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NATIONAL ENGINEERING SERVICES PAKISTAN (Pvt.) LTD.Job No.: Project: GATTWALA TO SAHIANWALA (M-3) INTERCHANGE CHAKJUMRABy: Subject: Prestressed Girder 26.7 m span Chk.: Date:

SPAN OF GIRDERS =38.48MetresC/C Spacing Of Girders = 3.012MetresWIDTH OF BRIDGE=18.2MetresOverhang Portion =1.57MetresSPAN OF DIAPHRAGM =15.06MetresC/C Spacing Of Diaph. = 12.83MetresNO. OF GIRDERS=6NO. OF DIAPHRAGMS=4

COMPUTATION OF SECTION PROPERTIES

PROPERTIES OF MAIN GIRDER

CALCULATION OF EFFECTIVE FLANGE WIDTH

( i ) be=Span/4.0be=9620mm

( ii ) be=12hf + bw or 1/2 Width of top flange

be=3350mm```User Defined Sections data 16m25m27m30m38.4840m45m( iii ) be= C/C Spacing of GirderB1 = 5504501000800130013001300be=3012mmB2 = 600600600600800800800B3 = 200180200200200200225B4 = 1751351000150150150Therefore Effective Flange Width =3012mmReduced Effective Flange Width =2694mmSt = 225225225225225225225D1 = 1300160019002000245024502800INPUT DATAD2 = 200200130250170170170Span38.48INPUTCOMPOSITE SECTIONONLY GIRDERD3 = 0070150808080B1 = 1300mmTOTAL DEPTH OF GIRDER =2675.00mm2450.00mmD4 = 1501501000150150150B2 = 800mm1.00B SLAB =3012.00mmmmD5 = 250200250200350350350B3 = 200mmD SLAB =225.00mmmmD6 = 200300200300250250250B4 = 150mm2.00B TOP FLANGE =1300.00mm1300.00mmD TOP FLANGE =170.00mm170.00mmS.No.SectionCoverSt = 225mm3.00B TOP TRIANGLE =400.00mm400.00mmXYXYD1 = 2450mmD TOP TRIANGLE =80.00mm80.00mm1.000.000.00D2 = 170mm4.00B TOP RECTANGLE =150.00mm150.00mm2.00400.000.00325.000.00D3 = 80mmD TOP RECTANGLE =80.00mm80.00mm3.00400.00250.00325.00250.00D4 = 150mm5.00B TOP TRIANGLE =150.00mm150.00mm4.00100.00600.0025.00600.00D5 = 350mmD TOP TRIANGLE =150.00mm150.00mm5.00100.002050.0025.002050.00D6 = 250mm6.00B WEB =200.00mm200.00mm6.00250.002200.00600.007.00B BOTTOM TRIANGLE =300.00mm300.00mm7.00650.002280.00 GIRDER SECTIOND BOTTOM TRIANGLE =350.00mm350.00mm8.00650.002450.008.00B BOTTOM FLANGE =800.00mm800.00mm9.00-650.002450.00D BOTTOM FLANGE =250.00mm250.00mm10.00-650.002280.00CONCRETE STRENGTH FOR SLAB =28Mpa=4Ksi11.00-250.002200.00CONCRETE FOR GIRDER =35Mpa=5Ksi12.00-100.002050.00-25.002050.00CONCRETE FOR COMPOSITE SEC. =35Mpa=5Ksi13.00-100.00600.00-25.00600.0014.00-400.00250.00-325.00250.0015.00-400.000.00-325.000.00OUTPUTCOMPOSITE SECTIONONLY GIRDER16.000.000.00AREA (Ax) =1688200mm2 =1010500mm2AREA (Reduced) =1616653.30734064mm2 =1010500mm2y' LOCATON OF N.A FROM BOTTOM =1748.8378639313mm =1260.7587003134mmM.O.I (Ix) (Iz) =1470521632086.3
A satisfied Microsoft Office user: formula to be checkedmm4 =825506943329.76
A satisfied Microsoft Office user: formula to be checkedmm4M.O.I (Iy) =419543872684.705mm4 =54170208333.3333mm4SHEAR AREA (Ay) (Web) =535000mm2 =490000mm2SHEAR AREA (Az) (Flang) =677700mm2 =SECTION MODULUS (BOTTOM) Zb =0.8409m3 =0.6548m3SECTION MODULUS (TOP) Zt =1.5878m3 =0.6941m3

TORSIONAL CONSTANT 'C' FOR MAIN GIRDERPARTBTCB/TSLAB2694.01225511441853111.97TOP FLANGE1338.095238095228589400071134.70WEB145020038666666677.25BOTTOM FLANGE882.35425157575242132.08TOTAL33678616522.8447mm4

PROPERTIES OF EXTERIOR GIRDER

CALCULATION OF EFFECTIVE FLANGE WIDTH

( i ) be= be of Interior Girderbe=3012mm

( ii ) be= 1/2 be of Interior Girder + overhang

be=3076mm

INPUTCOMPOSITE SECTION ONLY GIRDERTOTAL DEPTH OF GIRDER =2675mm =2450mmB SLAB =3012mm =mmD SLAB =225mm =mmB TOP FLANGE =1300mm =1300mmD TOP FLANGE =170mm =170mmB TOP LARGE TRIANGLE =400mm =400mmD TOP LARGE TRIANGLE =80mm =80mmB TOP RECTANGLE =150mm =150mmD TOP RECTANGLE =80mm =80mmB TOP SMALL TRIANGLE =150mm =150mmD TOP SMALL TRIANGLE =150mm =150mmB WEB =200mm =200mmB BOTTOM TRIANGLE =300mm =300mmD BOTTOM TRIANGLE =350mm =350mmB BOTTOM FLANGE =800mm =800mmD BOTTOM FLANGE =250mm =250mmCONCRETE STRENGTH FOR SLAB =28Mpa =28MpaCONCRETE FOR GIRDER =35Mpa =35MpaCONCRETE FOR COMPOSITE SEC. =35Mpa

OUTPUTCOMPOSITE SECTION ONLY GIRDERAREA (Ax) =1688200mm2 =1010500mm2AREA (Reduced) =1616653.30734064mm2 =1010500mm2y' LOCATON OF N.A FROM BOTTOM =1748.8378639313mm =1260.7587003134mmM.O.I (Ix) =1470521632086.3
A satisfied Microsoft Office user: formula to be checkedmm4 =825506943329.76
A satisfied Microsoft Office user: formula to be checkedmm4M.O.I (Iy) =419543872684.705mm4 =54170208333.3333mm4SHEAR AREA (Ay) =535000mm2 =490000mm2SHEAR AREA (Az) =677700mm2SECTION MODULUS (BOTTOM) Zb =0.8408564696m3 =0.6548m3SECTION MODULUS (TOP) Zt =1.5877583145m3 =0.6941m3

TORSIONAL CONSTANT C FOR EXTERIOR GIRDERPARTBTCB/TSLAB2694.01225511441853111.97TOP FLANGE1338.095238095228589400071134.70WEB145020038666666677.25BOTTOM FLANGE882.35425157575242132.08TOTAL33678616522.8447mm4

PROPERTIES OF INTERIOR DIAPHRAGM

CALCULATION OF EFFECTIVE FLANGE WIDTH

( i ) be=12hf + bwbe=2900

( i ) be=Span / 4.0

be=3765

( i ) be= C/C Spacing of Diaphragmbe=12826.6666666667

INPUTTOTAL DEPTH OF DIAPHRAGM (upto top of slab) =1925mmB SLAB =2900mmD SLAB =225mmB WEB =200mmD WEB =1700mm

OUTPUTAREA (Ax) =992500mm2y' LOCATON OF N.A FROM BOTTOM =1482.78mmM.O.I (Ix) =291712366511.86
A satisfied Microsoft Office user: formula to be checkedmm4M.O.I (Iy) =458427083333.333mm4SHEAR AREA (Ay) =385000mm2SHEAR AREA (Az) =652500mm2

TORSIONAL CONSTANT C FOR INTERIOR DIAPHRAGMPARTBTCB/TSLAB2900225550546875012.89WEB170020045333333338.50TOTAL10038802083.3333mm4

PROPERTIES OF EXTERIOR DIAPHRAGM

CALCULATION OF EFFECTIVE FLANGE WIDTH

( i ) be=0.8*Span/4.0be=602.4

( i ) be=12*hf/2 + bw

be=1550

INPUTTOTAL DEPTH OF DIAPHRAGM =1925mmB SLAB =602.4mmD SLAB =225mmB WEB =200mmD WEB =1700mm

OUTPUTAREA (Ax) =475540mm2y' LOCATON OF N.A FROM BOTTOM =1124.33mmx' LOCATON OF N.A FROM LEFT =445.05mmM.O.I (Ix) =172231260516.509
A satisfied Microsoft Office user: formula to be checkedmm4M.O.I (Iy) =9155100798.99336mm4SHEAR AREA (Ay) =385000mm2SHEAR AREA (Az) =135540mm2

TORSIONAL CONSTANT C FOR EXTERIOR DIAPHRAGMPARTBTCB/TSLAB60222511436187502.68WEB170020045333333338.50TOTAL5676952083.33333mm4

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LOSSES NATIONAL ENGINEERING SERVICES PAKISTAN (Pvt.) LTD.Job No.: Project: GATTWALA TO SAHIANWALA (M-3) INTERCHANGE CHAKJUMRABy: Subject: Prestressed Girder 26.7 m spanChk.: Date:

CALCULATION OF LOSSES

Span =38.48(m)

fc' =5000(psi)fci' =5000(psi)3.958293750.3856750991Es =28000000(psi)193192561.795426(KN/m2)Eci = 4286825.74873297(psi)815.67Girder Self Wt. Momemt Mo =493.77(T-m)D.L.Moments(slab+diaph) Mdp=321.91(T-m)341D.L.Moments(w.surface+footpath+barrier) Mdc=247.00(T-m)From ModelW(bal) L2/8y = M/y24.7166666667Total Dead Load Moments Md =1062.67(T-m)Pe=Live Load Moments with Impact Ml =362.00(T-m)From ModelPe=1007.0751829522ton978.7355528013Pi=1258.8439786902tonEffective Prestress Req'd=1258.84(Tons)

Concrete Beam Section Data:

Sectional Area Ac =1.0105(m2)Moment Of Inertia Ic =0.8255(m4)Sectional Modulus Bottom Zb =0.6548(m3)Sectional Modulus Top Zt =0.6941(m3)

Composite Beam Section Data:

Sectional Area Ac =1.6882(m2)Sectional Modulus Bottom Zbc=0.8409(m3)Sectional Modulus Top Ztc=1.5878(m3)

Prestress Cable Data: MID SECTION END SECTION

Breaking Load Fpu = 26.584(Tons)Strong Hold TablefpuAJacking Force = 0.75*Fpu = 19.938(Tons)5/0.6"13370063636/0.6"1598406363Wobble Coofficent, K =0.0033(per meter)ACI Code: for Grouted Tendons in metal 7/0.6"1869806363Curvature Coofficient, =0.25sheathing Wire Strand8/0.6"21311207563Anchorege Set " L"=0.005(m)9/0.6"23912607563Relative Humidity RH =50%10/0.6"2661400817511/0.6"29215408175Eccentricity e =1.086(m)Tendon Vertical distance from bottom at mid Span12/0.6"31916808175of Tendons for girder section only12313/0.6"34618209090Approx. Losses=20%12512512514/0.6"3721960909025025015/0.6"39921009090456

No.of Strands provided=45Tendon Vertical distance from bottom at end72123No. of tendons =59/0.6"4008001200160020002450FRICTRION LOSSES456

Pj = Px * ( 1 + K*L + * )stressing from1ends

CableLengthDipApK*L+*PjPx Pby ACI(m)(m)(m2)(rad)MuO.K.Minimum Reinforcement = 0.004 AMoment to be resisted by non prestressed reinforcement =0K-in=0.0Ton-mA =0.341sq. mMinimum Reinforcement to be Provided0.001364sq. m =2.11sq. inch

CALCULATIONS FOR SHEAR

V L.L = For live load at critcal section from face=40.00TonFrom ModelVgirder+Vslab = For Dead load at critcal section from face=73.00TonFrom ModelVslab = For slab load at critcal section from face=25.32TonVsdl = For superimposed dead loads =25.00TonFrom Model at critcal section from faceML.L = For live load at critcal section from face=152.00Ton - mFrom ModelMgirder = For girder load at critcal section from face=58.00Ton - mMslab = For slab load at critcal section from face=10.00Ton - mMsdl = For superimposed dead loads =100.00Ton - mFrom Model at critcal section from faceb' = Thickness of web of the girder=0.200m=7.87inchesd = 0.8 h=2.140m=84.25inches

fc' = Concrete strength of girder=5,000Psifsy = Steel strength=60,000PsiMd = ( girder + slab)=68.00Ton - mV dead load = V girder + V slab=73.00TonVu = 1.3(V dead load + 1.67xV live load)=214.24Ton=472.18Kips

Vi =1.3(V dead load + V sdl + 1.67x VL.L) - (V dead load + Vsdl)=116.24Ton=256.19Kips=256192.96lbs

Total height of composite section=2.675m=105.32inchx = distance from end to the critical section=2.675my = centroid of tendons from bottom at critical section=0.935m

d = distance of centroid of girder section from bottom=1.261me = d-y=0.326mpe=6784.75kN =691.62tonsfpe = pe / Ac + pe * e / Zb =1028.73Ton /m2=210.75k/ft2=1462.80lbs/in2

fd = stress due to unfactored dead loads = Md / Zb=222.78Ton /m2=45.61k /ft2=316.78lbs/in2

Mcr = I / Yb ( 6 ( fc' )1/2 + fpe - fd )=928.61Ton-m=6715.05kip- feet

Mmax = 1.3 (Md + Msdl + 1.67 M L.L) - (Md + Msdl) =380.39Ton - m=2750.74kip- feet=3.301E+07lb - in

Vci = 0.6(fc')1/2 b'd + Vd + Vi (Mcr/Mmax)=369.53Tons=814.45kips

Check: 1.7(fc')1/2b'd=36.18TonsOK

fpc = Pe/Ac=409.68Ton /m2=83.88k /ft2

Vp = Vertical component of effective prestress force=73.45Ton=161.88kips=Vcw = (3.5(fc')1/2 + 0.3 fpc)b'd + Vp=200.55Tons=442.02kips

Shear Strength provided by concrete = lesser of Vci & Vcw=200.55Tons=442.02kips Vc =170.47Tons=375.71kips

Vu=214.24Tons=472.18kipsVS = Vu - Vc =43.77Tons=96.47kips

VS Should not be taken greater than 8(fc')1/2b'd 8(fc')1/2b'd=170.27Tons=375.27kipsVS< 8(fc')1/2b'dOK

Area of shear reinforcement provided/leg=0.20in2No. of shear reinforcement legs provided=2Nos.s = Avfyd/Vs (USING #4 FOUR LEGGED STIRRUPS)=17.46in=443mm

When VS exceeds 4(fc')1/2b'd4(fc')1/2b'd85.13Tons=187.64kips

CRITERIA FOR MAXIMUM SPACINGi ) Spacing should not be greater than=24.00inchesii ) Spacing should not be greater than 0.75h=78.99inchesiii ) Spacing = Av fsy/50b' ( if Av = 0.4 in)=59.74inches

s required(Min. of Three & s calculated)=17.46inches c/c=443mm

CHECK FOR HORIZONTAL SHEARbv = width of girder section at top=1.30m=51.18inchd = 0.8h (h is total depth of girder puls slab)=2.14m=84.25inchVnh = 80 bv d=156.52Tons=344.97kips

Vnh =133.04Tons=293.22kipsVu=214.24Tons=472.18kips

Vu>fVnh stirrups of pre cast girder must be extend into the deck slab

CALCULATIONS FOR END BLOCK REINFORCEMENT

Jacking Force in Cable = Pj =179.3TonsEffective Force after Losses = Pe=138.3Tons

fc' of girder =3516.68Ton /m2=5000lbs/in2fci' i.e conc. Strength at jacking=3516.68Ton /m2=5000lbs/in2fy=42200.21Ton /m2=60000lbs/in2Height of girder=2.45m

Try Size of Anchorage Plate (Square)=300mmDia of Sheathing (hole)=75mmSize of symmeterical concrete blockaround anchorage plate=360mm

Anchorage Plate Area = A1=0.0856m2Concrete block Area = A2=0.2520m2

Check at Service Loads:

After Losses Bearing Stress = Pe / A1=1616.3Ton /m2=2298.0lbs/in2Allowable Anchorage Bearing Stress=3165.0Ton /m2=4500.0lbs/in2Anchorage Plate Size is O.K.

Check at Ultimate Loads:

At Jacking Bearing Stress = 1.15 Pj / A1 =2408.7Ton /m2=3424.7lbs/in2

Allowable Bearing Stress at Jacking =i) 0.8 fci' ( A2 / A1 - 0.2 )1/2 =5143.2Ton /m2=7312.5lbs/in2ii) 1.5 0.85 fci' ( A2 / A1 )1/2=4616.4Ton /m2=6563.6lbs/in2

Minimum of the two4616.4Ton /m2=6563.6lbs/in2but should be less than 1.25 fci'=4395.9Ton /m2=6250.0lbs/in2Increase the Size of Anchorage PlateAnchorage Plate Size is O.K.

After Losses Bearing Stress = 1.15 Pe / A1=1858.7Ton /m2=2642.7lbs/in2

Allowable Bearing Stress after Losses =0.6 fc' ( A2 / A1 )1/2=3620.7Ton /m2=5148.0lbs/in2but should be less than fc'=3516.7Ton /m2=5000.0lbs/in2Increase the Size of Anchorage PlateAnchorage Plate Size is O.K.

Ref. Stronghold Brocheure1/2 of symmeterical concrete block = Yo =180mm1/2 of steel anchor plate = Ypo=150mmYpo / Yo=0.833Bursting Force/Jacking Force = Fbst / Pk=0.15From Table II Stronghold BrochureArea of Steel = As = Fbst / ( 0.9 fy )=0.0006999439m2=1.09in2Horizontal and Vertical over a Length of 2Yo = 360mm from face behind each anchor

Height of Plate/Height of Girder = hb / h=0.1224