pressure Pv =2203.06KgEccentricity of vertical component of earth pressure =0.13mTotal earth pressure =7257.6Kg/mIt acts at a hieght of1.54mfrom the baseStability calculations:-Load(Kg)Lever arm about CMoment(Kg-m)Weight of the rectangular portion of stem =2100.00Kg1.102310.00Weight of the rectangular portion of stem =1050.00Kg1.271330.00Wieght of base slab =3000.00Kg1.5004500.00Wieght of soil on heel including surcharge =14688.00Kg2.0029376.00Vertical component of earth pressure =2203.06Kg1.072357.2723041.06Kg39873.27Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.Horizontal earth pressure force =6915.151.54m-10649.3329223.94Lever arm x =M=1.27mVEccentricuty e = b/2-x =0.23m1.5 Hence,the structure is safeMoment of overturning force,ie,Horizontal component of earth pressure about toe 'C' =10649.33KgmMoment of restoring forces about toe 'C' =39873.27KgmFactor of safety against overturning =3.74>2.0 Hence safe.Design of heel:-Length of heel =1.60mDownward load intensity due to self weight of base slab =3000.00Kg/mDownward load intensity due to soil including surcharge =14688.00Kg/mTOTAL17688.00Kg/mThe upward pressure distribution below the base slab is as given below:-FG4147.39Kg/sqm11213.311.00m0.40m1.60mThe upward pressure intensity at point 'F' is=8858.00Kg/sqmThe upward pressure intensity at point 'G' is=7915.88Kg/sqmTotal upward pressure force on heel portion due to soil reaction =9650.62Kg/mThe distance of centroid of upward soil reaction from 'G' is =0.72mThe distance of centroid of downward load intensity from 'G' is =0.80mResultant moment =7233.85Kg-m/mFactored bending moment Mu =10850.78KgmEffective depth required d =Mu/0.138fckb =177.35mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =0.928From table 2 of SP 16,percentage of steel required =0.276Area of steel required =943.92sqmmHence provide 12mm dia HYSD bars@ 110mm c/c spacingHence Ast provided =1027.64sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =120.56KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.35N/sqmm0.35Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =600.00sqmmTaking 10mm dia HYSD bars,the spacing comes to 150mmHence provide 10mm dia bars @ 150mm c/cDesign of wall or stem:-Factored bending moment Mu =15974.00KgmEffective depth required d =Mu/0.138fckb =215.18mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =1.366From table 2 of SP 16,percentage of steel required =0.407Area of steel required =1391.94sqmmHence provide 16mm dia HYSD bars@ 125mm c/c spacingHence Ast provided =1607.68sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =103.73KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.30N/sqmm0.3Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =450.00sqmmProvide 1/3rd of above reinforcement on earthen side =150.00sqmm167.4666666667Provide 8mm dia @ 200mm c/c on earthen sideProvide 2/3rd of above reinforcement on other side =300.00sqmm334.9333333333Provide 8mm dia @ 150mm c/c on other sideProvide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rods287.0857142857Design of Toe:-Length of toe =1.00mDownward load intensity due to self weight =3000.00Kg/mDownward load intensity due to soil including surcharge =0.00Kg/mTOTAL3000.00Kg/mThe upward pressure distribution below the base slab is as given below:-FG4147.39Kg/sqm11213.311.00m0.40m1.60mThe upward pressure intensity at point 'F' is=8858.00Kg/sqmThe upward pressure intensity at end of toe is=11213.31Kg/sqmTotal upward pressure force on heel portion due to soil reaction =10035.66Kg/mThe distance of centroid of upward soil reaction from 'F' is =0.52mThe distance of centroid of downward load intensity from 'G' is =0.50mResultant moment =3714.10Kg-m/mFactored bending moment Mu =5571.16KgmEffective depth required d =Mu/0.138fckb =127.08mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =0.476From table 2 of SP 16,percentage of steel required =0.14Min.percentage of steel as per IS 456 =0.15Area of steel required =513.00sqmmHence provide 12mm dia HYSD bars@ 150mm c/c spacingHence Ast provided =753.60sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =105.53KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.31N/sqmm0.32Hence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =600.00sqmmTaking 10mm dia HYSD bars,the spacing comes to 150mmHence,provide 10mm dia bars @ 150mm c/c

Retaining wallDESIGN OF CANTILEVER RETAINING WALLData:-Height of Retaining wall(h) =4.39mHeight of wall above G.L=4.39mHeight of wall below G.L=0.00mDensity of back fill soil&material in toe portion(y) =1800Kg/CumGrade of concrete =M20Grade of steel =Fe415Ground water Table level =Angle of shearing resistance of back fill material&material at toe portion(Q) =30Angle of face of wall supporting earth with horizontal(a)(In degrees)87.44(in clock wise direction)Slope of back fill(b) =0Angle of wall friction (q) =15Undrained Cohesion ( c) =1600Kg/sqmSafe bearing capacity(SBC) =6500Kg/sqmSurcharge over the back fill(s) =0.60m(Assumed)Characteristic compressive strength =20N/sqmmTensile strength of steel =415N/sqmmUnit weight of RCC =2500Kg/CumUnit weight of PCC =2400Kg/CumCoefficient of active earth pressure by Coulomb's theory2Ka =Sin(a+Q)sina sin(a-q)sin(Q+q)sin(Q-b)sin(a+b)Sin(a+Q) =SIN[3.14*(87.44+30)/180] =0.888Sin(a-q) =SIN[3.14*(87.44-15)/180] =0.953Sina =SIN[3.14*(87.44)/180] =0.999Sin(Q+q) =SIN[3.14*(30+15)/180] =0.707Sin(Q-b) =SIN[3.14*(30-0)/180] =0.5Sin(a+b) =SIN[3.14*(87.44+0)/180] =0.999From the above expression,Ka =0.32Dimensions of the Cantilever wall(Assumed for preliminary design):-Thickness of base slab =0.40mWidth of the heel slab =2.50mThickness of stem at bottom =0.40mThickness of stem at top =0.20mLength of the toe =1.20m4.39mF GC1.20m2.50mEarth pressure at top including surcharge = Kays =345.6Kg/sqmEarth pressure at bottom including surcharge = Kay(s+h) =2874.2Kg/sqmPressure distribution is as shown below:-345.64.39m2874.2345.6Area of the rectangular portion =1517.18Area of the triangular portion =6308.967826.14Taking moments of the areas about the toe of the wallS.NoDescriptionAreaLever armMoment1Rectangular1517.182.1953330.21012Triangular6308.961.46333333339232.11146666677826.1412562.3215666667Height from the bottom of the wall =1.61mThe active Earth pressure acts on the abutment as shown below:-0.2017.564.390m1.61m87.440.40m0.07Total earth pressure acting on the wall per 1m length P =7826.14KgHorizontal component of the earth pressure Ph =7461.82KgVertical component of the earth pressure Pv =2360.02KgEccentricity of vertical component of earth pressure =0.13mTotal earth pressure =7826.1Kg/mIt acts at a hieght of1.61mfrom the baseStability calculations:-Load(Kg)Lever arm about CMoment(Kg-m)Weight of the rectangular portion of stem =2195.00Kg1.302853.50Weight of the rectangular portion of stem =1097.50Kg1.471609.67Wieght of base slab =3700.00Kg1.8506845.00Wieght of soil on heel including surcharge =19760.40Kg2.4548412.98Vertical component of earth pressure =2360.02Kg1.272997.2329112.92Kg62718.38Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.Horizontal earth pressure force =7461.821.61m-11977.5350740.85Lever arm x =M=1.74mVEccentricuty e = b/2-x =0.11m1.5 Hence,the structure is safeMoment of overturning force,ie,Horizontal component of earth pressure about toe 'C' =11977.53KgmMoment of restoring forces about toe 'C' =62718.38KgmFactor of safety against overturning =5.24>2.0 Hence safe.Design of heel:-Length of heel =2.10mDownward load intensity due to self weight of base slab =3700.00Kg/mDownward load intensity due to soil including surcharge =19760.40Kg/mTOTAL23460.40Kg/mThe upward pressure distribution below the base slab is as given below:-FG6464.81Kg/sqm9271.91.20m0.40m2.10mThe upward pressure intensity at point 'F' is=8361.49Kg/sqmThe upward pressure intensity at point 'G' is=8058.02Kg/sqmTotal upward pressure force on heel portion due to soil reaction =15248.97Kg/mThe distance of centroid of upward soil reaction from 'G' is =1.01mThe distance of centroid of downward load intensity from 'G' is =1.05mResultant moment =9207.50Kg-m/mFactored bending moment Mu =13811.26KgmEffective depth required d =Mu/0.138fckb =223.70mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =1.181From table 2 of SP 16,percentage of steel required =0.57Area of steel required =1949.40sqmmHence provide 16mm dia HYSD bars@ 100mm c/c spacingHence Ast provided =2009.60sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =123.17KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.36N/sqmm0.36Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =600.00sqmmTaking 12mm dia HYSD bars,the spacing comes to130.95mmHence provide 10mm dia bars @ 125mm c/cDesign of wall or stem:-Factored bending moment Mu =17966.30KgmEffective depth required d =Mu/0.138fckb =255.14mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =1.536From table 2 of SP 16,percentage of steel required =0.477Area of steel required =1631.34sqmmHence provide 16mm dia HYSD bars@ 125mm c/c spacingHence Ast provided =1747.48sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =111.93KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.33N/sqmm0.33Hence,the depth provided is safe from beam shear point of viewHence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =450.00sqmmProvide 1/3rd of above reinforcement on earthen side =150.00sqmm167.4666666667Provide 8mm dia @ 200mm c/c on earthen sideProvide 2/3rd of above reinforcement on other side =300.00sqmm334.9333333333Provide 8mm dia @ 150mm c/c on other sideProvide 10mm bars at 300mm c/c vertically on the outer face to support horizontal rods287.0857142857Design of Toe:-Length of toe =1.20mDownward load intensity due to self weight =3700.00Kg/mDownward load intensity due to soil including surcharge =0.00Kg/mTOTAL3700.00Kg/mThe upward pressure distribution below the base slab is as given below:-FG6464.81Kg/sqm9271.91.20m0.40m2.10mThe upward pressure intensity at point 'F' is=8361.49Kg/sqmThe upward pressure intensity at end of toe is=9271.90Kg/sqmTotal upward pressure force on heel portion due to soil reaction =10580.03Kg/mThe distance of centroid of upward soil reaction from 'F' is =0.61mThe distance of centroid of downward load intensity from 'G' is =0.60mResultant moment =4237.27Kg-m/mFactored bending moment Mu =6355.90KgmEffective depth required d =Mu/0.138fckb =151.75mmOver all depth provided =400.00mmEffective depth provided(Assuming 50mm cover) d =342.00mmMu/bd2 =0.543From table 2 of SP 16,percentage of steel required =0.158Min.percentage of steel as per IS 456 =0.15Area of steel required =540.36sqmmHence provide 12mm dia HYSD bars@ 150mm c/c spacingHence Ast provided =753.60sqmmCheck for shear:-The critical section for beam shear is at distance of 'd' from the face of the supportHence,the factored design shear force VFd =103.20KNat a distance 'd' from the face of the supportNominal shear stress Tv =0.30N/sqmm0.30Hence,no shear reinforcement is required.Provide temperature re inforcement @ 0.15%Area required =600.00sqmmTaking 10mm dia HYSD bars,the spacing comes to130.95mmHence,provide 10mm dia bars @ 125mm c/c

Raft_DesignDESIGN OF RAFT FOR SKEW BRIDGEName of the work:-Construction of High Level Bridge at 1/2Km on the R/F BN Road to ChelisingamThe plan of the raft and position of abutments& piers is as shown below:-Length of the Raft:-=38.892mWidth of the Raft:-=8.75mTotal load on the Raft:-Dead Load:-Wt.of Deck slab =4028.00KnWt.of wearing coat =559.45KnWt.of bed blocks over piers = 2x1.00x7.5x0.3x2.5 =0.00tWt.of dirt wall over abutments =150.78KnWt.of bed blocks over piers =195.60KnWt.of piers = 2x1x7.5x3.98x2.4 =0.00tWeight of kerb =237.95KnWeight of hand rails(verticals) =232.40KnWeight of hand rails(horizontals) =54.15KnWt.of abutmentsFooting-I =586.80KnFooting-II =645.48KnFooting-III =704.16KnFooting-IV =0.00KnWt.of abutments =1941.52KnWt.of piersFooting-I =704.16KnFooting-II =938.88KnFooting-III =1173.60KnFooting-IV =0.00KnWt.of piers =2505.24KnTotal14658.17KnDead load stress =43.07Kn/SqmLive Load:-Taking two lanes of IRC Class-A loadingWheel width in the direction of movement =0.2+0.2+0.25/2 = 0.625m2.72.711.411.46.86.8 6.86.81.13.2 1.24.33.03.03.014.4670.62538.892mCentre of gravity of loading from 1st 2.7t load ==8.72mCentre of gravity from the end of raft =9.345mEccentricity =10.101mStress due to live load = 2xP(1+6e/b)(Taking two lanes)AMax.stress =25.29Kn/SqmMin.stress =-18.91Kn/SqmTotal stress due to dead load and live loadMax.Stress =68.36Kn/SqmMin.Stress =24.16Kn/SqmAssuming the depth of raft as 60cmStress due to self weight of raft =15.00Kn/SqmStress due to wieght of base concrete =4.80Kn/SqmHence,the Max.stress on the soil =88.16Kn/SqmWhich is less than 11t/sqm(Soil testing report)Hence safe.Net Max.upward pressure acting on Raft =68.36Kn/SqmNet Min.upward pressure acting on Raft =24.16Kn/SqmThe design stress =46.26Kn/SqmHence,the UDL/m width on the raft =46.26Kn/mDesign of Raft:-The raft will be analysed as a continuous beam of 1m width with the loadingas shown below:-61.263.655.606.806.806.805.603.65UDL of46.26Kn/mAfter analysis the bending moment diagram on TENSION SIDE side is enclosed:From the above BMD,it can be inferred that,Max.bending moment at supports =308.15KNmMax.bending moment in span =118.00KNmDesign Negative bending moment Mu =462.23KNmDesign Positive bending moment Mu =177.00KNmEffective depth required d =Mu/0.138fckb =366.03mmOver all depth provided =600.00mmEffective depth provided(Assuming 50mm cover) d =542.00mmBottom steel at end supports:-Mu/bd2 =1.573From table 3 of SP 16,percentage of steel required =0.474Area of steel required =2569.08sqmmHence provide 20mm dia HYSD bars(Cranks)@ 200mm c/c spacing as per drawingalong with 16mm dia HYSD bars extra@ 200mm c/cHence Ast provided at bottom =2574.80sqmmBottom steel at intermediate supports:-Mu/bd2 =0.982From table 3 of SP 16,percentage of steel required =0.291Area of steel required =1577.22sqmmHence provide 20mm dia HYSD bars(Cranks)@ 200mm c/c spacing as per drawingHence Ast provided at bottom =1570.00sqmmTop steel:-Mu/bd2 =0.603From table 3 of SP 16,percentage of steel required =0.175Area of steel required =948.50sqmmHence provide 20mm dia HYSD bars@ 200mm c/c spacing as per drawingHence Ast provided at top =1570.00sqmmProvide distribution reinforcement of 0.15% both at top and bottomArea =900.00sqmmAdopting 12mm dia bars,the spacing required is =174.44mmHence provide 10mm dia bars @ 150mm c/c spacing at top& bottom as distribution steelHence distribution steel provided =1046.67sqmmEffective depth = 300-50-6 =0.244mClear span between abutments = 3.00-2x(0.125+2x(0.15)) =2.150mEffective span = 2.15+0.244/2 =2.27mClear span between piers = 8.00-(2x0.5) =7.00mFor continuous slab,clear span will be the effective span,effective span =2.27mThe raft is proposed to be designed for the Max.stress of 5.47t/sqmDistribution Factors:-KEKK/EKJoint at End pointBA0.75/6.70.250.45BC1/7.00.55Joint at intermediateCB1/7.00.290.5pierCD1/7.00.5Fixed End Moments:-End span = 4.09x6.72/12 =15.30t/mIntermediate span = 4.09x72/12 =16.70t/mMoment Distribution:-ABCDEF0.450.550.50.50.50.50.550.45-15.315.3-16.716.7-16.716.7-16.716.7-15.315.315.37.650.00.00.00.00.00.0-7.65-15.3022.95-16.716.7-16.716.7-16.716.7-22.950-2.81-3.443.442.81-1.721.720.860.86-0.86-0.860.43-0.430.43-0.43-0.194-0.2370.2150.215-0.215-0.2150.2370.1940.108-0.119-0.1080.1080.119-0.108-0.049-0.0590.1140.114-0.114-0.1140.0590.049019.897-19.89816.05-16.04916.049-16.0519.898-19.8970Assuming 1m width of raft,the UDL on the raft is88.160t/SqmThe raft is treated as simply supported beam with over hangsHence,the Max.positive moment = wl2/8 =56.89t-mMax.Negative moment for over hangs = wl12/2 =3.97t-mThe Final superimposed bending moment diagram is as given below:-16.0516.0519.919.99.004.9754.975The Max.Negative moment is 19.9 t-m and Max.Positive moment is 9.00t-mAllowing 15% of redistribution of moments from supports to centreMax.negative moment =3.970t-mMax.positive moment =56.890t-mHence,the design moment =56.890t-mDepth required = 3.53x10585.95528889097.7x100Hence provide overall depth of 30cm,the effective depth available is300-50-6 =24.4Area of steel required = 3.53x105127.27sqcmat centre2000x0.916x24.4Spacing of 12mm dia bars required = 1.13x100/7.9 =14.30379746841.1304However provide 12mm bars at 125mm c/c at centreArea of steel required = 0.25x1058.88sqcmfor over hangs2000x0.916x24.4Spacing of 12mm dia bars required = 1.13x100/0.56 =201.78571428571.1304However provide 12mm bars at 250mm c/cProvide distribution reinforcement of 0.12% both at top and bottomArea =3.60sqcmAdopting 10mm dia bars,the spacing required is = 0.785x100/3.6 =21.80555555560.785Hence provide 10mm dia bars @ 175mm c/c spacingThe details of Reinforcement is as shown below:-12mm bars@ 125 c/c(Curtail 50% of cranks at the centre of abutment3.00m12mm bars@250mm c/c

Hydraulic DesignHydraulic designHydraulic Particulars:-1.Maximum Flood Level7.950m2.Ordinary Flood level3.Lowest Bed level5.6204.Average bed slope0.000067(1 in 15000)5.Rugosity Coefficient(n)0.033(As per table 5 of IRC:SP 13)6.Vertical clearence proposed0.450(As per clause 15.5 of IRC:SP 13&as per profile)6.Bottom of deck proposed8.555(MFL+Vertical clearence)7.Road Crest level9.280(Bottom of deck level+thickness of deck slab)8.Width of carriage way5.500Discharge Calculations:-1)Catchment area method:-Catchment area from topo sheet(Enclosed) =24.82sqkmUsing Ryve's formula Discharge Q = CA2/3 =72.33Cumecs1)Area Velocity method:-a)At the proposed bridge site:-Maximum Flood level7.950mSlope0.000067Rugosity Coefficient0.033S.NoChainageR.LDepth ofAverageDistanceAreaWettedflowdepth of(m)(Sqm)perimeter(m)flow(m)(m)109.960.000.000.000.000.00259.950.000.005.000.000.003109.9300.000.005.000.000.004158.5800.000.005.000.005.185207.8500.100.055.000.255.056257.5600.390.255.001.235.017307.6600.290.345.001.705.008357.5300.420.365.001.785.00940.06.7901.160.795.003.955.051045.06.7101.241.205.006.005.001151.79.7700.000.626.704.157.371255.09.8000.000.003.300.000.001360.09.8200.000.005.000.000.0019.0542.66Hydraulic RadiusR=Total area/Wetted perimeter =0.45Velocity V =1/nX(R2/3XS1/2)0.15m/secDischarge Q =AXV2.86Cumecsb)At 400m downstream of proposed bridge site(As per IRC SP-13):-Maximum Flood level7.550mSlope0.00007Rugosity Coefficient0.033S.NoChainageR.LDepth ofAverageDistanceAreaWettedflowdepth of(m)(Sqm)perimeter(m)flow(m)(m)109.640.000.000.000.000.00259.630.000.005.000.000.003109.6100.000.005.000.000.004158.2600.000.005.000.005.185207.5300.020.015.000.055.056257.2400.310.175.000.825.017307.0600.490.405.002.005.008356.8700.680.595.002.935.00940.06.4701.080.885.004.405.051045.06.3901.161.125.005.605.001153.09.4500.000.588.004.647.371255.09.4800.000.002.000.000.001360.09.5000.000.005.000.000.0020.4442.66Hydraulic RadiusR=Total area/Wetted perimeter =0.48Velocity V =1/nX(R2/3XS1/2)0.15m/secDischarge Q =AXV3.07Cumecsc)At 400m Upstream of proposed bridge site(As per IRC SP-13):-Maximum Flood level8.350mSlope0.00007Rugosity Coefficient0.033S.NoChainageR.LDepth ofAverageDistanceAreaWettedflowdepth of(m)(Sqm)perimeter(m)flow(m)(m)1010.280.000.000.000.000.002510.270.000.005.000.000.0031010.2500.000.005.000.000.004158.9000.000.005.000.005.185208.1700.180.095.000.455.056257.8800.470.335.001.635.017307.9800.370.425.002.105.008357.8500.500.445.002.185.00940.07.6800.670.595.002.935.051045.07.6800.670.675.003.355.001153.010.0900.000.348.002.687.371254.010.1200.000.001.000.000.001360.010.1400.000.006.000.000.0015.3142.66Hydraulic RadiusR=Total area/Wetted perimeter =0.36Velocity V =1/nX(R2/3XS1/2)0.13m/secDischarge Q =AXV1.99CumecsDesign Discharge =72.330CumecsDesign Velocity =0.15m/secAfflux Calculations(H.F.L Condition):-Un obstructed linear water way =L =41.70mTotal water way provided = l =30.00mDesign discharge Q =72.33CumecsLinear water way L =30.00mDepth of down stream water Dd =0.70mWidth of the channel at HFL =41.70mCase(a) Assume that afflux is less than 1.4Dd:-Using Orifice formula for calculation of dischargeQ = Co X (2g)1/2 X L X Dd X [h+(1+e)u2/2g]1/2In the present case,l/L =0.72Corresponding to this value the coefficient Co from IRC SP:13--2004 =0.865Corresponding to this value the coefficient e from IRC SP:13--2004 =0.9Hence0.8081037512= h+0.0968399592u2 ------------- (1)At just upstream of the bridgeQ = W X (Dd + h) X u1.7345323741=(0.70+h) X uu =1.7345323741----------------(2)(0.70+h)Substituting,the above value in eq (1)'20.8081037512=h+ 0.096840X 1.73453(0.70+h)Solving by trial and error method,assume h =0.30m0.808104 =1.193933716Not satisfiedassume h =0.057m0.808104 =0.8076853719Hence afflux h =0.057mVelocity u =2.291m/secCase(b) Assume that afflux is more than 1.4Dd:-Applying Broad crested wier formula,Q = 1.706 CW LH3/2As per clause 15.2 of IRC SP:13-2004,the value of CW for narrow bridge opening with or without floor =0.94Hence H =1.31mH = Du + u2/2g DuDu =1.31mAgain applying Q = Du x W x uu =1.324m/secDu = H - u2/2gHence, Du =1.221Hence afflux h = Du - Dd =0.521From the above calculations,it is inferred that afflux is less than 1/4 th Ddand hence afflux to be adopted is from the Orifice formula,which is equal to0.057mVentway Calculations(H.F.L Condition):-Assuming the stream to be truly alluvial,the regime width is equal to linear waterway required for the drain.Hence,as per Lacey's silt theory,the regime width W = 4.8Q1/2 = 4.8*72.330.5 =40.82mBut the actual top width is much less than the above regime width.Hence,the stream is no truly alluvial in nature.It is quasi-alluvial.As per IRC:SP--13,the ventway calculations for quasi-alluvial streams are as given below:-Assuming afflux =x =0.20mWidth of channel at H.F.L(b+h) =41.70mEffective span =7.32mEffective linear water way =36.60mDepth of flow =di =2.33mHead due to velocity of approach =(Vmax2/2g)X[di/(di+x)]20.001mCombined head due to Velocity of approach andhi =0.201mafflux (0.15+0.06)Velocity through vents Vv =0.90X(2ghi)1/2 =1.79m/secLinear water way requiredLWW = Qd/(VvXdi) =17.37mNo.of vents required =LWW /LC=2.3729508197Say---3 VentIn quasi-alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scourdepth and expensive training works.Hence No.of vents required as per the width of the stream at H.F.L=5.6967213115No.of vents to be provided5NosNo.of piers =4NosScour Depth Calculations:-As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequatemargin of safety for foundations and protection worksHence,the discharge for design of foundations =1.30XDesign Discharge =96.20CumecsLacey's Silt factor ' f ' = 1.76Xm1/2(Due to pebbles&boulders in the bed) =2.00Discharge per metre width of foundations = q =3.207Normal scour depth D = 1.34(q2/f)1/3 =2.30mMaximum scour depth Dm = 1.5XD =3.45m(For design of abutment foundations,as per clause 110.1.4.2 of IRC:5--1985)Depth of foundation = Dm + Max.of 1.2m or 1/3 Dm =4.65mBottom level of foundation =3.30mDepth of foundation below low bed level =2.32mThe Minimum Safe Bearing capacity of the soil is considered as 11 KN/m2 at a depth of 2.00m below LBLHence open foundation in the form of raft foundation is proposed at a depth of 2.90m below LBL,ie,at a level of+3.280mAs the foundations are proposed below the Max.scour level,bed protection is not needed from scour depthconsiderations.But,the velocity through vents is more than 2m/s.Hence,it is advisable to provide flexible apronto protect against excessive scouring action.Design of LAUNCHING/FLEXIBLE APRONS:-Size of stones as per clause 5.3.7.2 of IRC 89-1985Diametre (d) = (Vmax/4.893)2 =0.13mSay0.30mWeight of each stone considering the specific gravity of stone as 2.65Weight of stone =4/3x x(d/2)3 x 2.65 x 1000 =37.48KgSay40KgWeight of each stone shall not be less than 40 Kg.Dimensions of apron as per clause 5.3.5.2 of IRC 89-1985( T ) = 0.06 x (Qdf)1/3 =0.275Thickness of apron at inner edge(near raft) = 1.5 x T =0.413mSay0.60mThickness of apron at outer edge = 2.25 x T =0.619mSay0.90mHence provide a thickness of 0.60m at near end and 0.9m at the outer endWidth of Launching Apron on U/S Side:-The launching aprons are designed to reach a level of 1.50 times the normal scour depth1.5 x D =3.450mBottom level of apron after launching = HFL-1.5 X D =4.50mDepth below top of the raft =-0.60mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at U/S =-1.20mAs per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width =4.0mWidth of Launching Apron on D/S Side:-The launching aprons are designed to reach a level of 2.00 times the normal scour depth2.0 x D =4.600mBottom level of apron after launching = HFL-2 X D =3.35mDepth below top of the raft =0.55mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at D/S =1.10mAs per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width =6.0mDesign of Protection works:-Afflux =0.057mDepth of flow =di =0.00mHead due to velocity of approach =(Vmax2/2g)X[di/(di+x)]20.000mCombined head due to Velocity of approach andhi =0.000maffluxVelocity through vents Vv =0.90X(2ghi)1/2 =0.00m/secLinear water way requiredLWW = Qd/(VvXdi) =0.00m96.20Hence O.KAs per the clause 5.1.3(iv),of IRC SP:82-2008 for the beds consisting of boulders upto 200mm size,the permissiblevelocity through vents is 2.5m/s and for beds containing larger sized boulders or rocky strata permissible velocity is 6m/s.As the bed of the proposed stream is rocky strata,increased velocity of 2.68m/sec is allowed through vents withoutrigid floor protection.Hence rigid floor protection is not proposed.However,suitably designed flexible aprons with cut-off walls are proposed on both upstream and down stream sides toprotect against the probable eddies formed due to uneven spacing of vents along the causeway.Design of cut-off walls/Toe walls:-Though,it is sufficient to take the D/S side cut-off upto 1.27 times the normal scour depth as percaluse 703.2.3.2 of IRC 78-1983 considering that the reach is straight.1.27XNormal scour depth from HFL =2.92mDepth of bottom of Cut-off wall from HFL =2.92mBottom level of cut-off wall =0.00Depth of bottom of D/S side Cut-off wall from LBL0.00mAs per the clause 6.4.2(v),of IRC SP:82-2008,the minimum depth of cut-off wall on U/S side is 2.0m below bedlevel and 2.5m below bed level on D/S side.Depth of bottom of D/S side Cut-off wall from LBL2.50mDepth of bottom of U/S side Cut-off wall from LBL2.00mAs rigid floooring is not being proposed,there is no need to provide cut-off walls.But toe walls are proposed to a depthof 0.90m to protect the flexible apron.Design of LAUNCHING/FLEXIBLE APRONS:-Size of stones as per clause 5.3.7.2 of IRC 89-1985Diametre (d) = (Vmax/4.893)2 =0.81mSay0.30mWeight of each stone considering the specific gravity of stone as 2.65Weight of stone =4/3x x(d/2)3 x 2.65 x 1000 =37.48KgSay40KgWeight of each stone shall not be less than 40 Kg.Dimensions of apron as per clause 5.3.5.2 of IRC 89-1985( T ) = 0.06 x (Qdf)1/3 =0.275Thickness of apron at inner edge(near raft) = 1.5 x T =0.413mSay0.60mThickness of apron at outer edge = 2.25 x T =0.619mSay0.90mHence provide a thickness of 0.60m at near end and 0.9m at the outer endWidth of Launching Apron on U/S Side:-The launching aprons are designed to reach a level of 1.50 times the normal scour depth1.5 x D =3.450mBottom level of apron after launching = HFL-1.5 X D =0.00mDepth below top of the raft =0.00mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at U/S =0.00mAs per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width =4.0mWidth of Launching Apron on D/S Side:-The launching aprons are designed to reach a level of 2.00 times the normal scour depth2.0 x D =4.600mBottom level of apron after launching = HFL-2 X D =0.00mDepth below top of the raft =0.00mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at D/S =0.00mAs per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width =6.0mSolving h = 1.7 cm,hence,it can be neglectedScour Depth Calculations:-As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequatemargin of safety for foundations and protection worksHence,the discharge for design of foundations =1.30XDesign Discharge =96.20Cumecs(1.3*16.95)Lacey's Silt factor ' f ' = 1.76Xm1/2(Due to pebbles&boulders in the bed) =1.80Discharge per metre width of foundations = q =0(22.54/8.00)Normal scour depth D = 1.34(q2/f)1/3 =0.00m[1.34*(2.818^2/1.0)0.33]Maximum scour depth Dm = 1.5XD =0.00m(For design of abutment foundations,as per clause 110.1.4.2 of IRC:5--1985)(1.5*2.66)Depth of foundation = Dm + Max.of 1.2m or 1/3 Dm =0.00m(3.99+1.2)Bottom level of foundation = (9.23-5.19)0.00mDepth of foundation below low bed level = [6.54-4.75)] =0.00mThe Minimum Safe Bearing capacity of the soil is considered as 15 KN/m2 at a depth of 1.50m below LBLHence open foundation in the form of raft is proposed at a depth of 1.80m below LBL,ie,at a level of0.00mThough, cut-off walls and aprons are not required from scour depth point of view,down stream side apron withcut-off wall is advisable due to check dam located on upstream side.Design of cut-off walls:-Though,it is sufficient to take the D/S side cut-off upto 1.27 times the normal scour depth as percaluse 703.2.3.2 of IRC 78-1983 considering that the reach is straight.1.27XNormal scour depth from HFL =0.00mDepth of bottom of Cut-off wall from HFL =0.00mBottom level of cut-off wall =0.00Depth of bottom of D/S side Cut-off wall from LBL0.00mDepth of bottom of U/S side Cut-off wall from LBL3.20mDesign of LAUNCHING APRONS:-Size of stones as per clause 5.3.7.2 of IRC 89-1985Diametre (d) = (Vmax/4.893)2 =0.00mSay0.30mWeight of each stone considering the specific gravity of stone as 2.65Weight of stone = 4/3x x(d/2)3 x 2.65 x 1000 =37.48KgSay40KgWeight of each stone shall not be less than 40 Kg.Dimensions of apron as per clause 5.3.5.2 of IRC 89-1985( T ) = 0.06 x (Qdf)1/3 =0.275Thickness of apron at inner edge(near raft) = 1.5 x T =0.413mSay0.90mThickness of apron at outer edge = 2.25 x T =0.619mSay1.30mHence provide a thickness of 0.60m at near end and 0.9m at the outer endWidth of Launching Apron on U/S Side:-The launching aprons are designed to reach a level of 1.50 times the normal scour depth1.5 x D =0.000mBottom level of apron after launching = HFL-1.5 X D =0.00mDepth below top of the raft =0.00mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at U/S =0.00mSay8.0mWidth of Launching Apron on D/S Side:-The launching aprons are designed to reach a level of 2.00 times the normal scour depth2.0 x D =0.000mBottom level of apron after launching = HFL-2 X D =0.00mDepth below top of the raft =0.00mThe apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89Hence the width of launching apron at D/S =0.00mSay16.0mSection of Raft,Cut-off walls&Launching apronsU/SD/S8.0m16.0m1.3m0.9m3.2m4.4mAssistant Exe.EngineerDeputy Exe.EngineerExecutive EngineerPR,IchapuramPR,IchapuramPR,TekkaliSuperintending EngineerPR,Srikakulam

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