Steel Truss Bridge Design Example

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Steel Truss Bridge Design Example

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<p>Property Calculation for trus bridge</p> <p>Bas_data1.0IntroductionThis design note consists of 40m through trussed bridge.The analysis of the structure has been done by a complete mathematical modelling using STAAD-Pro analysis software, while the design is done manually in line with the procedure &amp; parameters laid down in the following standards:1.IRC:6-20002.IRC:21-20003.IRC:22-19864.IRC:24-20015.IS:11384-19856.BS:5400-Part5:1979Design of truss superstructurespan (centre to centre of bearings): 55.0m2.0Basic Design Data:Statical scheme:Main Girders:Simply supported N type trusses (2 sets)with concrete deck at the top actingcompositely with the main longitudinalsCross Bracings:at locations of the joint of verticals &amp; the top&amp; bottom chordTop chord bracings:No bracing as the composite deck will servethe purposeBottom chord bracing :At every panel, as crossed braces.Span of Main girders:40m(c/c of bearing)Carriageway width:4.25mCrash barrier width:0.45mCentral median:0m(including crash barrier)Gap between crash barrier:0mand structureExtra widening for curvature:0m on each sideTotal clear width of structure:5.15m(span of cross girders)Wearing coarse thickness:75mm to be provided100mm for design purposeCross fall on roadway:2.5% in both directionsMinimum depth of slab:200mmLive load:24 RDensity of concrete:2.5t/m3Density of wearing coarse:2.3t/m3Density of steel:7.85t/m3Grade of Concrete:"1" 00Grade of Steel:Fe 540Yeild Stress of Steel:390MPaModulus of Elasticity of Steel:2.11E+05MPaModulus of Elasticity of Conc.:27500.00MPa(as per IRC:21-2000 cl.303.1)Coefficient of thermal expansionSteel:0.000012/CConcrete:0.000012/C(as per IRC:22)For class 25t tracked vehicle, impact factor(as per IRC:6-2000 cl.211.2 &amp; figure 5)1.154</p> <p>SECTIONAL PROPERTYDesign of Through Steel BridgeE+ffective Span 40.0mCalculation of Member propertiesSteel Members:Bottom chord.(ND-1)250Cross sectional area (A) (m2):0.01010.010--C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--Ix-y (torsional constant) (m4):0.00016019640.00016--230Bottom chord.(ND-2)250Cross sectional area (A) (m2):0.01010.010--C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--Ix-y (torsional constant) (m4):0.00016019640.00016--230Bottom chord.(ND-3)250Cross sectional area (A) (m2):0.01010.010--180C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--Ix-y (torsional constant) (m4):0.00016019640.00016--230Top chord.ND-1250Cross sectional area (A) (m2):0.01010.010--C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--FXIx-y (torsional constant) (m4):0.00016019640.00016--230Top chord.ND-2250Cross sectional area (A) (m2):0.01010.010--C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--Ix-y (torsional constant) (m4):0.00016019640.00016--230Top chord.ND-3250Cross sectional area (A) (m2):0.01010.010--C.g. distance from top (m):0.13750.138--27510255C.g. distance from left (m):0.1250.125--10Ix-x (I about x-axis) (m4):0.00011545850.00012--Iy-y (I about y-axis) (m4):0.0000995240.00010--Ix-y (torsional constant) (m4):0.00016019640.00016--230Vertical Member.1008Cross Sectional Area (m2)0.0035C.g. distance from bottom (m)0.1250C.g. distance from left (m)0.05008234IX-X (m4)0.00003198IY-Y (m4)0.00000134Torsional Constant (m4)0.00000007Zt (m3)0.0003Zb (m3)0.00038ZLeft (m3)0.0000100ZRight (m3)0.0000Diagonal Member.250Cross sectional area (A) (m2):0.00770.008--C.g. distance from top (m):0.1250.125--2508234C.g. distance from left (m):0.1250.125--8Ix-x (I about x-axis) (m4):0.000075670.00008--Iy-y (I about y-axis) (m4):0.000075670.00008--Ix-y (torsional constant) (m4):0.00011337990.00011--234Bottom Transverse chord.(ISMB 500)15017.4Cross Sectional Area (m2)0.0096C.g. distance from bottom (m)0.2500C.g. distance from left (m)0.07509.4465.2IX-X (m4)0.0003829IY-Y (m4)0.0000098Torsional Constant (m4)0.00000058Zt (m3)0.0015Zb (m3)0.001517.4ZLeft (m3)0.0001150ZRight (m3)0.0001Top Transverse chord.(ISMB 350)14014.2Cross Sectional Area (m2)0.0066C.g. distance from bottom (m)0.1750C.g. distance from left (m)0.07008.1321.6IX-X (m4)0.0001346IY-Y (m4)0.0000065Torsional Constant (m4)0.00000029Zt (m3)0.0008Zb (m3)0.000814.2ZLeft (m3)0.0001140ZRight (m3)0.0001Top &amp; Bottom Bracing Member.Cross sectional area (A) (m2):0.00011360.00011(2-22f hole on each leg)0.00000C.g. distance from top (m):0.037800.038Ix-x (I about x-axis) (m4):0.000000260.000000258Iy-y (I about y-axis) (m4):0.000002560.000022Ix-y (tortional constant) (m4):0.000100.00010.000002-ISA50x50x6zt (m3):0.000010.0000Face to facezb (m3):0.000000.0000with20 mmgap in betweenTop Main Transverse Member.325Cross sectional area (A) (m2):0.01260.013--C.g. distance from top (m):0.16250.163--32510305C.g. distance from left (m):0.16250.163--010Ix-x (I about x-axis) (m4):0.00020858250.00021--Iy-y (I about y-axis) (m4):0.00020858250.00021--Ix-y (torsional constant) (m4):0.00031255880.00031--305Top Main Transverse Member.1508Cross Sectional Area (m2)0.0043C.g. distance from bottom (m)0.1250C.g. distance from left (m)0.07508234IX-X (m4)0.0000437IY-Y (m4)0.0000045Torsional Constant (m4)0.00000008Zt (m3)0.0003Zb (m3)0.00038ZLeft (m3)0.0001150ZRight (m3)0.0001Top And Bottom Main Chord.30025Cross Sectional Area (m2)0.0213C.g. distance from bottom (m)0.150016027.5C.g. distance from left (m)0.150055085025250IX-X (m4)0.0003169816IY-Y (m4)0.00011281000Torsional Constant (m4)0.0000039519243.5Zt (m3)0.0021Zb (m3)0.002125ZLeft (m3)0.0008300ZRight (m3)0.0008</p> <p>yyxxyyxxyyxxYYXXyyxxyyxx</p> <p>design of trans memberDesign Of Bottom Transverse Member0.925m10.87dead load6.412kn6.412kn4.313SIDL6mDEAD LOAD ANALYSIS1Load calculation.I)Due to deck slab==0.23182*2.5*1.875*1010.8665625kn/mii)Due to kerb &amp; railing ==2.461*1.875+0.454*1.8755.465625kniii)Due to future overlay==0.1*1.875*2.3*104.3125kn/miv)Using ISMB550 as member=1.037kn/m2Moment calculationI)Moment due to dead load==10.866563*6*6/848.89953125knmii)Moment due to Railing &amp; Kerb==5.465*(6/2-0.925)11.341171875knmiii)Moment due to overlay butemen==4.3125*6*6/819.40625knmiv)Moment due to ISMB550=1.037*6*6/84.6665knmLIVE LOAD ANALYSIS64.04kn64.04kn5201560AB6mReaction at A=Ra==64.04(2.98+5.06)/685.8136KNMMoment at mid span=263.7858832knmLoad combination1Dead load + Deck Load=53.56603125knm2SIDL+LL=294.533305075knmOnly steel memberZ required=357106.875mm3357.106875cm3Using ISMB 550Zxx=2359.8cm3Check for only steel memberCalculated bending compression stress=22.70MpaHence okCalculated bending tension stress=22.70MpaHence okCheck for composite sectionStress at level15.4889316961MpaHence okStress at level4-96.3345569941MpaHence ok</p> <p>Sec-prop3.0Calculation of section propertiesModular ratio(m):10Creep Factor(Kc):0.5Moduar ratio for permanent loadings(mp):20Moduar ratio for transient loadings(mt):10Sectional Properties of Top Chord:2575Member Profile:200Basic Property of ISMC 225:0(refer IS:808-1989)1800Sectional Area (A):25.9cm2IXX :2694.6cm4IYY :187.2cm40CYY :2.3cmThickness of Flange (Av.), tf =12.4mm2-ISMC225Thickness of Web, tw =6.4mmBack to backFor Steel Only Case:Area of Top Chord:(25.9*2*100-2*12.4*22-2*2*6.4*22)/10^6 =0.0041m2(Assuming 2-22f hole on the web &amp; 1-22f hole on top flanges of the channels)C.g. Distance from top:0.1mIx-x (I about x-axis) (m4):2*(2694.6*1e+04)/1e+012 =0.000054m4Iy-y (I about y-axis) (m4):2*(187.2*10000+25.9*100*(2.3*10+80)^2)/1e+012 =0.000059m4For Composite (short term loading) Case:m = mtArea of Top Chord:0.0041+(2575/10*200)/10^6 =0.0556m2C.g. Distance from top:(0.0041*(0.2+0.1)+(2575*200/10*200/2)/1e+09)/0.0555712 =0.115mIx-x (I about x-axis) (m4):0.000054+0.0040712*(0.2+0.1-0.115)^2+ (2575*200^3/12+(2575*200*(200/2-0.115*1000)^2))/10/1e+012 =0.000376m4Iy-y (I about y-axis) (m4):0.000059+((200*2575^3/12)/10)/1e+012 =0.028515m4For Composite (long term loading) Case:m = mpArea of Top Chord:0.00407+(2575*200+(6+0)/2*1)/(20*10^6) =0.0298m2C.g. Distance from top:(0.0041*(0.2+0.1)+(200*2575*100)/20/1e+09)/0.0298 =0.127mIx-x (I about x-axis) (m4):0.00005+0.0041*(0.2+0.1-0.12744)^2+((2575*200^3/12+2575*200*(127.44-200/2)^2)/20)/1e+012 =0.000282m4Iy-y (I about y-axis) (m4):0.000059+((200*2575^3/12)/20)/1e+012 =0.014287m4The other properties are calculated in line to above calculation &amp; are tabulated as below:MemberProfileItemValueSteel onlymt *mp #Top Chord2575Cross cestional area (A) (m2):0.004070.055570.02982200(2-22f hole on web, 1-22f hole on flange)C.g. distance from top (m):0.1000.1150.1271Ix-x (I about x-axis) (m4):0.0000540.0003760.00028000Iy-y (I about y-axis) (m4):0.0000590.0285150.014287Ix-y (tortional constant) (m4):0.00010.00010.00016550zt (m3):0.00050.00330.0022zb (m3):0.00020.00080.00102-ISMC225Back to backwith160 mmgap in betweenBottom ChordCross sectional area (A) (m2):0.00407(2-22f hole on web, 1-22f hole on flange)C.g. distance from top (m):0.100Ix-x (I about x-axis) (m4):0.000054Iy-y (I about y-axis) (m4):0.000059Ix-y (tortional constant) (m4):0.000100zt (m3):0.0005zb (m3):0.00052-ISMC225Back to backwith160 mmgap in betweenVerticalsCross cestional area (A) (m2):0.00511(2-22f hole on web)C.g. distance from top (m):0.100Ix-x (I about x-axis) (m4):0.000036Iy-y (I about y-axis) (m4):0.000022Ix-y (tortional constant) (m4):0.0001zt (m3):0.0004zb (m3):0.00042-ISMC200Face to facewith160 mmedge to edge dist.DiagonalsCross cestional area (A) (m2):0.00511(2-22f hole on web)C.g. distance from top (m):0.100Ix-x (I about x-axis) (m4):0.000036Iy-y (I about y-axis) (m4):0.000022Ix-y (tortional constant) (m4):0.00012-ISMC150zt (m3):0.0004Face to facezb (m3):0.0004with160 mmedge to edge dist.Back to backwith20 mmthick gusset plateBottom BracingCross cestional area (A) (m2):0.00057(2-22f hole on web)C.g. distance from top (m):0.004Ix-x (I about x-axis) (m4):0.0000001Iy-y (I about y-axis) (m4):0.0000001Ix-y (tortional constant) (m4):0.0001zt (m3):0.000036zb (m3):0.000003ISMA 50x50x6Transversals at cross bracing locationCross cestional area (A) (m2):0.00370(2-22f hole on web)C.g. distance from top (m):0.075Ix-x (I about x-axis) (m4):0.000016Iy-y (I about y-axis) (m4):0.000006Ix-y (tortional constant) (m4):0.0001zt (m3):0.0002zb (m3):0.00022-ISMC150Back to backwith20 mmgap in betweenTransversals at locations other than X-bracingsCross cestional area (A) (m2):0.00169(2-22f hole on web)C.g. distance from top (m):0.075Ix-x (I about x-axis) (m4):0.000007Iy-y (I about y-axis) (m4):0.000001Ix-y (tortional constant) (m4):0.0001zt (m3):0.0001zb (m3):0.0001ISMB150Transvers DiagonalsCross cestional area (A) (m2):0.00140(2-22f hole on web)C.g. distance from top (m):0.075Ix-x (I about x-axis) (m4):0.000008Iy-y (I about y-axis) (m4):0.000001Ix-y (tortional constant) (m4):0.0001zt (m3):0.0001zb (m3):0.0001ISMC150* mt = Properties of composite section using modular ratio as mt# mp = Properties of composite section using modular ratio as mp</p> <p>YYYXXYYXXYYXXYYXXYYXXYYXXYYXXYXXYYXX</p> <p>Composite PropertyCalculation of Member propertiesComposite MembersGrade of Concrete ="1"0E of Concrete =25491.17N/mm2E of Steel =211000N/mm2Modular Ratio for Short term loading =8.28Modular Ratio for Long term loading =16.55MemberProfileSectional PropertiesShort Term a =8.28Long Term a =16.55Transverse Girders (ISMB 550)1875(all in Steel units, except where specified otherwise)190200Cross Sectional Area (m2)0.0734Cross Sectional Area (m2)0.0508Area steel only(m2)0.0131Area steel only(m2)0.0131C.g. distance from bottom (m)0.5179C.g. distance from bottom (m)0.3389C.g. distance from left (m)0.9375C.g. distance from left (m)0.9375IX-X (m4)0.0016IX-X (m4)0.00158IY-Y (m4)0.0177IY-Y (m4)0.011111.2515.619.3Torsional Constant (m4)0.00001Torsional Constant (m4)0.000002Z1 (m3) (in concrete units)0.0537Z1 (m3) (in concrete units)0.0585Z2 (m3) (in concrete units)0.2961Z2 (m3) (in concrete units)0.1108Z3 (m3)0.0358Z3 (m3)0.0067190Z4 (m3)0.0031Z4 (m3)0.004419.3ZA (m3) (in concrete units)0.1562ZA (m3) (in concrete units)0.1952ZA (m3)0.0189ZA (m3)0.0118ZB (m3)0.1862ZB (m3)0.1163ZC (m3)0.1862ZC (m3)0.1163Transverse Girders (Type 2)70937.5Cross Sectional Area (m2)0.0455Cross Sectional Area (m2)0.0333190200C.g. distance from bottom (m)0.4858C.g. distance from bottom (m)0.4513C.g. distance from left (m)0.3788C.g. distance from left (m)0.3332IX-X (m4)0.0015IX-X (m4)0.0013IY-Y (m4)0.0045IY-Y (m4)0.00328Torsional Constant (m4)0.00001Torsional Constant (m4)0.000002515.619.311.2Z1 (m3) (in concrete units)0.0437Z1 (m3) (in concrete units)0.0697Z2 (m3) (in concrete units)0.1580Z2 (m3) (in concrete units)0.1955Z3 (m3)0.0191Z3 (m3)0.0118Z4 (m3)0.0030Z4 (m3)0.002919019.3ZA1 (m3) (in concrete units)0.0595ZA1 (m3) (in concrete units)0.0793ZA3 (m3)0.0072ZA3 (m3)0.0048ZB (m3)0.0211ZB (m3)0.0192ZC (m3)0.0211ZC (m3)0.0192ZD (m3)0.0112ZD (m3)0.0090ZE (m3)0.0112ZE (m3)0.0090ZF3 (m3)0.0119ZF3 (m3)0.0097ZF1 (m3) (in concrete units)0.0987ZF1 (m3) (in concrete units)0.1605Longitudinal Girders (Type 1)13051305Cross Sectional Area (m2)0.0895Cross Sectional Area (m2)0.0579140200C.g. distance from bottom (m)0.3058C.g. distance from bottom (m)0.2948C.g. distance from left (m)1.3050C.g. distance from left (m)1.3050IX-X (m4)0.0002IX-X (m4)0.0002IY-Y (m4)0.0477IY-Y (m4)0.02988Torsional Constant (m4)0.00001Torsional Constant (m4)0.000002275.212.47.5Z1 (m3) (in concrete units)0.0096Z1 (m3) (in concrete units)0.0167Z2 (m3) (in concrete units)0.8879Z2 (m3) (in concrete units)0.2685Z3 (m3)0.1073Z3 (m3)0.0162Z4 (m3)0.0008Z4 (m3)0.000714012.4ZA1 (m3) (in concrete units)0.3023ZA1 (m3) (in concrete units)0.3775ZA3 (m3)0.0365ZA3 (m3)0.0228ZB (m3)-0.6808ZB (m3)-0.4251ZC (m3)-0.6808ZC (m3)-0.4251ZD (m3)0.6808ZD (m3)0.4251ZE (m3)0.6808ZE (m3)0.4251ZF3 (m3)0.0365ZF3 (m3)0.0228ZF1 (m3) (in concrete units)0.0138ZF1 (m3) (in concrete units)0.0076Longitudinal Girders (Type 3)13051305Cross Sectional Area (m2)0.0895Cross Sectional Area (m2)0.0579140200C.g. distance from bottom (m)0.3058C.g. distance from bottom (m)0.29481.25280.390C.g. distance from left (m)1.3050C.g. distance from left (m)1.3050IX-X (m4)0.0002IX-X (m4)0.0002IY-Y (m4)0.0477IY-Y (m4)0.02988Torsional Constant (m4)0.00001Torsional Constant (m4)0.000002275.212.47.5Z1 (m3) (in concrete units)0.0096Z1 (m3) (in concrete units)0.0167Z2 (m3) (in concrete units)0.8879Z2 (m3) (in concrete units)0.2685Z3 (m3)0.1073Z3 (m3)0.0162Z4 (m3)0.0008Z4 (m3)0.000714012.4ZA1 (m3) (in concrete units)0.3023ZA1 (m3) (in concrete units)0.3775ZA3 (m3)0.0365ZA3 (m3)0.0228ZB (m3)0.6808ZB (m3)0.4251ZC (m3)0.6808ZC (m3)0.4251ZD (m3)0...</p>

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