Effective Slab Width for Composite Steel Bridge Members (2005) / Chapter Skim
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Appendix O: Design Examples
Appendix O: Design Examples
Pages 89-153
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From page 89... ...
O-1 APPENDIX O DESIGN EXAMPLES Appendix O has not been edited by TRB.
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From page 90... ...
The girder is laterally braced at a spacing of 7 meters and 6 meter in the positive and negative moment regions, respectively. The locations of the cross frames avoid interference with the field splice.
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From page 91... ...
This design incorporates the following structural steels: Grade 345W : Top flange in the positive moment region and the entire web Grade 485W HPS : Both flanges in the negative moment regions and the bottom flange in the positive moment region Grade 420 : Deck reinforcing steel The concrete compressive strength is 28 MPa with a modular steel-to-concrete ratio, n=8. The deck reinforcing steel has a minimum yield stress of 420 MPa.
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From page 92... ...
Elevation View of Interior Girder 4 at 7000 mm = 28000 mm 30000 mm End bearing 10000 mm cross frame connection plates intermediate stiffeners cross frame connection plate Bolted field splice Pier bearing
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From page 93... ...
• This example assumes no lateral load will be applied to the flanges of interior girders in either the positive or negative moment regions. • Other design assumptions are stated within the design calculations.
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From page 94... ...
Art ...............................Area of the top layer of reinforcing steel within the effective slab width. As_bottom_min .................Minimum cross-sectional area of bottom reinforcing steel per unit deck width required in the negative moment region for empirical deck design.
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From page 95... ...
df.t ...............................Distance from the bottom of girder to the centroid of the top flange. DFM1..........................Moment load distribution factor for one lane loaded case.
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From page 96... ...
DM4 .............................Moment load distribution factor for four lanes loaded case including multiple presence factor. Applies to the exterior girder.
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From page 97... ...
fDW_cf ..........................Stress in the compression flange calculated from unfactored wearing surface dead load. fDW_tf...........................Stress in the tension flange calculated from unfactored wearing surface dead load.
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From page 98... ...
fLL_IM_tf .......................Stress in the tension flange calculated from unfactored live load plus impact. fmid ..............................Stress in compression flange calculated from Mmid.
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From page 99... ...
m4 ...............................Multiple presence factor for four lanes loaded. MAD ..........................Remaining flexural resistance in flange calculated by subtracting stresses due to dead loads factored by the strength I load combination in terms of stress.
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From page 100... ...
R1................................Moment load distribution factor for one lane loaded case excluding the multiple presence factor. R2................................Moment load distribution factor for two lanes loaded case excluding the multiple presence factor.
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From page 101... ...
spacingtop_max ..............Maximum spacing of top reinforcing steel based on empirical deck design. STop_Steel_LT..................Long-term elastic section modulus of the girder with respect to outer fiber of the top flange steel.
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From page 102... ...
Vfat_min ........................Minimum shear force at point of interest due to fatigue load combination. Used in the design of the shear connectors.
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From page 103... ...
γ fws ................................Specific gravity of future wearing surface. λf ...................................Slenderness ratio of the compression flange.
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From page 104... ...
NG 1− := girder spacing S 3690mm= DEFINITION OF GEOMETRIC PARAMETERS General: NG 5:= number of girders NL 3:= number of traffic lanes Lengths: Lspan 40 m := span length Thicknesses: tdeck 240 mm := slab thickness w/ IWS ts 200 mm := structural thickness thaunch 50 mm := haunch thickness ctop 60 mm := top reinforcement cover thickness [S5.12.3] cbottom 25 mm := bottom reinforcement cover thickness [S5.12.3]
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From page 105... ...
load wtfws 1.2 kN m 2 = =25 psfγconc 2402 kg m 3 ⋅ := Steel Reinforcement Properties: Ec 0.043 γ conc m 3 ⋅ kg 1.5 ⋅ f'c_deck MPa⋅ ⋅ := Fyr 420 MPa⋅ := =60 ksi yield stress Ec 26785.9MPa= [S5.4.2.4-1] Es 200000 MPa⋅ := modulus of elasticity Steel Properties: Steel Decking Properties: Fy.345 345 MPa⋅ := grade 345 steel ⎟ ⎠ ⎞ ⎟ ⎠ ⎞
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From page 106... ...
A handling suggestion for shipping and constructability is to provide a minimum flange width as calculated below: Lpick 0.75 Lspan⋅ := Lpick 30 m= pick length bf Lpick 85 := bf 352.9 mm= handling suggestion [C6.10.3.4-1 '04] PRELIMINARY PLATE SIZING Flange Sizing Considerations: Flange Width Considerations: • Consider wider compression flanges for the bottom flange in the negative moment region Use minimum of 300 mm in width to allow room for shear studs.
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From page 107... ...
Lspan 30 1333 mm= Summary Trial Girder Dimensions: Positive Flexure: Negative Flexure: Top flange width: bf.t 400 mm⋅ := =15.75 in bf.t.n 450 mm⋅ := =17.72 in Top flange thickness: tf.t 25 mm⋅ := = 1 in tf.t.n 40 mm⋅ := =1.58 in Bottom flange width: bf.b 400 mm⋅ := 14mm 40mm 1300mm 14mm 400mm 25mm 400mm25mm 450mm 540mm40mm 1300mm
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From page 108... ...
2⋅ +:= If.b 4.39 109× mm4= Iw tw D3 12 ⋅ Aw dw dBot_Steel_NC− ( ) 2⋅ +:= Iw 2.56 109× mm4= INC If.t If.b+ Iw+:= INC 1.13 10 10 × mm 4 = STop_Steel_NC INC dTop_Steel_NC := STop_Steel_NC 1.68 10 7 × mm 3 = SBot_Steel_NC INC dBot_Steel_NC := SBot_Steel_NC 1.68 10 7 × mm 3 = NON COMPOSITE SECTION PROPERTIES Non-Composite Cross-Sectional Properties in the Positive Moment Region: overall depth: d tf.t D+ tf.b+:= d 1350mm= area of top flange: Af.t bf.t tf.t⋅ := Af.t 10000mm 2 = area of bottom flange: Af.b bf.b tf.b⋅ := Af.b 10000mm 2 = area of web: Aw D tw⋅ := Aw 18200mm 2 = total area of girder: Ag Af.t Af.b+ Aw+:= Ag 38200mm 2 = girder self-weight: wtg Ag wtsteel⋅:= wtg 2.94 kN m = dist.
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From page 109... ...
2⋅ +:= If.b.n 8.53 109× mm4= Iw.n tw.n D3 12 ⋅ Aw.n dw.n dBot_Steel_NC.n− ( ) 2⋅ +:= Iw.n 2.59 109× mm4= INC.n If.t.n If.b.n+ Iw.n+:= INC.n 2.02 10 10 × mm 4 = STop_Steel_NC.n INC.n dTop_Steel_NC.n := STop_Steel_NC.n 2.77 10 7 × mm 3 = SBot_Steel_NC.n INC.n dBot_Steel_NC.n := SBot_Steel_NC.n 3.12 10 7 × mm 3 = Non-Composite Cross Sectional Properties in the Negative Moment Region: overall depth: dn tf.t.n D+ tf.b.n+:= dn 1380mm= area of top flange: Af.t.n bf.t.n tf.t.n⋅ := Af.t.n 18000mm 2 = area of bottom flange: Af.b.n bf.b.n tf.b.n⋅ := Af.b.n 21600mm 2 = area of web: Aw.n D tw.n⋅ := Aw.n 18200mm 2 = total area of girder: Ag.n Af.t.n Af.b.n+ Aw.n+:= Ag.n 57800mm 2 = girder self-weight: wtg.n Ag.n wtsteel⋅ := wtg.n 4.45 kN m = dist.
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From page 110... ...
DFM1fatigue DFM1 1.20 := DFM1fatigue 0.443= LIVE LOAD GIRDER DISTRIBUTION FACTORS Interior Beam Moment: Kg term: [S4.6.2.2.1-1 '03] dTop_Steel_NC_avg dTop_Steel_NC dTop_Steel_NC.n+ 2 := INC_avg INC INC.n+ 2 := INC_avg 1.58 10 10 × mm 4 = Ag_avg Ag Ag.n+ 2 := Ag_avg 4.8 10 4 × mm 2 = Distance between C.O.G.
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From page 111... ...
Truck width: wtruck 1800 mm⋅ := Spacing between trucks: struck 1800 mm⋅ := Number of design lanes: Figure : Position of Truck Reaction for Exterior Girder Distribution Factor 600 mm 1200 mm 4800 mm 2400 mm 6000 mm 3690 mm 7380 mm ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠
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From page 112... ...
⋅ x1 2 x2 2 + x3 2 + x4 2 + x5 2 +( ) +:= R4 0.93= DM4 m4 R4⋅ := DM4 0.60= Distance between girders and center of bridge: x1 wbridge 2 woh−:= x1 7.38m= dist to girder 1 from CL x2 x1 S− := x2 3.69m= dist to girder 2 from CL x3 x2 S− := x3 0m= dist to girder 3 from CL x4 x3 S−:= x4 3.69− m= dist to girder 4 from CL x5 x4 S−:= x5 7.38− m= dist to girder 5 from CL Xext x1:= Xext 7.38m= dist to exterior girder from CL Multiple Presence Factors: m1 1.20:= m3 0.85:= R NL NB Xext NL eΣ ⋅ NB x 2Σ +
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From page 113... ...
Distance to driving loads: Driving woh S+ wp− Struck_parapet− wtruck 2 − := Driving 2310 mm= Distance to resisting girder: Resisting S:= Resisting 3690mm= Distribution Factor Moment: Figure : Position of Truck Tire Reactions for Lever Rule One Lane Loaded: DMFLever1_f Driving Resisting := DMFLever1_f 0.626= DMFLever1 DMFLever1_f 1.20⋅ := DMFLever1 0.751= 600 mm 1800 mm 3690 mm600 mm 1410 mm
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From page 114... ...
DFVskew_corr 1.0 0.2 Lspan ts 3 ⋅ Kg 0.3 ⋅ tan θ ( ) ⋅ +:= DFVskew_corr 1.061= Governing Distribution Factors: (skew corrected)
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From page 115... ...
S η i γ i⋅ Qi⋅ φ Rn⋅ ≤ Rr General Considerations for Limit States
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From page 116... ...
⋅ := Interior Girder Component Dead Load: DC1attachments 0.17 kN m = DC1attachments 5% DC1girder⋅ := DW 3.60 kN m =DW wtfws wroadway⋅ NG := DC1girder 3.32 kN m = DC1girder 0.75 wtg⋅ 0.25 wtg.n⋅+:= Superimposed Component Dead Loads: DW - wearing surface load• acts on long-term composite section• assumed to be carried equally by all girders• DC1sipf 2.65 kN m = DC2p 1.44 kN m =DC2p wtp NG := DC1sipf wtsipf S⋅:= DC1haunch 0.47 kN m = wtp 7.2 kN m ⋅:= DC1haunch wtconc bf.t thaunch⋅ ( ) ⋅:= Superimposed Component Dead Loads: DC2 - acts on long-term composite section• assumed to be carried equally by all girders• Component Dead Loads: DC1 - acts on non-composite section• DESIGN LOADS ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦
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From page 117... ...
The minimum amount of reinforcement in positive moment regions shall be: For each bottom layer, 0.570 mm2/mm in both directions For each top layer, 0.380 mm 2/mm in both directions Reinforcement shall be Grade 420 or higher and the spacing shall not exceed 450 mm If the skew exceeds 25 degrees the specified reinforcement in both directions shall be doubled in the zones of the deck. Each end zone shall be taken as the longitudinal distance equal to the effective len the slab specified in Article 9.7.2.3.
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From page 118... ...
16M bars spaced at 300 mm. As_bottom_min 0.67 mm 2 mm =As_bottom_min 1 3 As_neg_min⋅ := Longitudinal reinforcing bars in bottom layer of negative moment region: As_neg_min 2.00 mm 2 mm = As_neg_min ts 0.01⋅ mm mm := In negative-flexure regions of any continuous span, the specified minimum longitudinal• reinforcement shall not be less than 1% of the total cross-sectional area of the slab.
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From page 119... ...
16M bars spaced at 300 mm. spacing provided 300mm:= As_top_provided A19 spacingprovided A16 spacingprovided +:= As_top_provided 1.61 mm 2 mm = Transverse reinforcing bars in negative moment region: The transverse steel in both the top and bottom layers is the same as previously determined for the positive moment regions.
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From page 120... ...
2⋅ + Ideck Adeck.ST ydeck dTop_Steel_ST+( ) 2⋅ ++ ...:= STop_Steel_ST IST dTop_Steel_ST := SBot_Steel_ST IST dBot_Steel_ST := Short-term section properties: IST 3.004 10 10 × mm 4 =Short-term moment of inertia: dTop_Steel_ST 91.6mm=Short-term distance from top of steel to NA: dBot_Steel_ST 1258.4mm=Short-term distance from bottom of steel to NA: STop_Steel_ST 3.28 10 8 × mm 3 =Short-term section modulus top section: SBot_Steel_ST 2.387 10 7 × mm 3 =Short-term section modulus bottom section: COMPOSITE SECTION PROPERTIES Positive Moment Region: Short-term composite section: n 8:= [C6.10.1.1.1b]
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From page 121... ...
3 n⋅ 24=Long-term composite section:
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From page 122... ...
Assumes no net axial force Section forces: Rebar area determined by summing the reinforcement area in the deck design section across the effective slab width. Art A16 300 mm⋅ beff⋅ := Art 2447.7 mm 2 = Arb A16 300 mm⋅ beff := Arb 2447.7 mm 2 = Ptr Fyr Art⋅ := Ptr 1.0 10 3 × kN= Ps 0.85 f'c_deck⋅ beff ts⋅ ( )
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From page 123... ...
ys 301.1 mm=ys 0.5 ts⋅ ybar+ thaunch+:= Distance from PNA to the slab's NA: yrt 67.3 mm=yrt ybar Crt− := Distance from PNA to the top reinforcement: yrb 151.2 mm=yrb Crb:= Distance from PNA to the bottom reinforcement: ytf 111.4 mm=ytf thaunch ts+ tf.t 2 + ybar− := Distance from PNA to the top flange's NA: yw 773.9 mm=yw 0.5 D thaunch+ ts+ tf.t+ ybar−:= Distance from PNA to the web's NA: ybf 1436.3 mm=ybf d thaunch+ ts+ tf.b 2 − ybar− := Distance from PNA to the bottom flange's NA: ybar 151.2 mm=From top of the slabybar YIV:= Distance to PNA:
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From page 124... ...
Moment of inertia of section: IComp.n 2.628 10 10 × mm 4 = Distance from top of steel to NA: dTop_Steel_Comp.n 611.7 mm= Distance from bottom of steel to NA: dBot_Steel_Comp.n 768.3 mm= Section modulus top section: STop_Steel_Comp.n 4.297 10 7 × mm 3 = Section modulus bottom section: SBot_Steel_Comp.n 3.421 10 7 × mm 3 = Negative Moment Region: Composite Section: For interior beams, the effective flange width may be taken as the least of: Leff_neg 20m:= 12 ts D+ 3.7m= 12 ts bf.t.n 2 + 2.625 m= S 3.69m= [S4.6.2.6] beff.n S:= beff.n 3.69 10 3 × mm= [Proposed]
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From page 125... ...
2⋅ + ...:= Ideck.ST.n 3.075 10 8 × mm 4 =Ideck.ST.n beff.n ts 3 ⋅ 12 n⋅ := dBot_Steel_ST.n 1005.9 mm=dBot_Steel_ST.n dn dTop_Steel_ST.n−:= dTop_Steel_ST.n 374.1 mm=dTop_Steel_ST.n Ag.n ygirder.n⋅ Adeck.ST.n ydeck.n⋅+ Ag.n Adeck.ST.n+ := ydeck.n 150.0 mm=ydeck.n thaunch ts 2 +:= ygirder.n 731.7 mm=ygirder.n dTop_Steel_NC.n:= Adeck.ST.n 92250.0 mm 2 =Adeck.ST.n ts beff.n⋅ n := Short-term composite section for negative flexure: For members with shear connectors provided throughout their entire length that also satisfy the provisions of Artical 6.10.1.7, flexural stresses caused by service II loads applied to the composite section may be computed using the short-term or long-term composite section, as appropriate.
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From page 126... ...
2⋅ + ...:= Ideck.LT.n 3.075 10 8 × mm 4 =Ideck.LT.n beff.n ts 3 ⋅ 12 n⋅ := dBot_Steel_LT.n 1005.9 mm=dBot_Steel_LT.n dn dTop_Steel_ST.n := dTop_Steel_LT.n 529.7 mm=dTop_Steel_LT.n Ag.n ygirder.n⋅ Adeck.LT.n ydeck.n⋅ + Ag.n Adeck.LT.n+ := Adeck.LT.n 30750.0 mm 2 =Adeck.LT.n ts beff.n⋅ 3 n := Long-term composite section negative flexure: ⎤ ⎦ ⎤ ⎦
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From page 127... ...
Section forces: Art.n beff.n As_top_provided⋅ := Art.n 5940.9mm 2 = Arb.n beff.n As_bottom_provided⋅ := Arb.n 3321.0mm 2 = Prt.n Fyr Art.n⋅ := Prt.n 2495.2kN= Ps.n 0 kN⋅ := Ps.n 0.0kN= Prb.n Fyr Arb.n⋅ := Prb.n 1394.8kN= Pt.n Fy.485 tf.t.n⋅ bf.t.n⋅ := Pt.n 8730.0kN= Pw.n Fy.345 tw.n⋅ D⋅:= Pw.n 6279.0kN= Pc.n Fy.485 tf.b.n⋅ bf.b.n⋅ := Pc.n 10476.0kN= Crb.n thaunch cbottom+ db_16+ 13 mm⋅ +:= Crt.n thaunch ts+ ctop− db_16− 17.5 mm⋅ − := Figure : Plastic Moment Forces Crb.n 103.9mm= Possible plastic neutral axis locations: Case I - PNA in web Case II - PNA in top flange wP Pt Pc Prb Ps Prt ⎞ ⎟ ⋅⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠
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From page 128... ...
[S6.10.1 '04] This example was organized to consecutively check the Articles listed above for an interior girder only.
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From page 129... ...
WEB PROPORTIONS: [S6.10.2 '04] Positive Moment Region Cross Section Proportional Limits: ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠
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From page 130... ...
Tension Flange: Iyt tf.b bf.b 3 ⋅ 12 := Compression Flange: Iyc tf.t bf.t 3 ⋅ 12 := Check_Flange_Proportion_Limit "OK" 0.1 Iyc Iyt ≤ 10≤if "Proportion not within bounds" otherwise := Check_Flange_Proportion_Limit "OK"= Establishes I-section proportional limits in order to ensure validity of equations in specification.• Ensures more efficient flange proportions and prevents the use of sections that may be• particularly difficult to handle during construction.
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From page 131... ...
Tension Flange: Iyt.n tf.t.n bf.t.n 3 ⋅ 12 := Compression Flange: Iyc.n tf.b.n bf.b.n 3 ⋅ 12 := Check_Flange_Proportion_Limitn "OK" 0.1 Iyc.n Iyt.n ≤ 10≤if "Proportion not within bounds"otherwise := Check_Flange_Proportion_Limitn "OK"= Negative Moment Region Cross Section Proportional Limits: [S6.10.2 '04]
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From page 132... ...
ff 0.95 Rh⋅ Fyf⋅ ≤Flexure check for top flange steel: Positive Moment Region: [S6.10.4 '04] SEVICE LIMIT STATE: Control of Permanent Deflection ⎤ ⎦ ⎤ ⎦
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From page 133... ...
⋅+ 12 2 ⋅β+:= Rh 0.96= Flexure check for bottom flange steel: Check_Ten_Flange_Service_II "OK" fserviceII_tf 0.95 Rh⋅ Fyt⋅ ≤ if "Permanent deflection limitation exceeded"otherwise := Check_Ten_Flange_Service_II "OK"= PR_Ten_Flange_Service_II fserviceII_tf 0.95 Rh⋅ Fyt⋅ ( ) := PR_Ten_Flange_Service_II 92.9%= Flexure check for bottom flange steel: ff 1 2 fl⋅ + 0.95 Rh⋅ Fyf⋅ ≤ [S6.10.4.2.2-2 '04]
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From page 134... ...
⋅ + 12 2 β⋅+:= Rh 0.98= Flexure check for top flange steel: Check_Ten_Flange_Service_IIn "OK" fserviceII_tf.n 0.95 Rh⋅ Fyt.n⋅ ≤ if "Permanent deflection limitation exceeded"otherwise := Check_Ten_Flange_Service_IIn "OK"= PR_Ten_Flange_Service_IIn fserviceII_tf.n 0.95 Rh⋅ Fyt.n⋅ ( ) := PR_Ten_Flange_Service_IIn 55.5%= Negative Moment Region: Flexure check for top flange steel: ff 0.95 Rh⋅ Fyf⋅ ≤ [S6.10.4.2.2-2 '04]
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From page 135... ...
ff 1 2 fl⋅ + 0.95 Rh⋅ Fyf⋅ ≤Flexure check for bottom flange steel: ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦
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From page 136... ...
kn 30.0=kn 9 Dc.n D 2 := Dc.n 711.5 mm= [D6.3.1 '04] Dc.n fserviceII_cf.n fserviceII_cf.n fserviceII_tf.n+ dn⋅ tf.b.n− := fserviceII_tf.n 251.7 MPa= fserviceII_cf.n 301.0 MPa= Flange stress due to service II loads: [S6.10.4.2.2-4 '04]
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From page 137... ...
Nominal Flexural Resistance: [S6.10.7.1.1-2 '04] Mu 1 3 fl⋅ Sxt⋅ + f Mn⋅≤ φ Strength limit state check: section "Compact"= section "Compact" 2 Dcp⋅ tw 3.76 Es Fyc ⋅ ≤ max Fyc Fyt 485 MPa ≤ ⋅ D tw 150≤ ⋅ if "Non-compact" otherwise := Dcp 126.2mm=Dcp max ybar tf.t− 0 mm := [D6.3.2 '04]
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From page 138... ...
( ) := Nominal Flexural Resistance: Myt 9828.4 kN m⋅ = Myt η 1.25 MDC1⋅ 1.25 MDC2⋅ + 1.5 MDW⋅ + MAD+( )
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From page 139... ...
φ f 1.0:= Resistance factor for flexure: Sxt 2.0 10 7 × mm 3 =Sxt Myt Fyt := [S6.10.7.1.1 '04] Elastic section modulus for tension flange: fl 0 MPa⋅ := [S6.10.1.6 '04]
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From page 140... ...
Resistance of unstiffened web in positive moment region: [S6.10.9.2 '04] Plastic shear force: Vp 0.58 Fyw⋅ D⋅ tw⋅ := Vp 3641.8kN= [S6.10.9.2-2 '04]
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From page 141... ...
Depth of web in compression in elastic range: [S6.10.7.1.1-1 '04] Sections that satisfy the following requirements shall qualify as compact sections: the specified minimum yield strengths of the flanges and web do not exceed• 485 MPa, the web satisfies the requirement of Article 6.10.2.1.1,• and: the section satisfies the slenderness limit: 2 Dc⋅ tw 5.7 Es Fyc.n ⋅ ≤ • [S6.10.7 '04]
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From page 142... ...
λpf.n 7.7=λ pf.n 0.38 Es Fyc.n ⋅:= [S6.10.8.2.2-3 '04] λ f.n 6.8=λ f.n bf.b.n 2 tf.b.n⋅ := Slenderness ratio of compression flange: Web_slenderness "[6.10.8 '04]
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From page 143... ...
Nominal flexural resistance of the flange to local buckling: Rh 0.98=Rh 12 β 3ρ ρ 3− ( ) ⋅ + 12 2 β⋅+:= β 1.133=β 2 Dn⋅ tw.n⋅ Afn := Afn 18000.0mm 2 =Afn Af.t.n Dn dBot_Steel_Comp.n tf.t.n− if Af.b.n otherwise := Dn 728.3mm= Dn dTop_Steel_Comp.n tf.t.n− ( )
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From page 144... ...
⋅ SBot_Steel_Comp.n +:= f2.n 467.2MPa= Lateral torsional buckling resistance: [S6.10.8.2.3 '04] Unbraced length: Lb.n 6000mm:= Depth of web in compression for non-composite section in elastic range: Dc.n dBot_Steel_Comp.n tf.b.n−:= Dc.n 728.3mm= Radius of gyration about vertical axis: rt.n bf.b.n 12 1 1 3 Dc.n tw.n⋅ bf.b.n tf.b.n⋅ ⋅+ ⋅ := rt.n 144.9mm= [S6.10.8.2.3-10 '04]
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From page 145... ...
:= 1. compact unbraced length: Nominal flexural resistance of the flange to lateral torsional buckling: [S6.10.8.2.3-8 '04]
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From page 146... ...
Lb.n Lr.n≤( ) ⋅ if Fnc_3.n Lb.n Lr.n>if := Nominal flexural resistance of the flange to lateral torsional buckling: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠
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From page 147... ...
Vp 3641.8 kN=Vp 0.58 Fyw.n⋅ D⋅ tw.n⋅:= Plastic shear force: [S6.10.9.2 '04] Resistance of unstiffened web in negative moment region: [S6.10.9 '04]
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From page 148... ...
C 1.0 D tw.n 1.12 Es k⋅ Fyw.n ⋅ |
From page 149... ...
3rd Interior Panel From Pier: Because the distance between the previous stiffener and the 1st cross frame from the pier is the same, there in no need to check the next panel. The panel will have the same shear resistance with lesser applied design shear force.
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From page 150... ...
O-62 O.9 Summary 14mm 40mm 1300mm 14mm 400mm 25mm 400mm25mm 450mm 540mm40mm 1300mm Positive Moment Regions Negative Moment Regions O.10 Shears and Moments Diagrams
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From page 151... ...
M o m en t ( kN -m ) DC1 DC2 DW CL Bearing Dead load inflection point Figure O-5 Moments calculated from unfactored permanent dead loads.
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From page 152... ...
Sh ea r (k N ) Design Tandem Design Truck Fatigue Truck Figure O-8 Shears calculated from unfactored live loads excluding girder distribution factors.
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From page 153... ...
Fatigue Moments (Includes GDF) Figure O-9 Maximum moments calculated from unfactored live loads including girder distribution factors.
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