ring girder (japan-1)

Ring Girder(Japan)

JapanDesign of Ring Girder (Simply Supported) ( Bureau of Reclamation Method -ref : Japannese text )Project : Interstate Raw Water TransferJuly 26, 2002Part of works : 3000 mm FID x 45 m Span Pipeline Stream CrossingC:\WINDOWS\DESKTOP\ZAF's DoCuMenT\Formulae\misc\[ring girder (japan-1).xls]Japan1. Pipe DataPipe shell outer dia.(OD)=3110(mm)EJEJPipe shell internal dia.(ID)=3060(mm)Pipe shell mean dia.(Dm)=3085(mm)48 mPipe shell mean radius(rm)=1542.5(mm)Simply supportedPipe FID(FID)=3000(mm)Pipe shell thick(t)=25.0(mm)Concrete lining(tc)=30.0(mm)Operating pressure(P)=100.0(m)=0.981(N/mm2) =10.0(Bars)2. Loading and ReactionsDensity of water(q)=9.81(kN/m3)Density of steel(gs)=77.0(kN/m3)Density of concrete lining(gc)=23.0(kN/m3)Span bet. ring girder support(l)=48.00(m)Vertical Loading :Weight of pipe shell=18.66(kN/m)Weight of water=69.34(kN/m)Weight of lining=6.57(kN/m)Live load=0.5(kN/m)Others dead load=0.0(kN/m)Pipe weight when full(Wv)=95.07(kN/m)Pipe dead weight when empty(Wv')=25.22(kN/m)Horizontal Loading :Wind load=2.25(kN/m)Others=0.0(kN/m)Total horizontal load(Wh)=2.3(kN/m)Support reaction factor=0.50(Qs = Factor x L x Wv)Reaction at support (full)(Q)=2281.6(kN)Reaction at support (empty)(Qs)=605.40(kN)3. Stress in Pipe Shell(i) Pipe Section Properties and Allowable StressSectional area(A)=242295(mm2)Moment of inertial(Ip)=2.883E+11(mm4)Section modulus(Z)=1.854E+08(mm3)Radius of gyration(r)=1090.7(mm)Modulus of elasticity(E)=2.10E+05(N/mm2)Poisson ratio(v)=0.30Grade of steel=500Min yield strength(Ys)=345(N/mm2)Allowable bending stress(fbc / fbt)=172.5(N/mm2)Allowable axial stressfac=172.5(N/mm2)The minimum of :(a)Pc=187.4(N/mm2)For l/r =44.01(as per BS 449)(b)Ys / 2=172.5(N/mm2)Allowable shear stress=115(N/mm2)(For l/r = 30)l/r=44.0130.00K2=1.71.7E=210000(N/mm2)210000Min. yield strength Ys=345(N/mm2)250Euler critical stressCo=1070.2504878619(N/mm2)2302.9076935875h=0.05809715430.02700Allowable axial stress for l/r =44.01=187.4(N/mm2)Allowable axial stress for l/r =30.00=142.8(N/mm2)(Detrmined based on l/r = 30)Allowable axial stress for l/r = 0=215(N/mm2)Allowable axial stress=187.4(N/mm2)(i) Ring Stress Due to Internal PressureRing stressst=P. ri / t=.981*( 3060/2)/25.0=60.04(N/mm2)(< 172.5, ok)(ii) Critical Buckling Load When Pipe is EmptyCritical buckling loadPk=2E / (1-v2) . (t / Do)2=2*2.10E+05/(1-0.30^2)*(25.0/ 3110)^3=0.24(N/mm2)(iii) Vertical Bending Stress at Mid-SpanBending Moment at mid-span(Mmid)=27379.5(kNm)Bending stress(f)=147.7(N/mm2)(< 172.5, ok)(iv) Horizontal Bending Stress at Mid-SpanBending Moment at mid-span(Mmid)=648.0(kNm)Bending stress(f)=3.5(N/mm2)(< 172.5, ok)(v) Axial Stress Due to Longitudinal Thrust Force(a) Thrust due to friction of between bearing pad and supportThrust ForceP1=mRFriction coefficientm=0.15Support reactionR=2281.6(kN)P1=342.2(kN)(b) Thrust due to friction of the expansion jointThrust ForceP2=F' . p . DoF'=6.9(N/mm)Do=3110.0(mm)P2=67.1(kN)(c) Thrust due to internal pressure acting on the pipe end circumference at the expansion jointThrust ForceP3=P . p . Dm . tP=0.981(N/mm2)Dm=3085(mm)t=25.0(mm)P3=237.7(kN)Total axial forceSP=P1 + P2 + P3=647.0(kN)Axial stresssp=SP/A=2.67(N/mm2)(vi) Rim Bending Stress Due to Internal Pressure (see ring girder data)Rim bending stressspr=1.82 (Ar - Bo . t) . P. riArtAr=31089(mm2)Bo=643.5(mm)t=25.0(mm)ri=1530.0(mm)spr=52.7(N/mm2)(vii) Stress Combination(a) At ring girder support :Axial stresssc = sp=2.7(N/mm2)Bending stresssbc = spr=52.7(N/mm2)Combined stress : sc / fac + sbc / fbc=2.7/172.5+52.7/172.5=0.32(< 1.0, ok)(b) At mid span :Axial stresssc = sp=2.7(N/mm2)Bending stresssbc=147.7(N/mm2)Combined stress : sc / fac + sbc / fbc=2.7/172.5+147.7/172.5=0.87(< 1.0, ok)(c) Combined max horizontal and vertical bending stressMax horizontal bending stresssh=3.50(N/mm2)Max vertical bending stresssv=147.69(N/mm2)sT=(sh2 + sv2)1/2=(3.50^2+147.69^2)^0.5=147.74(N/mm2)(< 172.5, ok)(viii) Check ShearMax shearMax Q=2281.6(kN)Max shear stresst=2 MaxQ / A=18.83(N/mm2)(< 115.0, ok)4. Check DeflectionFree End Condition :dmax=5/384 . WL4/EI=5/384*95.07*(48.00*1000)^4/2.10E+05/2.883E+11=108.5(mm)L / dmax=442(> 350, ok)Fixed End Condition :dmax=1/384 . WTL4/EI=108.5/5=21.7(mm)L / dmax=2211(> 350, ok)5. Check Longitudinal Thermal ExpansionCoefficient of thermal expansion a=1.20E-05per degrees CChange in temperatureDT=25oCChange in lengthDL = a . DT . L=14.4(mm)6. Ring Girder DataBo = 643.5Centroidal radius, RXpipe shell (flange)0.78(rm . t)1/2b' =312t =25.0di =90.9NAd = 300.0do =234.1Ht1 =25Ring stiffener (web)Q/4Q/4Section Y-YNo. of ring stiffener=2Ring stiffener plate thickness(t1)=25.0(mm)Depth of ring stiffener plate(d)=300.0(mm)t1 + 2 x 0.78(rm . t)1/2=331.3(mm)c/c spacing of ring stiffeners(b')=312.2(mm)( 360, ok)Check Longitudinal Thermal ExpansionCoefficient of thermal expansion a=1.20E-05per degrees CChange in temperatureDT=20oCChange in lengthDL = a . DT . L=6(mm)Design of SupportSection PropertiesLibrarySectionSelf Wt.Depth DWidth BrxxryyIxxIyySect. ACyNo.Name(Kg/m)(mm)(mm)(cm)(cm)(cm4)(cm4)(cm2)(cm)6178 x 7620.84177.876.27.102.25133813426.68.26-2 nos b/b41.68177.876.27.108.9926764304.053.2-Provide pair nos. of178 x 76 [back to back as support as shown.Gap betrween [ =9.0mmAxial load per shoeP=461.3/22 x 178 x 76 channel=230.6(kN)9.0Axial stressfc=230.6*10/ 53.2=43.4(N/mm2)Height of supportH=1425(mm)Effective lengthl = 2 x H=2850(mm)Max slenderness ratiol/r=31.69(l/rxx)(For l/r = 30)l/r=31.6930.00K2=1.71.7E=210000(N/mm2)210000Ys=250(N/mm2)250Euler critical stressCo=2064.3671302186(N/mm2)2302.9076935875h=0.03011988850.02700Allowable axial stress for l/r =31.69=142.2(N/mm2)Allowable axial stress for l/r =30.00=142.8(N/mm2)(Detrmined based on l/r = 30)Allowable axial stress for l/r = 0=155(N/mm2)Allowable axial stress=142.2(N/mm2)(> 43.4, ok)Design of Sole Plate400119.3111.1400Dimension of sole plateLength=400(mm)Width=400(mm)The greater overhangA=119.3(mm)The smaller overhangB=111.1(mm)Concrete gradefcu=30.00(N/mm2)Allowable bearing pressurefbear=5.4(N/mm2)Bearing pressurew=2.88(N/mm2)(< 5.4, ok)Allowable plate bending stressPbct=185(N/mm2)Required plate thicknesst=(3*2.88/ 185*( 119.3^2-111.1^2/4))^0.5=22.8(mm)Provided plate with thickness=25(mm)SUMMARYRing Stiffener Plate200 x 9 thick ring plateSupport178 x 76 c-channel back to backSole plate400 x 400 x 25 thick MS plateThermal ExpansionEstimated change in length, DL=6 mm

RBS 4360 : 1986, Table 13For Grade 43A Steel, Minimum yield strength, Re :t