Effective Slab Width for Composite Steel Bridge Members (2005)

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O-1 APPENDIX O DESIGN EXAMPLES Appendix O has not been edited by TRB.

O-2 APPENDIX O DESIGN EXAMPLE: Two-Span Continuous Steel Hybrid Plate Girder Bridge O.1 Introduction This example focuses primarily on the design of an interior girder for a two-span continuous superstructure. The interior girder is designed according to the Third Edition of AASHTO LRFD Bridge Design Specification (AASHTO 2004). The specifications are applied in design through a line girder analysis. O.2 Cross Section Description The superstructure consists of 5 girders spaced at 3,690 mm spanning a length equal to 40 m measured from girder abutment bearing to pier bearing. The superstructure is offset to an 18 degree skew at both abutments and at the pier. The deck consists of a 200 mm structural thickness with a 40 mm integral wearing surface (IWS). Figure O-1 shows a typical bridge cross section. 4 @ 3690mm=14760mm600mm 600mm 3 Lanes @ 3600mm=10800mm 3000mm 480mm480mm 1200mm 50mm Haunch 240mm w/ 40mm IWS FWS (122.5 kg/m )2 Figure O-1 Typical Bridge Cross Section O.3 Framing Plan Description A field splice is located in each of the two spans. The field splice provides a girder length that can be transported and erected easily. The splices are located at a distance of 75 percent of the span length from each abutment bearing point, which is close to the dead load inflection point. 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. The cross frames are oriented at 18 degrees, parallel to the skew at the support. If the orientation of the frames exceeds 20 degrees, intermediate cross frames shall be positioned normal to the main members. Figure O-2 shows a framing plan.

O-3 30000 mm 4 at 7000 mm spacing = 28000 mm 40000 mm 18° Bearing End Field Splice Pier Bearing Figure O-2 Bridge Framing Plan O.4 Material Properties High performance steel (HPS) flanges were implemented in this design. The entire length of the bottom flange and the top flange in the negative moment regions are designed with HPS following industry guidelines for the most economical configuration (Figure O-3). Each of the I- section structural steels are designed with weathering steel. 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. The deck was designed according to empirical design criteria, which is valid between girders where internal arching can develop. Grade 345W (F = 345 MPa)y Grade 485W (F = 485 MPa)y Figure O-3 Hybrid Configuration

O -4 O.5 Girder Elevation Description The elevation view of the interior girder is provided in Figure O-4. Figure O-4. 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

O-5 O.6 Design Assumptions • Average daily truck traffic (ADTT) is 2500 with a 75 year design life. • The concrete haunch is assumed to have no structural contribution to the resistance of the girder and is assumed a constant 50 mm along the entire girder length. • The plates and girder attachments are assumed to be five percent of the total girder weight. • The ratio of positive moment stiffness to negative moment stiffness is assumed equal to one in the structural analysis. • The future wearing surface and parapet loads are assumed to be shared equally by all girders. • 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.

O-6 O.7 Notations Variable 1 ..................Description A.................................Fatigue detail category constant. A10 ..............................Cross-sectional area of number 10 metric bar reinforcement. A16 ..............................Cross-sectional area of number 16 metric bar reinforcement. A19 ..............................Cross-sectional area of number 19 metric bar reinforcement. Adeck.LT........................Area of structural concrete effective slab for long-term composite section. Adeck.ST........................Area of structural concrete effective slab for short-term composite section. ADTT.........................Average daily truck traffic. ADTTSL......................Average daily truck traffic for a single lane. Af.b..............................Cross-sectional area of bottom flange. Af.t ..............................Cross-sectional area of top flange. Afn ..............................Area of the flange governed by the variable Dn. Ag ...............................Cross-sectional area of girder. Ag_avg ..........................Averaged cross-sectional area of the girder in the positive and the negative moment regions. Arb ..............................Area of the bottom layer of reinforcing steel within the effective slab width. 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. As_bottom_provided ............Cross-sectional area of bottom reinforcing steel per unit deck width provided in the negative moment region. As_neg_min .....................Minimum cross-sectional area of reinforcing steel per unit deck width required in the negative moment region for empirical deck design. As_top_min .....................Minimum cross-sectional area of top reinforcing steel per unit deck width required in the negative moment region for empirical deck design. As_top_provided ................Cross-sectional area of top reinforcing steel per unit deck width provided in the negative moment region. Asc ..............................Cross-sectional area of a shear connector. Aw...............................Cross-sectional area of web. awc...............................Ratio of twice the area of the web in compression at the strength limit state to the area of the compression flange. Factor used in the calculation of Rh. beff...............................Structural effective slab width. bf.b...............................Bottom flange width. bf.t ...............................Top flange width. C.................................Ratio of the shear buckling stress to the shear yield strength. c1 ................................Skew correction factor variable. Category.....................Fatigue detail category.

O-7 Variable 1 ..................Description Cb................................Moment gradient correction factor. cbottom ..........................Bottom reinforcing steel concrete cover with respect to structural thickness. CDi .............................Factored construction dead load. Applied to the interior girder. CL ..............................Unfactored construction live load. CLi..............................Factored construction live load. Applied to the interior girder. Crb...............................Distance from top of the structural slab to the centroid of the bottom reinforcing steel. Crt ...............................Distance from top of the structural slab to the centroid of the top reinforcing steel. ctop ..............................Top reinforcing steel concrete cover with respect to structural thickness. D.................................Total depth of web excluding flange thickness. d..................................Height of girder. Sum of web depth and flange thickness. dBot_Steel_LT ..................Distance from the elastic neutral axis of the long-term composite girder to the bottom fiber of steel. dBot_Steel_NC ..................Distance from the elastic neutral axis of the girder cross-section to the bottom fiber of steel. dBot_Steel_ST...................Distance from the elastic neutral axis of the short-term composite girder to the bottom fiber of steel. Dc ...............................Depth of web in compression for the non-composite section in the elastic range. DC1attachments ...............Unfactored load from plates and attachments. Applied to the girder as a uniform load. DC1e...........................Sum of unfactored non-composite section dead loads. Applied to the exterior girder as a uniform load. DC1girder......................Unfactored load from the girder self-weight. Applied to the girder as a uniform load. DC1haunch ....................Unfactored load from the haunch. Applied to the girder a line load. DC1i ...........................Sum of unfactored non-composite section dead loads. Applied to the interior girder as a uniform load. DC1sipf ........................Unfactored load from the stay-in-place forms applied to the girder as a uniform load. DC1slab.e ......................Unfactored load from the exterior girder slab self-weight Applied to the exterior girder as a uniform load. DC1slab.i ......................Unfactored load from the interior girder slab self-weight. Applied to the interior girder as a uniform load. Dcp ..............................Depth of web in compression at plastic moment. de ................................Distance from the exterior web of the exterior beam ant the interior edge of the curb or traffic barrier. df.b...............................Distance from the bottom of girder to the centroid of the bottom flange. 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. DFM1fatigue ..................Moment load distribution factor for fatigue loading case.

O-8 Variable 1 ..................Description DFM2..........................Moment load distribution factor for two lanes loaded case. DFME .........................Governing skew corrected moment load distribution factor. Applies to the exterior girder. DFME_F ......................Governing skew corrected moment load distribution factor for fatigue loading case. Applies to the exterior girder. DFMI ..........................Governing skew corrected moment load distribution factor. Applies to the interior girder. DFMI_F .......................Governing skew corrected moment load distribution factor for fatigue loading case. Applies to the interior girder. DFMskew_corr................Moment load distribution skew correction factor. DFn..............................Nominal fatigue resistance. DFTH ...........................Constant-amplitude fatigue threshold stress. DFV1 ..........................Shear load distribution factor for one lane loaded case. DFV2 ..........................Shear load distribution factor for two lanes loaded case. DFVE..........................Governing skew corrected shear load distribution factor. Applies to the exterior girder. DFVE_F .......................Governing skew corrected shear load distribution factor for fatigue loading case. Applies to the exterior girder. DFVE1.........................Shear load distribution factor for one lane loaded case calculated using the lever rule. Equal to DMFLever1. Applies to the exterior girder. DFVE2.........................Shear load distribution factor for two lanes loaded case. Applies to the exterior girder. DFVI...........................Governing skew corrected shear load distribution factor. Applies to the interior girder. DFVI_F........................Governing skew corrected shear load distribution factor for fatigue loading case. Applies to the interior girder. DFVskew_corr ................Shear load distribution skew correction factor. DM1 .............................Moment load distribution factor for one lane loaded case including multiple presence factor. Applies to the exterior girder. DM2 .............................Moment load distribution factor for two lanes loaded case including multiple presence factor. Applies to the exterior girder. DM3 .............................Moment load distribution factor for three lanes loaded case including multiple presence factor. Applies to the exterior girder. DM4 .............................Moment load distribution factor for four lanes loaded case including multiple presence factor. Applies to the exterior girder. DMFLever1 ................Moment load distribution factor for one lane loaded case with respect to the lever rule. Applies to the exterior girder. DMFLever1_f ..............Moment load distribution factor for fatigue loading case with respect to the lever rule. Applies to the exterior girder. Dn ...............................Minimum of the distances between the non-composite section neutral axis to the top and bottom of the web. do ................................Stiffener spacing. Dp ...............................Depth from top of structural slab to the plastic neutral axis of the

O-9 Variable 1 ..................Description composite section. Driving .......................Distance to centroid of driving forces with respect to the lever rule. dstud .............................Diameter of shear connector. Dt ................................Depth from top of structural slab to the bottom of the girder. dTop_Steel_LT ..................Distance from the elastic neutral axis of the long-term composite girder to the top fiber of steel. dTop_Steel_NC..................Distance from the elastic neutral axis of the girder cross-section to the top fiber of steel. dTop_Steel_NC_avg ............Averaged distance from the elastic neutral axis of the girder cross- section to the top fiber of steel in the positive and negative moment regions. dTop_Steel_ST ..................Distance from the elastic neutral axis of the short-term composite girder to the top fiber of steel. dw................................Distance from the bottom of girder to the centroid of the web. e..................................Correction factor for moment distribution in an exterior girder. e1 ................................Correction factor for shear distribution in an exterior girder. Ec ................................Modulus of elasticity of concrete. eg ................................Distance between the centroid of the non-composite girder and the centroid of the structural deck. eR1...............................Distance between centerline of bridge and first (exterior) design truck. eR2...............................Distance between centerline of bridge and second design truck. eR3...............................Distance between centerline of bridge and third design truck. eR4...............................Distance between centerline of bridge and fourth design truck. Es ................................Modulus of elasticity of steel. f`c_deck .........................Compressive strength of concrete deck. f2 .................................Stress in compression flange calculated from M2. fbu................................Flange bending stress neglecting lateral bending stress. Fcr ...............................Critical buckling stress. Fcrw .............................Critical buckling stress of the web. fDC1_cf..........................Stress in the compression flange calculated from unfactored non- composite dead loads. fDC1_tf ..........................Stress in the tension flange calculated from unfactored non- composite dead loads. fDC2_cf..........................Stress in the compression flange calculated from unfactored superimposed dead loads. fDC2_tf ..........................Stress in the tension flange calculated from unfactored superimposed dead loads. 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. fl .................................Flange lateral bending stress. f1 .................................The maximum stress calculated from; 1.) two times fmid minus f2

O-10 Variable 1 ..................Description and 2.) fo. fLL_IM_cf .......................Stress in the compression flange calculated from unfactored live load plus impact. fLL_IM_tf .......................Stress in the tension flange calculated from unfactored live load plus impact. fmid ..............................Stress in compression flange calculated from Mmid. Fnc...............................Nominal flexural resistance of the compression flange in terms of stress. Fnc.FLB .........................Nominal flexural resistance with respect to flange lateral buckling in terms of stress. Fnc.LTB .........................Nominal flexural resistance of the compression flange to lateral torsional buckling in terms of stress. Fnc_1 ............................Nominal flexural resistance of the compact compression flange in terms of stress. Fnc_2 ............................Nominal flexural resistance of the noncompact compression flange in terms of stress. Fnc_3 ............................Nominal flexural resistance of the slender compression flange in terms of stress. fo .................................Stress in compression flange calculated from Mo. fserviceII_cf .....................Stress in the compression flange calculated using service II load factors. fserviceII_tf ......................Stress in the tension flange calculated using service II load factors. fstrI_cf ...........................Stress in the compression flange calculated using strength I load factors. fstrI_tf............................Stress in the tension flange calculated using strength I load factors. Fu ................................Minimum tensile strength of a shear stud connector. Fy.345 ...........................Yield stress of steel (50 ksi). Fy.485 ...........................Yield stress of high performance steel (70 ksi). Fyc...............................Yield stress of compression flange steel. Fyr ...............................Yield stress of deck reinforcing steel. Fyr.FLB..........................Yield stress of compression flange used to calculate flange lateral buckling resistance. Fyt ...............................Yield stress of tension flange steel. Fyw ..............................Yield stress of web steel. hstud .............................Height of shear connector. Ideck .............................Moment of inertia of the deck about its centroid with respect to the horizontal axis. Ideck.LT .........................Long-term moment of inertia of the deck about its centroid with respect to the horizontal axis. If.b ...............................Moment of inertia of the bottom flange about its centroid with respect to the horizontal axis. If.t ................................Moment of inertia of the top flange about its centroid with respect to the horizontal axis. ILT ...............................Long-term moment of inertia of the composite section about its

O-11 Variable 1 ..................Description centroid with respect to the horizontal axis. INC ..............................Moment of inertia of the girder about its centroid with respect to the horizontal axis. INC_avg .........................Averaged moment of inertia of the girder about its centroid with respect to the horizontal axis in the positive and negative moment regions. IST ...............................Short-term moment of inertia of the composite section about its centroid with respect to the horizontal axis. Iw ................................Moment of inertia of the web about its centroid with respect to the horizontal axis. Iyc................................Moment of inertia of the compression flange about its vertical axis. Iyt ................................Moment of inertia of the tension flange about its vertical axis. k..................................Shear buckling coefficient. Kg ...............................Longitudinal stiffness parameter used in the calculation of load distribution factors. Lb................................Unbraced length. Leff ..............................Slab effective length based on empirical deck design. Lp................................Lateral bracing limit for flexural capacity governed by plastic bending. Lpick ............................Length of girder to be erected (picked) for erection and transport. Lr ................................Lateral bracing limit for flexural capacity governed by inelastic lateral tosional buckling. Lspan ............................Span length from abutment bearing to pier bearing. m1 ...............................Multiple presence factor for one lane loaded. m2 ...............................Multiple presence factor for two lanes loaded. M2...............................Largest moment at either brace point. m3 ...............................Multiple presence factor for three lanes loaded. 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. MDC1 ...........................Moment calculated from unfactored non-composite dead loads. MDC2 ...........................Moment calculated from unfactored superimposed dead loads. MDW............................Moment calculated from unfactored wearing surface dead load. Mfat_max .......................Maximum stress at point of interest due to fatigue load combination. Mfat_min........................Minimum stress at point of interest due to fatigue load combination. Mfat_range......................Stress range calculated from Mfat_min and Mfat_max at point of interest. min_edge_dist ............Minimum shear connecter edge distancespacing. min_stud_spacing ......Minimum center-to-center shear connecter spacing. MLL_IM ........................Moment calculated from unfactored live load plus impact. Mmid............................Moment calculated at the mid-span of the unbraced region. Mn...............................Nominal flexural resistance. Mo...............................Moment at brace point opposite to M2.

O-12 Variable 1 ..................Description Mp...............................Plastic moment resistance of composite section. Mu_const........................Moment due to factored construction loads. Mu_strength_I ..................Factored strength I moment. Myt ..............................Yield moment of the tension flange. n..................................Modular ratio with respect to steel and concrete. n..................................Number of stress range cycles per truck. N.................................Number of stress cycles during the design life. Nc ...............................Number of stress cycles on the shear connector during its design life. ns ................................Number of shear connectors in a cross-section. NDL .............................Number of design lanes. NG...............................Number of girders. nstud_min........................Minimum number of required shear connectors to satisfy the strength limit state. Number_Studs............Number of shear connectors provided across the region of interest. Over_Placement.........Factored combined construction live and dead loads. Applies to regions where the wet concrete is in placement. p..................................Single lane adjustment factor. P .................................The minimum of P1p and P2p. P1p...............................Nominal shear force according to the structural deck area. P2p...............................Nominal shear force according to the girder area. Pbr ...............................Yield force of bottom reinforcing steel within effective slab width. Pc ................................Yield force of compression flange. Pitch ...........................Chosen pitch satisfying the pitchmax and pitchmin requirements. pitchmax .......................Maximum pitch required satisfying fatigue requirement for shear connector design. pitchmin .......................Minimum pitch for shear connector design. Previously_Placed .....Factored construction dead load including slab weight. Applies to regions where concrete has been placed and live load is no longer present. Ps ................................Compressive crushing force of concrete effective slab width. Pt.................................Yield force of tension flange. Ptr................................Yield force of top reinforcing steel within effective slab width. Pw ...............................Yield force of web. Q.................................First moment of the transformed area of the deck about the short- term neutral axis. Qr................................Factored shear resistance of an individual shear connector at the strength limit state. 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. R3................................Moment load distribution factor for three lanes loaded case excluding the multiple presence factor. R4................................Moment load distribution factor for four lanes loaded case

O-13 Variable 1 ..................Description excluding the multiple presence factor. Rb................................Load shedding factor for the composite section. Resisting.....................Distance to centroid of resisting forces with respect to the lever rule. Rh................................Hybrid factor. A flange stress reduction factor. rt .................................Radius of gyration about the vertical axis. S .................................Center to center girder spacing. SBot_Steel_LT ..................Long-term elastic section modulus of the girder with respect to outer fiber of the bottom flange steel. SBot_Steel_NC..................Elastic section modulus of the girder with respect to outer fiber of the bottom flange steel. SBot_Steel_ST ..................Short-term elastic section modulus of the girder with respect to outer fiber of the bottom flange steel. spacingbottom_max..........Maximum spacing of bottom reinforcing steel based on empirical deck design. spacingprovided..............Provided reinforcing steel spacing. 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. STop_Steel_NC .................Elastic section modulus of the girder with respect to outer fiber of the top flange steel. STop_Steel_ST..................Short-term elastic section modulus of the girder with respect to outer fiber of the top flange steel. struck ............................Design truck spacing. Struck_parapet...................Minimum spacing between design truck and parapet. Sxt ...............................Elastic section modulus for the flange calculated according to MAD. tcore..............................Thickness of deck core with respect to structural thickness. tdeck .............................Thickness of deck including integral wearing surface. tf.b................................Thickness of bottom flange. tf.t ................................Thickness of top flange. thaunch...........................Thickness of haunch. Transverse_Spacing ...The center-to-center transverse shear connector spacing. ts .................................Structural thickness of the deck slab excluding integral wearing surface. tw ................................Thickness of web. Unplaced ....................Factored construction dead load excluding slab weight. Applies to regions where concrete has not yet been placed. Vcr...............................Shear buckling force. VDC1............................Shear calculated from unfactored non-composite dead loads. VDC2............................Shear calculated from unfactored superimposed dead loads. VDW ............................Shear calculated from unfactored wearing surface dead load. Vf................................Shear force range calculated from Vfat_min and Vfat_max used in the

O-14 Variable 1 ..................Description design of the shear connectors. Vfat_comb.......................Shear force range calculated from Vfatigue_min and Vfatigue_max at point of interest. Vfat_max ........................Maximum shear force at point of interest due to fatigue load combination. Used in the design of the shear connectors. Vfat_min ........................Minimum shear force at point of interest due to fatigue load combination. Used in the design of the shear connectors. Vfatigue_max ...................Maximum shear force at point of interest due to fatigue load combination. Vfatigue_min....................Minimum shear force at point of interest due to fatigue load combination. Vp ...............................Plastic shear force. Vsr...............................Horizontal shear fatigue force range per unit length. Vu_const ........................Shear calculated from factored construction loads. wbridge..........................Width of bridge. wlane ............................Width of lane. woh ..............................Width of overhang measured from centerline of exterior girder. wp ...............................Width of parapet. wroadway .......................Width of clear roadway. wshdr_lf .........................Width of left shoulder. wshdr_rt .........................Width of right shoulder. wtconc ..........................Unit weight of concrete. wtfws............................Unit weight of future wearing surface. wtg ..............................Weight of girder per unit length. wtruck ...........................Width of design truck. wtsteel...........................Unit weight of steel. x1 ................................Distance between the centerline of the bridge and the first exterior girder. x2 ................................Distance between the centerline of the bridge and the first interior girder. x3 ................................Distance between the centerline of the bridge and the second interior girder. x4 ................................Distance between the centerline of the bridge and the third interior girder. x5 ................................Distance between the centerline of the bridge and the second exterior girder. Xext .............................Distance between the centerline of the bridge and the girder of interest. ybar ..............................Distance to the plastic neutral axis from the top of the girder. ybf ...............................Distance from the centroid of the bottom flange to the PNA. ydeck ............................Distance between the centroid of the effective slab and the top of the girder. YII ...............................Location of the plastic neutral axis for case II. yrb ...............................Distance from the centroid of the bottom deck reinforcement to the

O-15 Variable 1 ..................Description PNA. yrt ................................Distance from the centroid of the top deck reinforcement to the PNA. ys ................................Distance from the centroid of the structural slab to the PNA. ytf ................................Distance from the centroid of the top flange to the PNA. yw................................Distance from the centroid of the web to the PNA. Zr ................................Shear fatigue strength of a shear connector. Greek Variable 1..........Description α ...................................Factor for calculation of shear fatigue resistance of a shear connector. β ...................................Web to flange area ratio used in the calculation of the hybrid factor Rh. Φf ...................................Resistance factor for flexure. Φv...................................Resistance factor for flexure. γ conc ...............................Specific gravity of concrete. γΔ f ................................Stress at point of interest calculated from Mfat_range. γ fws ................................Specific gravity of future wearing surface. λf ...................................Slenderness ratio of the compression flange. λpf ..................................Slenderness ratio limit for a compact flange. λrf ..................................Slenderness ratio limit for a noncompact flange. λrw .................................Slenderness ratio limit for a noncompact web. η ...................................Load modifier. ηΔ ..................................Ductility load factor. ηΙ ...................................Importance load factor. ηΡ ..................................Redundancy load factor. ρ ...................................Minimum of the ratio of web to compression flange yield stress and 1. 1. Variables having a subscript (n) or (neg) refer to the negative moment region.

O-16 O.8 MathCad Worksheet for Bridge Design deck core thickness [C9.7.2.4] tcore 115mm= Widths: In order to satisfy conditions for empirical deck design the overhang width must be at least 5 times the structural thickness of the slab or 3.0 times the structural thickness of the slab if the parapet is considered structurally continuous. For this design we will assume the parapet as a structural component. Therefore, the overhang width is defined as follows: woh 3.0 ts⋅ := overhang width woh 600mm= wshdr_lf 1.2 m⋅ := left shoulder width wshdr_rt 3.0 m⋅ := right shoulder width wp 480 mm⋅ := parapet width wlane 3600 mm⋅:= lane width wbridge wlane NL⋅ wshdr_lf+ wshdr_rt+ wp 2⋅ +:= wbridge 15960mm= wroadway wlane NL⋅ wshdr_lf+ wshdr_rt+:= wroadway 15000mm= S wbridge 2 woh⋅ −( ) 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] tcore ts cbottom− ctop− :=

O-17 wtsipf 718.2 Pa⋅ := stay-in-place forms Fy.485 485 MPa⋅ := grade 485 steel wtsteel 77 kN m 3 ⋅ := unit weight Definition of Steel Grade Locations: Positive Moment Region: Fyc Fy.345:= Fyc 345.0MPa= Fyc =50 ksi Yield strength of web in positive moment region: Fyw Fy.345:= Fyw 345.0MPa= Yield strength of tension flange in positive moment region: Fyt Fy.485:= Fyt 485.0MPa= Fyt =70 ksi Negative Moment Region: Fyc.n Fy.485:= Fyc.n 485.0MPa= Yield strength of web in negative moment region: Fyw.n Fy.345:= Fyw.n 345.0MPa= Yield strength of tension flange in negative moment region: Fyt.n Fy.485:= Fyt.n 485.0MPa= DEFINITION OF MATERIAL PROPERTIES Concrete Properties: Future Wearing Surface: f'c_deck 28 MPa⋅ := compressive strength γ fws 122.5 kg m 2 := F.W.S. specific gravity = 4 ksi wtconc 23.56 kN m 3 ⋅ := =150 pcf wtfws g fws⋅γ := F.W.S. 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 ⎟ ⎠ ⎞ ⎟ ⎠ ⎞

O-18 compactness limit [S6.10.2.2-1 '04] bf D 6 ≥ [S6.10.2.2-2 '04] tf 1.1 tw⋅ ≥ [S6.10.2.2-3 '04] 0.1 Iyc Iyt ≤ 10≤ [S6.10.2.2-4 '04] A field splice is located at 0.75 Lspan for this example. 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. • and top flange in the positive moment region for constructability to increase lateral stability. Transition flanges in thickness (not width) at shop welded splices if possible.• Flange Thickness Considerations: • Do not exceed 50 mm for Thermo Mechanical Controlled Processing (TMCP) Provide at least 19 mm in thickness to avoid weld distortion. • Web Sizing Considerations: Consider unstiffened webs for span lengths less than 35 m.• • For web depths between 1300-1800 mm subtract 2-3 mm from the unstiffened web Consider unstiffened webs if the web depth is less than 1300 mm. • design and provided stiffeners as required. Provided the thinnest web possible for webs greater than 1800 mm in depth.• Preliminary Flexural Considerations: Cross-sectional Proportion Limits: [S6.10.2 '04] Web Proportions: [S6.10.2.1 '04] D tw 150≤ slenderness limit [S6.10.2.1-1 '04] Flange Proportions: [S6.10.2.2 '04] bf 2 tf⋅ 12.0 ≥

O-19 =15.75 in bf.b.n 540 mm⋅ := =21.26 in Bottom flange thickness: tf.b 25 mm⋅ := = 1 in tf.b.n 40 mm⋅ := =1.58 in Web depth: D 1300 mm⋅ := =51.18 in D 1300 mm= =51.18 in Web thickness: tw 14 mm⋅ := =0.55 in tw.n 14 mm⋅ := =0.55 in Figure : Cross Section of Interior Girder in Positive Moment Region Figure : Cross Section of Interior Girder in Negative Moment Region Trial Depth Selection: Suggested minimum span-to-depth ratio for a continuous span design: D 0.027 Lspan⋅ := D 1080 mm= [Table 2.5.2.6.3-1] Suggested optimal depth for the hybrid configuration choosen: (Horton, 2002) 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

O-20 dist. to cent. of bottom flange: df.b 0.5 tf.b⋅ := df.b 13mm= dist. to cent. of web: dw tf.b 0.5 D⋅ +:= dw 675mm= dBot_Steel_NC Af.t df.t⋅ Af.b df.b⋅ + Aw dw⋅+ Ag := dBot_Steel_NC 675mm= dTop_Steel_NC d dBot_Steel_NC− := dTop_Steel_NC 675mm= If.t bf.t tf.t 3 12 ⋅ Af.t df.t dBot_Steel_NC− ( )2⋅ +:= If.t 4.39 109× mm4= If.b bf.b tf.b 3 12 ⋅ Af.b dBot_Steel_NC df.b−( )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. to cent. of top flange: df.t tf.b D+ 0.5 tf.t⋅ +:= df.t 1337.5mm=

O-21 df.t.n 1360mm= dist. to cent. of bottom flange: df.b.n 0.5 tf.b.n⋅ := df.b.n 20mm= dist. to cent. of web: dw.n tf.b.n 0.5 D⋅ +:= dw.n 690mm= dBot_Steel_NC.n Af.t.n df.t.n⋅ Af.b.n df.b.n⋅ + Aw.n dw.n⋅ + Ag.n := dBot_Steel_NC.n 648.3mm= dTop_Steel_NC.n dn dBot_Steel_NC.n−:= dTop_Steel_NC.n 731.7mm= If.t.n bf.t.n tf.t.n 3 12 ⋅ Af.t.n df.t.n dBot_Steel_NC.n− ( )2⋅ +:= If.t.n 9.12 109× mm4= If.b.n bf.b.n tf.b.n 3 12 ⋅ Af.b.n dBot_Steel_NC.n df.b.n−( )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. to cent. of top flange: df.t.n tf.b.n D+ 0.5 tf.t.n⋅ +:=

O-22 Kg 4.06 10 11 × mm 4 = Range of applicability: 1100 S≤ 4900mm≤ 110 ts≤ 300mm≤ 6000 L≤ 73000mm≤ Nb 4≥ 4 109 Kg≤ 3 10 12 ⋅ mm 4≤ [Table S4.6.2.2.2b-1 '03] One lane loaded: [Table S4 .6.2.2.2b-1 '03] DFM1 0.06 S 4300 mm⋅ ⎞ ⎟⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 0.4 S Lspan 0.3 Kg Lspan ts 3 ⋅ 0.1 ⋅ +:= DFM1 0.531= Two or more design lanes: [Table S4 .6.2.2.2b-1 '03] DFM2 0.075 S 2900 mm⋅ 0.6 S Lspan 0.2 Kg Lspan ts 3 ⋅ 0.1 ⋅ +:= DFM2 0.81= Fatigue factors: For single-lane loading to be used for fatigue design, remove the multiple presence factor of 1.20. 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. of girder and C.O.G. of slab: eg dTop_Steel_NC_avg thaunch+ ts 2 +:= eg 853.365 mm= Figure : eg factor n 8:= [C6.10.1.1.1b '04] Kg n INC_avg Ag_avg eg 2 ⋅ +( )⋅ := ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠

O-23 NDL wroadway 3600 mm⋅ := NDL 4.2= NDL 4:= [S3.6.1.1.1 '99] Spacing Between Parapet and Truck: [S3.6.1.3.1 '99] Struck_parapet 600 mm⋅ := Truck reaction location from center of bridge: dist to R1 from CL eR1 wroadway 2 Struck_parapet− wtruck 2 − := eR1 6000mm= dist to R2 from CL eR2 wroadway 2 Struck_parapet− wtruck− struck− wtruck 2 − := eR2 2400mm= dist to R3 from CL eR3 wroadway 2 Struck_parapet− 2 wtruck⋅ − 2 struck⋅− wtruck 2 − := eR3 1200− mm= dist to R4 from CL eR4 wroadway 2 Struck_parapet− 3 wtruck⋅ − 3 struck⋅ − wtruck 2 − := eR4 4800− mm= Interior Beam Shear: [Table S4 .6.2.2.3a-1 '03] One lane loaded: DFV1 0.36 S 7600 mm⋅ +:= DFV1 0.846= Two or more lanes loaded: DFV2 0.20 S 3600 mm⋅ + S 10700 mm⋅ 2.0 −:= DFV2 1.106= Exterior Beam Moment: [Table S3 .6.1.1.2-1 '03] 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 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠

O-24 [C4.6.2.2.2d-1] m2 1.00:= m4 0.65:= One Lane Loaded: R1 1 5 Xext eR1( )⋅ x1 2 x2 2 + x3 2 + x4 2 + x5 2 +( )+:= R1 0.53= DM1 m1 R1⋅ := DM1 0.63= Two Lanes Loaded: R2 2 5 Xext eR1 eR2+( )⋅ x1 2 x2 2 + x3 2 + x4 2 + x5 2 +( )+:= R2 0.86= DM2 m2 R2⋅ := DM2 0.86= Three Lanes Loaded: R3 3 5 Xext eR1 eR2+ eR3+( )⋅ x1 2 x2 2 + x3 2 + x4 2 + x5 2 +( )+:= R3 0.99= DM3 m3 R3⋅ := DM3 0.84= Four Lanes Loaded: R4 4 5 Xext eR1 eR2+ eR3+ eR4+( )⋅ 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 +

O-25 Two or more Lanes Loaded: de woh wp− := de 120 mm= e 0.77 de 2800 mm⋅ +:= e 0.813= DMFLever2 e DFM2⋅ := DMFLever2 0.658= Distribution Factor Shear: One Lane Loaded: (beam distribution same as moment) DFVE1 DMFLever1:= DFVE1 0.751= Two or more lanes loaded: e1 0.6 de 3000 mm⋅ +:= e1 0.64= DFVE2 e1 DFV2⋅ := DFVE2 0.708= Exterior Beam Lever Rule: [Table 4.6.2.2.1-1 '03] 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

O-26 Moment: DFMI_F DFMskew_corr DFM1fatigue⋅ := DFMI_F 0.44= Shear: DFVI_F DFVskew_corr DFV1⋅ := DFVI_F 0.90= Exterior Max: Moment: DFME DFMskew_corr max DM1 DM3 DM2 DM4 DMFLever1 DMFLever2 ⋅ := DFME 0.84= Shear: DFVE DFVskew_corr max DFVE1 DFVE2( )( )⋅ := DFVE 0.80= Fatigue: Moment: DFME_F DFMskew_corr max DM1 1.2 DMFLever1_f ⋅ := DFME_F 0.62= Shear: DFVE_F DFVskew_corr DMFLever1_f⋅ := DFVE_F 0.66= Skew Correction Factors: [S4.6.2.2.2e-1 '03] If θ is less than 30o c1=0.0 If θ is greater than 60o use = 60o θ 18 deg⋅ := c1 0.25 Kg Lspan ts 3 ⋅ 0.25 ⋅ S Lspan 0.5 ⋅ := c1 0.081= DFMskew_corr 1 c1 tan θ ( )1.5⋅ −:= DFMskew_corr 0.985= [S4.6.2.2.3c-1 '03] DFVskew_corr 1.0 0.2 Lspan ts 3 ⋅ Kg 0.3 ⋅ tan θ ( )⋅ +:= DFVskew_corr 1.061= Governing Distribution Factors: (skew corrected) Interior Max: Moment: DFMI DFMskew_corr max DFM1 DFM2( )( )⋅ := DFMI 0.80= Shear: DFVI DFVskew_corr max DFV1 DFV2( )( )⋅ := DFVI 1.17= Fatigue: ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞

O-27 [S1.3.2.1-3]η 1.00=η 1 ηD η R⋅ I⋅η 1.0≤ For loads for which a minimum value of gi is appropriate: η 1.00=η η D η R⋅ I⋅η 0.95≥ [S1.3.2.1-2] For loads for which a maximum value of gi is appropriate: [S1.3.5]η I 1.00:=Operational Importance [S1.3.4]η R 1.00:=Redundancy [S1.3.3]η D 1.00:=Ductility [S1.3.2.1-1]S η i γ i⋅ Qi⋅ φ Rn⋅ ≤ Rr General Considerations for Limit States

O-28 DC1e 19.38 kN m = DC1e DC1slab.e DC1haunch+ 0.5 DC1sipf⋅+ DC1girder+ 0.5 DC1attachments⋅+:= DC1slab.e 14.18 kN m = DC1slab.e wtconc 0.5 S⋅ tdeck⋅ woh tdeck tf.t+( )⋅+ ⋅ := Exterior Girder Component Dead Load: DC1i 27.47 kN m = DC1i DC1slab.i DC1haunch+ DC1sipf+ DC1girder+ DC1attachments+:= DC1slab.i 20.86 kN m = DC1slab.i wtconc S tdeck⋅ ( )⋅ := 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 ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

O-29 ts 200mm= - O.K. This example assumes a structurally continuous parapet woh 3.0 ts woh 600mm= - O.K. f'c 28 MPa f'c_deck 28MPa= - O.K. Selected metric deck reinforcment properties: A10 71mm 2 := A16 199mm 2 := db_16 15.9 mm := A19 284mm 2 := Reinforcement Requirements - Positive Moment Regions [S9.7.2.5] 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. EMPIRICAL DECK DESIGN [S9.7.2.1] Check conditions for use of empirical design method [S9.7.2.2, S9.7.2.4] The empirical design method may only be used if the following conditions are satisfied: Cross frames are used throughout the cross-section at lines of support,• Supporting components are made of steel and/or concrete,• Deck is cast in place,• Deck is of uniform depth (except for haunches over girder flanges),• Deck is made composite with supporting elements (2 shear connectors min. at 600 mm spacing),• The ratio of effective length to design depth does not exceed 18.0 and is not less than 6.0,• Core depth of the slab is not less than 100 mm,• Minimum depth of slab is not less than 175 mm (excluding sacrificial wearing surface),• Effective Length does not exceed 4100 mm,• Overhang beyond the centerline of at least 5.0 times the depth of the slab (this condition also• satisfied if the overhang is at least 3.0 times the depth of the slab and a structurally continuous concrete barrier is made composite with the overhang. Effective length: [S9.7.2.3, S9.7.2.4] The effective length of slab for purposes of the empirical design method is the distance between flan tips, plus the flange overhang, taken as the distance from the extreme flange tip to the face of the we Leff S bf.t− bf.t tw− ( ) 2 +:= Leff 3483.0mm= Leff 4100mm≤ - O.K. 6 Leff ts ≤ 18 ≤ Leff ts 17.4= - O.K. tcore 100mm≥ tcore 115mm= - O.K. ts 175mm≥

O-30 As_bottom_provided 0.90 mm 2 mm =As_bottom_provided A10 spacingprovided A16 spacingprovided +:= spacing provided 300mm:=In bottom layer use no. 10M bars spaced at 300 mm alternating with no. 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. The reinforcement shall have a specified minimum yield strength not less than 400 MPa and a• size not exceeding no.19 bars to control slab cracking. The required longitudinal reinforcement is to be placed within two layers uniformly distributed• across the slab width: 1.) 2/3rds of the specified reinforcement shall be placed in the top layer longitudinally. 2.) 1/3rd of the specified reinforcement shall be placed in the bottom layer longitudinally. The transverse reinforcement need not be any different from that determined from the positive• flexure region. [S6.10.1.7 '04]Reinforcement Requirements - Negative Moment Region Use no. 16M bars spaced at 300 mm in the top and bottom layers of reinforcement in both the longitdinal and transverse directions. Spacing is chosen to be consistant with that provided in the negative moment region as determined by the following. spacing top_max 524 mm=spacing top_max A16 0.380 mm 2 mm := Reinforcement bars at top (longitudinal and transverse) in positive moment region: spacing bottom_max 349mm=spacing bottom_max A16 0.570 mm 2 mm := Reinforcement bars at bottom (longitudinal and transverse) in positive moment region:

O-31 Longitudinal reinforcing bars in top layer of negative moment region: As_top_min 2 3 As_neg_min⋅ := As_top_min 1.33 mm 2 mm = In the top layer use no. 19M bars spaced at 300 mm alternating with no. 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. The transverse steel in both the top and bottom layers will be no. 16M bars spaced at 300 mm. DECK REINFORCEMENT SUMMARY: #16M at 300 mm spacing #16M at 300 mm spacing 25 mm (min) core depth = 115 mm 60 mm (min) #16M at 300 mm spacing Figure : Positive Moment Region Deck Reinforcement - Emperical Design #16M alternating with #10M at 300 mm spacing #16M alternating with #19M at 300 mm spacing structural thickness = 200 mm #16M at 300 mm spacing Figure : Negative Moment Region Deck Reinforcement - Emperical Design

O-32 dBot_Steel_ST Ag dBot_Steel_NC⋅ Adeck.ST d ydeck+( )⋅ + Ag Adeck.ST+ := dTop_Steel_ST d dBot_Steel_ST− := Ideck beff ts 3 ⋅ 12 n⋅ := Ideck 3.075 10 8 × mm 4 = IST INC Ag dTop_Steel_NC dTop_Steel_ST−( )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] For interior beams, the effective flange width may be taken as the least of: Lext_eff 30m:= 12 ts⋅ D+ 3.7m= 12 ts⋅ bf.t 2 + 2.6m= S 3.69m= beff S:= beff 3.69 10 3 × mm= [Proposed] Adeck.ST ts beff⋅ n := Adeck.ST 92250mm 2 = ydeck thaunch ts 2 +:= ydeck 150mm=

O-33 Long-term section modulus bottom section: SBot_Steel_LT 2.209 10 7 × mm 3 = Long-term section modulus top section: STop_Steel_LT 7.503 10 7 × mm 3 = Long-term distance from bottom of steel to NA: dBot_Steel_LT 1.0 10 3 × mm= Long-term distance from top of steel to NA: dTop_Steel_LT 307.1mm= Long-term moment of inertia: ILT 2.304 10 10 × mm 4 = Long-term Section Properties: SBot_Steel_LT ILT dBot_Steel_LT :=STop_Steel_LT ILT dTop_Steel_LT := ILT INC Ag dTop_Steel_NC dTop_Steel_LT−( )2⋅+ Ideck.long Adeck.LT ydeck dTop_Steel_LT+( )2⋅++ ...:= Ideck.long 1.025 10 8 × mm 4 =Ideck.long 1 12 beff ts 3 ⋅ 3 n⋅ ⋅:= dTop_Steel_LT d dBot_Steel_LT−:= dBot_Steel_LT Ag dBot_Steel_NC⋅ Adeck.LT d ydeck+( )⋅ + Ag Adeck.LT+ := Adeck.LT 30750mm 2 =Adeck.LT ts beff⋅ 3 n⋅ := [S6.10.3.1.1b]3 n⋅ 24=Long-term composite section:

O-34 Pw 6279.0 kN= Pt Fyt bf.b⋅ tf.b⋅ := Pt 4850.0 kN= Figure : Plastic Moment Forces Bottom reinforcement Crb ts cbottom− db_16− db_16 2 − := Crb 151.2 mm= Top reinforcement Crt ctop db_16+ db_16 2 +:= Crt 83.85 mm= Possible Plastic Neutral Axis Locations: Case I - PNA in web Case II - PNA in top flange Case III - PNA in concrete deck, below Prb Case IV - PNA in concrete deck, at Prb Case V - PNA in concrete deck, above Prb, below Prt Case VI - PNA in concrete deck, at Prt Case VII - PNA in concrete deck, above Prt Determination of Plastic Neutral Axis [AASHTO Table D6.1-1] YIV Crb:= Case IV - PNA in the Deck Pt Pw+ Pc+ Ps Pbr+ Ptr+≥YIV 151.2 mm= tf.t 25 mm= Plastic-Moment Capacity for Positive Flexure [Appendix D6.1] 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⋅ ( )⋅ := Ps 17564.4 kN= Pbr Fyr Arb⋅ := Pbr 1.0 10 3 × kN= Pc Fyc bf.t⋅ tf.t⋅ := Pc 3450.0 kN= Pw Fyw D⋅ tw⋅ := wP Pt Pc Prb Ps Prt ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⋅⎠ ⎞ ⎟ ⎠

O-35 Mp 13281.9 kN m⋅ = Mp Ps 2 ts ybar 2( )⋅ Ptr yrt⋅ Pc ytf⋅ + Pw yw⋅ + Pt ybf⋅ +( )+:= Plastic moment capacity: (case IV) 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:

O-36 Aft.n bf.t.n tf.t.n⋅ := Aft.n 18000.0 mm 2 = Afb.n bf.b.n tf.b.n⋅ := Afb.n 21600.0 mm 2 = dBot_Steel_Comp.n Aft.n dn tf.t.n 2 − ⋅ Aw.n tf.b.n D 2 + ⋅+ Afb.n tf.b.n 2 ⋅ + Arb.n dn Crb.n+( )⋅ Art.n dn Crt.n+( )⋅ ++ ... Ag.n Arb.n+ Art.n+ := dTop_Steel_Comp.n dn dBot_Steel_Comp.n− := IComp.n INC.n Ag.n dTop_Steel_NC.n dTop_Steel_Comp.n− ( )2⋅ + Arb.n Crb.n dTop_Steel_Comp.n+( )2⋅ + ... Art.n Crt.n dTop_Steel_Comp.n+( )2⋅ + ... := STop_Steel_Comp.n IComp.n dTop_Steel_Comp.n := SBot_Steel_Comp.n IComp.n dBot_Steel_Comp.n := Bare Steel & Rebar Section Properties (Composite) 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] Art.n beff.n As_top_provided⋅ := Art.n 5940.9 mm 2 = Arb.n beff.n As_bottom_provided⋅ := Arb.n 3321.0 mm 2 = Crt.n thaunch ts+ ctop− db_16− 17.5 mm⋅ − := Crt.n 156.6 mm= Crb.n thaunch cbottom+ db_16+ 13 mm⋅ +:= Crb.n 103.9 mm= ⎤ ⎦ ⎤ ⎦⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞

O-37 SBot_Steel_ST.n 5.297 10 7 × mm 3 =Short-term section modulus bottom section: STop_Steel_ST.n 1.424 10 8 × mm 3 =Short-term section modulus top section: dBot_Steel_ST.n 1005.9 mm=Short-term distance from bottom of steel to NA: dTop_Steel_ST.n 374.1 mm=Short-term distance from top of steel to NA: IST.n 5.328 10 10 × mm 4 =Short-term moment of inertia: Short-term composite section for negative flexure: SBot_Steel_ST.n IST.n dBot_Steel_ST.n :=STop_Steel_ST.n IST.n dTop_Steel_ST.n := IST.n INC.n Ideck.ST.n+ Ag.n ygirder.n dTop_Steel_ST.n− ( )2⋅ + Adeck.ST.n ydeck.n dTop_Steel_ST.n+( )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. [S6.10.4.2.1]Composite Section - with deck effective in tension: Negative Moment Region: ⎤ ⎦ ⎤ ⎦

O-38 Long-term section modulus bottom section: SBot_Steel_LT.n 3.69 10 7 × mm 3 = Long-term section modulus top section: STop_Steel_LT.n 7.007 10 7 × mm 3 = Long-term distance from bottom of steel to NA: dBot_Steel_LT.n 1005.9 mm= Long-term distance from top of steel to NA: dTop_Steel_LT.n 529.7 mm= Long-term moment of inertia: ILT.n 3.712 10 10 × mm 4 = Long-term composite section negative flexure: SBot_Steel_LT.n ILT.n dBot_Steel_LT.n :=STop_Steel_LT.n ILT.n dTop_Steel_LT.n := ILT.n INC.n Ideck.LT.n+ Ag.n ygirder.n dTop_Steel_LT.n−( )2⋅ + Adeck.LT.n ydeck.n dTop_Steel_LT.n+( )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: ⎤ ⎦ ⎤ ⎦

O-39 Crt.n 156.6mm= Determination of Plastic Neutral Axis: [Table D6.1-2] Case I - PNA in web Pc.n Pw.n+ 16755.0kN= > Pt.n Prb.n+ Prt.n+ 12620.0kN= ybar.n D 2 Pc.n Pt.n− Prt.n− Prb.n− Pw.n 1+ := ybar.n 428.1mm= Distance from PNA to the bottom flange's NA: ybf.n D 0.5 tf.b.n⋅ + ybar.n− := ybf.n 891.9mm= Distance from PNA to the web's NA: yw.n 0.5 D⋅ ybar.n− := yw.n 221.9mm= Distance from PNA to the top flange's NA: ytf.n ybar.n 0.5 tf.t.n⋅ +:= ytf.n 448.1mm= Distance from PNA to the bottom reinforcement: yrb.n ybar tf.t.n+ thaunch+ cbottom+ 1.5 db_16⋅ +:= yrb.n 290.0mm= Distance from PNA to the top reinforcement: yrt.n ybar.n tf.t.n+ thaunch+ ts+ ctop− 1.5 db_16⋅ −:= yrt.n 634.2mm= Plastic moment capacity: (case I) [Table D6.1-2]Mp.n Pw.n 2 D ybar.n 2 D ybar.n− ( )2+ ⎤ ⎦ ⎤⎦⋅ Prt.n yrt.n⋅ Prb.n yrb.n⋅ ⋅ + Pt.n ytf.n+ Pc.n ybf.n⋅ +( )+ ...:= Mp.n 17521.1kN m⋅ = Plastic Moment Capacity for Negative Flexure [Appendix D6.1] 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 ⎞ ⎟ ⋅⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠

O-40 I - SECTION FLEXURAL MEMBERS [S6.10 '04] General: All types of I-section flexural members shall be designed as a minimum to satisfy: The cross section proportion limits specified in Article 6.10.2; The constructibility requirements specified in Article 6.10.3; The service limit state requirements specified in Article 6.10.4; The fatigue and fracture limit state requirements specified in Article 6.10.5; The strength limit state requirements specified in Article 6.10.6. [S6.10.1 '04] This example was organized to consecutively check the Articles listed above for an interior girder only.

O-41 Ensures some restraint will be provided by the flanges against web shear buckling.• Satisfies assumed boundary conditions for web-flange juncture in the web-bend-buckling• and compression-flange-local-buckling formulas. Check_Shear_Buckling_Limit "OK"= Check_Shear_Buckling_Limit "OK" min tf.t tf.b( )( ) 1.1 tw⋅ ≥ if "Limit not met"otherwise := [S6.10.2.2-3 '04]tf 1.1 tw⋅ ≥ Web shear buckling limit: Controls strength and moment-rotation characteristics of the I-section.• Ensures stiffened interior web panels to reach requirement for post-buckling shear.• Check_Flange_Web_Limit "OK"= Check_Flange_Web_Limit "OK" min bf.t bf.b( )( ) D6≥ if "Limit not met"otherwise := [S6.10.2.2-2 '04]bf D 6 ≥ Web depth to flange width aspect ratio: Limits distortion of flange when welded to the web.• Local buckling limit.• Check_Flange_Limit "OK"= Check_Flange_Limit "OK" max bf.t 2 tf.t bf.b 2 tf.b 12.0≤if "Limit not met"otherwise := [S6.10.2.2-1 '04]bf 2 tf 12.0≤ Flange weld distortion / Compactness limit: [S6.10.2.2 '04]FLANGE PROPORTIONS: • Satisfies elastic buckling of the web as a column subjected to a radial transverse• compression from the curvature of the flanges. Allows web-bend-buckling to be disregarded in design of composite sections in positive Allows for easier proportioning of the web in preliminary design. • flexure. Check_Web_Slenderness "OK"= Check_Web_Slenderness "OK" D tw 150≤if "Limit not met"otherwise := [S6.10.2.1.1 '04]D tw 150≤Web slenderness limit: [S6.10.2.1 '04]WEB PROPORTIONS: [S6.10.2 '04]Positive Moment Region Cross Section Proportional Limits: ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠

O-42 Positive Moment Region Cross Section Proportional Limits: [S6.10.2 '04] Flange proportion limit:0.1 Iyc Iyt ≤ 10≤ [S6.10.2.2-4 '04] 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.

O-43 [S6.10.2.2-2 '04] Check_Flange_Web_Limitn "OK" min bf.t.n bf.b.n( )( ) D6≥if "Limit not met"otherwise := Check_Flange_Web_Limitn "OK"= Web shear buckling limit: tf 1.1 tw⋅ ≥ [S6.10.2.2-3 '04] Check_Shear_Buckling_Limitn "OK" min tf.t tf.b( )( ) 1.1 tw⋅ ≥ if "Limit not met"otherwise := Check_Shear_Buckling_Limit n "OK"= Flange proportion limit: 0.1 Iyc Iyt ≤ 10≤ [S6.10.2.2-4 '04] 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] WEB PROPORTIONS: [S6.10.2.1 '04] Web slenderness limit: D tw 150≤ [S6.10.2.1.1-1 '04] Check_Web_Slendernessn "OK" D tw.n 150≤if "Limit not met"otherwise := Check_Web_Slendernessn "OK"= FLANGE PROPORTIONS: [S6.10.2.2 '04] Flange weld distortion limit: bf 2 tf 12.0≤ [S6.10.2.2-1 '04] Check_Flange_Limit n "OK" max bf.t.n 2 tf.t.n bf.b.n 2 tf.b.n 12.0≤if "Limit not met"otherwise := Check_Flange_Limitn "OK"= Web depth to flange width aspect ratio: bf D 6 ≥ ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟ ⎠

O-44 PR_Comp_Flange_Service_II 64.7%= PR_Comp_Flange_Service_II fserviceII_cf 0.95 Rh⋅ Fyc⋅ ( ):= Check_Comp_Flange_Service_II "OK"= Check_Comp_Flange_Service_II "OK" fserviceII_cf 0.95 Rh⋅ Fyc⋅≤ if "Permanent deflection limitation exceeded"otherwise := Flexure check for top flange steel: Rh 1.0:= Because the compression flange in the positive moment regoin is the same yield strength as the web the hybrid factor can be taken as: [S6.10.1.10.1 '04]Hybrid factor: fserviceII_cf 212.2MPa= fserviceII_cf η 1.0 fDC1_cf( )⋅ 1.0 fDC2_cf( )⋅ + 1.0 fDW_cf( )⋅ + 1.3 fLL_IM_cf( )⋅ + ⋅ := Appying Sevice II Factors: fLL_IM_cf 10.9MPa=fLL_IM_cf MLL_IM STop_Steel_ST :=MLL_IM 3565 kN⋅ m⋅ := fDW_cf 5.4MPa=fDW_cf MDW STop_Steel_LT :=MDW 404 kN⋅ m⋅ := fDC2_cf 2.1MPa=fDC2_cf MDC2 STop_Steel_LT :=MDC2 161 kN⋅ m⋅ := fDC1_cf 190.6MPa=fDC1_cf MDC1 STop_Steel_NC :=MDC1 3202 kN⋅ m⋅ := The compression-flange flexural stresses resulting from unfactored loads are as follows: [S6.10.4.2.2-1 '04]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 ⎤ ⎦ ⎤ ⎦

O-45 Hybrid factor: [S6.10.1.10.1 '04] ρ min Fyw Fyt 1.0 := ρ 0.7= Dn dBot_Steel_ST tf.b−:= Dn 1233.4mm= Afn Af.b:= Afn 10000.0mm 2 = β 2 Dn⋅ tw⋅ Afn := β 3.454= Rh 12 β 3ρ ρ 3− ( )⋅+ 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] The tension-flange flexural stresses resulting from unfactored loads are as follows: fDC1_tf MDC1 SBot_Steel_NC := fDC1_tf 190.6MPa= fDC2_tf MDC2 SBot_Steel_LT := fDC2_tf 7.3MPa= fDW_tf MDW SBot_Steel_LT := fDW_tf 18.3MPa= fLL_IM_tf MLL_IM SBot_Steel_ST := fLL_IM_tf 149.4MPa= Applying Service II Factors: fserviceII_tf η 1.0 fDC1_tf( )⋅ 1.0 fDC2_tf( )⋅ + 1.0 fDW_tf( )⋅ + 1.3 fLL_IM_tf( )⋅ + ⋅ := fserviceII_tf 410.3MPa= Flange lateral bending stress: [S6.10.1.6 '04] fl 0 MPa := ⎤ ⎦ ⎤ ⎦ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠

O-46 fserviceII_tf.n 251.7MPa= Hybrid factor: [S6.10.1.10.1 '04] ρ min Fyw Fyt.n 1.0 := ρ 0.7= Fyt.n.1 Fyt.n STop_Steel_Comp.n⋅ := Fyt.n.2 Fyc.n SBot_Steel_Comp.n⋅ := Dn dTop_Steel_Comp.n tf.t.n− ( ) Fyt.n.1 Fyt.n.2≤if dBot_Steel_Comp.n tf.b.n− ( ) otherwise := Dn 728.3mm= Afn Af.t.n Dn dTop_Steel_Comp.n tf.t.n−if Af.b.n otherwise := Afn 21600.0mm 2 = β 2 Dn⋅ tw.n⋅ Afn := β 0.94= Rh 12 β 3ρ ρ 3− ( )⋅ + 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] The tension-flange flexural stresses resulting from unfactored loads are as follows: MDC1.n 5592 kN⋅ m⋅ := fDC1_tf.n MDC1.n STop_Steel_NC.n := fDC1_tf.n 202.1MPa= MDC2.n 288 kN⋅ m⋅ := fDC2_tf.n MDC2.n STop_Steel_LT.n := fDC2_tf.n 4.1 MPa= MDW.n 721 kN⋅ m⋅ := fDW_tf.n MDW.n STop_Steel_LT.n := fDW_tf.n 10.3MPa= MLL_IM.n 3854 kN m := fLL_IM_tf.n MLL_IM.n STop_Steel_ST.n := fLL_IM_tf.n 27.1MPa= Appying Sevice II Factors: fserviceII_tf.n η 1.0fDC1_tf.n 1.0fDC2_tf.n+ 1.0 fDW_tf.n⋅ + 1.3 fLL_IM_tf.n⋅ +( )⋅ := ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠

O-47 PR_Comp_Flange_Service_IIn 66.3%= PR_Comp_Flange_Service_IIn fserviceII_cf.n 0.95 Rh⋅ Fyc.n⋅ ( ):= Check_Comp_Flange_Service_IIn "OK"= Check_Comp_Flange_Service_IIn "OK" fserviceII_cf.n 1 2 fl.n⋅ + 0.95 Rh⋅ Fyc.n⋅ ≤if "Permanent deflection limitation exceeded"otherwise := Flexure check for bottom flange steel: Rh 0.98= [S6.10.1.10.1 '04]Hybrid factor: fl.n 0 MPa⋅ := [S6.10.1.6 '04]Flange lateral bending stress: fserviceII_cf.n 301.0MPa= fserviceII_cf.n η 1.0 fDC1_cf.n( )⋅ 1.0 fDC2_cf.n( )⋅ + 1.0 fDW_cf.n⋅ 1.3 fLL_IM_cf.n( )⋅ ++ ... ⋅:= Appying Sevice II Factors: fLL_IM_cf.n 72.8MPa= fLL_IM_cf.n MLL_IM.n SBot_Steel_ST.n := fDW_cf.n 19.5MPa=fDW_cf.n MDW.n SBot_Steel_LT.n := fDC2_cf.n 7.8MPa= fDC2_cf.n MDC2.n SBot_Steel_LT.n := fDC1_cf.n 179.1MPa=fDC1_cf.n MDC1.n SBot_Steel_NC.n := The compression-flange flexural stresses resulting from unfactored loads are as follows: [S6.10.4.2.2-1 '04]ff 1 2 fl⋅ + 0.95 Rh⋅ Fyf⋅ ≤Flexure check for bottom flange steel: ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

O-48 PR_Web_Bend_Buckling_Service_IIn 62.1%= PR_Web_Bend_Buckling_Service_IIn fserviceII_cf.n Fcrw.n := Check_Web_Bend_Buckling_Service_IIn "OK"= Check_Web_Bend_Buckling_Service_IIn "OK" fserviceII_cf.n Fcrw.n≤if "Web bend buckling occurs"otherwise := [S6.10.1.9.1-1 '04]Fcrw.n 485.0 MPa=Fcrw.n min 0.9 Es kn D tw.n 2 Fyc.n := [S6.10.1.9.1-2 '04]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]fc Fcrw≤Web Bend Buckling Check: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎤ ⎦ ⎤⎦ ⎤ ⎦ ⎤ ⎦

O-49 [S6.10.7.1.2-3 '04]Mn 1.3 Rh⋅ My⋅ In continuous spans, the nominal flexural resistance of the section shall not exceed: [S6.10.7.1.2-2 '04] [S6.10.7.1.2-1 '04]Mn 11880.6kN m⋅ =Mn Mp Dp 0.1 Dt⋅ ≤ if Mp 1.07 0.7 Dp Dt ⋅ − ⋅ otherwise := Dt 1600.0mm=Dt ts thaunch+ d+:= Dp 401.1mm=Dp ts thaunch+ ybar+:= [S6.10.7.1.2 '04]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]Depth of web in compression at the plastic moment: [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 Dcp⋅ tw 3.76 Es Fyc ⋅ ≤ • [S6.10.7.1 '04]COMPACT SECTIONS: [S6.10.7 '04]Positive Moment Region: [S6.10.6 '04]STRENGTH LIMIT STATE: ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟ ⎠ ⎞⎟⎠

O-50 Mu_strength_I 11048.5 kN m⋅ = Mu_strength_I 1.25 MDC1⋅ 1.25 MDC2⋅ + 1.5 MDW⋅ + 1.75 MLL_IM⋅ +:= [S6.10.1.6 '04]Factored moment due to strength I load combination about major axis: Mn 12249.6 kN m⋅ = [S6.10.7.1.2-3 '04]Mn min Mp 1.3 Rh⋅ Myt⋅ ( )( ):= Nominal Flexural Resistance: Myt 9828.4 kN m⋅ = Myt η 1.25 MDC1⋅ 1.25 MDC2⋅ + 1.5 MDW⋅ + MAD+( )⋅ := MAD 5018.6 kN m⋅ = MAD SBot_Steel_ST Fyt η 1.25 MDC1⋅ SBot_Steel_NC ⋅ 1.25 MDC2⋅ 1.5 MDW⋅ + SBot_Steel_LT ⋅ ⋅:= Fyt η 1.25MDC1 SBot_Steel_NC 1.25MDC2 1.5 MDW⋅ + SBot_Steel_LT + MAD SBot_Steel_ST + ⋅ MLL_IM 3565 kN⋅ m⋅ := MDW 404 kN⋅ m⋅ := MDC2 161 kN⋅ m⋅ := MDC1 3202 kN⋅ m⋅ := [D6.2 '04]Yield moment bottom flange: Rh 0.96=Rh 12 β 3ρ ρ 3− ( )⋅ + 12 2 β⋅+:= β 3.454=β 2 Dn⋅ tw.n⋅ Afn := Afn 10000.0 mm 2 =Afn Af.b:= Dn 1233.4 mm=Dn dBot_Steel_ST tf.b− := ρ 0.7=ρ min Fyw Fyt 1.0 := [S6.10.1.10.1 '04]Hybrid factor: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠⎤ ⎦ ⎤ ⎦

O-51 PR_Ductility 59.7%=PR_Ductility Dp 0.42 Dt⋅( ):= [S6.10.7.3-1 '04]Check_Ductility "OK"=Check_Ductility "OK" Dp 0.42 Dt⋅ ≤ if "Brittle failure"otherwise := Dt 1600.0mm= Dp 401.1mm= [S6.10.7.3 '04]DUCTILITY REQUIREMENT: PR_Strength_I_Flexure 90.2%= PR_Strength_I_Flexure Mu_strength_I 1 3 fl⋅ Sxt⋅ + φ f Mn⋅ := Check_Strength_I_Flexure "OK"= [S6.10.7.1.1-2 '04]Check_Strength_I_Flexure "OK" Mu_strength_I 1 3 fl⋅ Sxt⋅ + f Mn⋅ ≤ φif "Flexural resistance failure"otherwise := Check Strength I Flexure: [S6.5.4.2 '04]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]Flange lateral bending stress:

O-52 [S6.10.9.3.2-4 '04] [S6.10.9.3.2-5 '04] [S6.10.9.3.2-6 '04] C 0.53= Shear buckling resistance: Vcr C Vp⋅ := Vcr 1922.1kN= [S6.10.9.3.3-1 '04] Shear resistance of unstiffened web: Vr_unstiffened φv Vcr⋅ := Vr_unstiffened 1922.1kN= End Panel From Abutment: [S6.10.9.3.3 '04] Shear from factored loads at abutment location: Vu_StrengthI 1772 kN⋅ := Check_Shear "OK-Unstiffened Design" Vu_StrengthI Vr_unstiffened≤if "Increase shear resistance"otherwise := Check_Shear "OK-Unstiffened Design"= PR_Shear Vu_StrengthI Vr_unstiffened := PR_Shear 92.2%= Positive Moment Region: [S6.10.7 '04] Shear: The provisions of Article 6.10.9 shall apply.• [S6.10.6.3 '04] Shear Resistance: Vr φ v Vn⋅ [S6.10.9 '04] 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] Shear buckling coefficient for unstiffened condition: k 5:= [S6.10.9.2 '04] C 1.0 D tw 1.12 Es k⋅ Fyw ⋅ <if 1.12 D tw Es k⋅ Fyw ⋅ 1.12 Es k⋅ Fyw ⋅ D tw ≤ 1.40 Es k⋅ Fyw ⋅≤ if 1.57 D tw 2 Es k⋅ Fyw ⋅ D tw 1.40 Es k⋅ Fyw ⋅ >if := ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎞⎟⎠⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠

O-53 fLL_I_cf.n 106.0MPa=fLL_I_cf.n MLL_IM.n SBot_Steel_Comp.n := fDW_cf.n 21.1MPa=fDW_cf.n MDW.n SBot_Steel_Comp.n := fDC2_cf.n 8.4MPa=fDC2_cf.n MDC2.n SBot_Steel_Comp.n := fDC1_cf.n 183.1MPa=fDC1_cf.n MDC1.n SBot_Steel_NC.n := The compression-flange flexural stresses with strength I factors applied is: fstrI_tf.n 439.5MPa= fstrI_tf.n η 1.25 fDC1_tf.n( )⋅ 1.25 fDC2_tf.n( )⋅ + 1.5 fDW_tf.n( )⋅ + 1.75 fLL_I_tf.n( )⋅ + ⋅ := fLL_I_tf.n 84.4MPa=fLL_I_tf.n MLL_IM.n STop_Steel_Comp.n :=MLL_IM.n 3625 kN⋅ m⋅ := fDW_tf.n 16.8MPa=fDW_tf.n MDW.n STop_Steel_Comp.n :=MDW.n 721 kN⋅ m⋅ := fDC2_tf.n 6.7MPa=fDC2_tf.n MDC2.n STop_Steel_Comp.n :=MDC2.n 288 kN⋅ m⋅ := fDC1_tf.n 206.7MPa=fDC1_tf.n MDC1.n STop_Steel_NC.n :=MDC1.n 5718 kN⋅ m⋅ := The tension-flange flexural stresses with strength I factors applied is: [D6.3.1 '04]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]Negative Moment Region: ⎤ ⎦ ⎤ ⎦

O-54 Rb 1.0= [S6.10.1.10.2-3 '04] [S6.10.1.10.2-2 '04]Rb 1.0 2 Dc.n⋅ tw.n λrw.n≤if min 1 awc 1200 300 awc⋅ + 2 Dc.n⋅ tw.n λ rw.n− ⋅ − 1.0 otherwise := [S6.10.1.10.2-5 '04]awc 0.9=awc 2 Dc.n⋅ tw.n⋅ bf.b.n tf.b.n⋅ := λ rw.n 115.7=λ rw.n 5.7 Es Fyc.n ⋅ := [S6.10.1.10.2-4 '04] [S6.10.1.10.2 '04]Load-shedding factor: [S6.10.8.2.2-5 '04]λ rf.n 11.4=λrf.n 0.56 Es Fyc.n ⋅:= [S6.10.8.2.2-4 '04]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] or [Optional Appendix A '04]"= Web_slenderness "[6.10.8 '04] or [Optional Appendix A '04]" 2 Dc.n⋅ tw.n 5.7 Es Fyc.n ⋅ ≤if "Slender web - [6.10.8 '04]" otherwise := Dc.n 663.0mm= [D6.3.1 '04]Dc.n fstrI_cf.n fstrI_cf.n fstrI_tf.n+ dn⋅ tf.b.n−:= fstrI_cf.n 456.5MPa= fstrI_cf.n η 1.25 fDC1_cf.n( )⋅ 1.25 fDC2_cf.n( )⋅ + 1.5 fDW_cf.n( )⋅ + 1.75 fLL_I_cf.n( )⋅ + ⋅ := ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠⎤ ⎦ ⎤⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

O-55 Fnc.FLB.n 476.3MPa= Fnc.FLB.n Rb Rh⋅ Fyc.n⋅ ( ) λf.n λpf.n≤ if 1 1 Fyr.n Rh Fyc.n⋅ − λf.n λpf.n− λrf.n λpf.n− ⋅ − Rb⋅ Rh⋅ Fyc.n⋅ otherwise := [S6.10.8.2.2-2 '04] [S6.10.8.2.2-1 '04]Fyr.n 339.5MPa= [S6.10.8.2.2-6 '04]Fyr.n 0.7 Fyc.n⋅ ( ) 0.7 Fyc.n⋅ Fyw.n≤ if Fyw.n otherwise := [S6.10.8.2 '04]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− ( ) Myt.n Myc.n≤ if dBot_Steel_Comp.n tf.b.n−( ) otherwise := Myc.n Fyc.n SBot_Steel_Comp.n⋅ :=Myt.n Fyt.n STop_Steel_Comp.n⋅ := ρ 0.71=ρ min Fyw.n Fyc.n 1.0 := [S6.10.1.10.1 '04]Hybrid factor: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

O-56 largest moment at either brace point: moment at brace point opposite to M2: MDC1mid.n 3747 kN⋅ m⋅ := MDC12.n 5592 kN⋅ m⋅ := MDC1o.n 1901 kN⋅ m⋅ := MDC2mid.n 193 kN⋅ m⋅ := MDC22.n 288 kN⋅ m⋅ := MDC2o.n 98 kN⋅ m⋅ := MDWmid.n 483 kN⋅ m⋅ := MDW2.n 721 kN⋅ m⋅ := MDWo.n 245 kN⋅ m⋅ := MLL_IMmid.n 2908 kN⋅ m⋅ := MLL_IM2.n 3854 kN⋅ m⋅:= MLL_IMo.n 1962 kN⋅ m⋅ := stress at middle of unbraced length: fmid.n 1.25 MDC1mid.n MDC2mid.n+( )⋅ 1.5 MDWmid.n( )⋅ + SBot_Steel_NC.n 1.75 MLL_IMmid.n( )⋅ SBot_Steel_Comp.n +:= fmid.n 329.7MPa= largest stress at either brace point: f2.n 1.25 MDC12.n MDC22.n+( )⋅ 1.5 MDW2.n( )⋅+ SBot_Steel_NC.n 1.75 MLL_IM2.n( )⋅ 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] Limiting unbraced lengths: Lp.n rt.n Es Fyc.n ⋅ := Lp.n 2942mm= [S6.10.8.2.3-4 '04] Lr.n π rt.n⋅ Es Fyc.n := Lr.n 9244.1mm= [S6.10.8.2.3-5 '04] Moment gradient factor: moment at middle of unbraced length: ⎞⎟⎠ ⎞⎟ ⎠

O-57 Fnc_3.n 476.3MPa= Fnc_3.n min Fcr.n Rb Rh⋅ Fyc.n⋅ := 3. slender unbraced length: Fnc_2.n 476.3MPa= Fnc_2.n min Cb 1 1 Fyr.n Rh Fyc.n⋅ − Lb.n Lp.n− Lr.n Lp.n− ⋅ − ⋅ Rb⋅ Rh⋅ Fyc.n⋅ Rb Rh⋅ Fyc.n⋅ := 2. non compact unbraced length: Fnc_1.n 476.3MPa= Fnc_1.n Rb Rh⋅ Fyc.n⋅ ( ):= 1. compact unbraced length: Nominal flexural resistance of the flange to lateral torsional buckling: [S6.10.8.2.3-8 '04]Fcr.n 1575.8MPa=Fcr.n Cb Rb⋅ π 2 ⋅ Es⋅ Lb.n rt.n 2 := Elastic lateral torsional buckling stress: Cb 1.4= [S6.10.8.2.3-7 '04] [S6.10.8.2.3-6 '04]Cb 1.0 f2.n 0 MPa⋅ fmid.n f2.n 1.0≥ if 1.75 1.05 f1.n f2.n ⋅− 0.3 f1.n f2.n 2 ⋅ + otherwise := [S6.10.8.2.3-11 '04]f1.n 192.2MPa=f1.n max 2 fmid.n f2.n− fo.n( )( ):= fo.n 192.2MPa= fo.n 1.25 MDC1o.n MDC2o.n+( )⋅ 1.5 MDWo.n( )⋅ + SBot_Steel_NC.n 1.75 MLL_IMo.n( )⋅ SBot_Steel_Comp.n +:= stress at brace point opposite of f2: Moment gradient factor: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎞⎟⎠ ⎞⎟ ⎠

O-58 PR_Ten_Flange_Yield_Str1n 92.3 %= PR_Ten_Flange_Yield_Str1n fstrI_tf.n fl.n+ φ f Rh⋅ Fyt.n⋅ := Check_Ten_Flange_Yield_Str1n "OK"= Check_Ten_Flange_Yield_Str1n "OK" fstrI_tf.n fl.n+ f Rh⋅ Fyt.n⋅ ≤ φ if "Tension flange yield occurs" otherwise := [S6.10.3.2.1-1 '04]fbu fl+ f Rh⋅ Fyt⋅ ≤ φCheck flange nominal yielding: [S6.10.3.2.2 '04]Discretely Braced Flanges in Tension: PR_Comp_Flange_StrIn 95.8%= PR_Comp_Flange_StrIn fstrI_cf.n 1 3 fl.n⋅ + φ f Fnc.n⋅ := Check_Comp_Flange_StrIn "OK"= [S6.10.3.2.1-2 '04]Check_Comp_Flange_StrIn "OK" fstrI_cf.n 1 3 fl⋅ + f Fnc.n⋅ ≤ φ if "Flexural resistance failure"otherwise := Check compression flange buckling: [S6.5.4.2 '04]φ f 1.0:= Resistance factor for flexure: Fnc.n 476.3 MPa=Fnc.n min Fnc.FLB.n Fnc.LTB.n := Fnc.LTB.n 476.3 MPa= Fnc.LTB.n Fnc_1.n Lb.n Lp.n≤ if Fnc_2.n Lp.n Lb.n<( ) Lb.n Lr.n≤( )⋅ if Fnc_3.n Lb.n Lr.n>if := Nominal flexural resistance of the flange to lateral torsional buckling: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠

O-59 Vr_unstiffened 1922.1 kN=Vr_unstiffened φ v Vcr⋅ := Shear resistance of unstiffened web: [S6.10.9.3.3-1 '04]Vcr 1922.1 kN=Vcr C Vp⋅:= Shear bucking resistance: C 0.53= [S6.10.9.3.2-6 '04] [S6.10.9.3.2-5 '04] [S6.10.9.3.2-4 '04]C 1.0 D tw.n 1.12 Es k⋅ Fyw.n ⋅<if 1.12 D tw.n Es k⋅ Fyw.n ⋅ 1.12 Es k⋅ Fyw.n ⋅ D tw.n ≤ 1.40 Es k⋅ Fyw.n ⋅≤ if 1.57 D tw.n 2 Es k⋅ Fyw.n ⋅ D tw.n 1.40 Es k⋅ Fyw.n ⋅>if := [S6.10.9.2 '04]k 5:= Shear buckling coefficient for unstiffened condition: [S6.10.9.2-2 '04]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]Vr φ v Vn⋅Shear Resistance: [S6.10.6.3 '04]The provisions of Article 6.10.9 shall apply.Shear: [S6.10.7 '04]Negative Moment Region: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟⎠⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

O-60 PR_Shear_1st_Int_Panel_Str_In 86.3%= PR_Shear_1st_Int_Panel_Str_In Vu_StrengthI φv Vn⋅ := Check_Shear_1st_Int_Panel_Str_In "OK"= Check_Shear_1st_Int_Panel_Str_In "OK" Vu_StrengthI φv Vn⋅≤if "Increase shear resistance"otherwise := Vn 2753.0kN= [S6.10.9.2-1 '04] [S6.10.9.3.2-2 '04] Vn Vp C 0.87 1 C− ( )⋅ 1 do D 2 + + ⋅ 2 D⋅ tw.n⋅ bf.t.n tf.t.n⋅ bf.b.n tf.b.n⋅+( ) 2.5≤ if C Vp⋅( ) otherwise := [S6.10.9.3.2-1 '04] C 0.63= [S6.10.9.3.2-6 '04] [S6.10.9.3.2-5 '04] [S6.10.9.3.2-4 '04]C 1.0 D tw.n 1.12 Es k⋅ Fyw.n ⋅<if 1.12 D tw.n Es k⋅ Fyw.n ⋅ 1.12 Es k⋅ Fyw.n ⋅ D tw.n ≤ 1.40 Es k⋅ Fyw.n ⋅≤if 1.57 D tw.n 2 Es k⋅ Fyw.n ⋅ D tw.n 1.40 Es k⋅ Fyw.n ⋅ >if := [S6.10.9.3.2-7 '04]k 5.9=k 5 5 do D 2 +:= do 3 m⋅:=Stiffener spacing from pier stiffener: Therefore, add a stiffener between pier and 1st cross frame: Check_Shearn "Increase shear resistance"= Check_Shearn "OK-Unstiffened Design" Vu_StrengthI Vr_unstiffened≤if "Increase shear resistance"otherwise := Vu_StrengthI 2377 kN⋅:=Shear from factored loads at pier: [S6.10.9.3.2 '04]1st Interior Panel From Pier: ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠

O-61 PR_Shear_3rd_Int_Panel_Str_In 69.8 %= PR_Shear_3rd_Int_Panel_Str_In Vu_StrengthI φ v Vn⋅ := Check_Shear_3rd_Int_Panel_Str_In "OK"= Check_Shear_3rd_Int_Panel_Str_In "OK" Vu_StrengthI φv Vn⋅≤ if "Increase shear resistance" otherwise := Vn 2753.0 kN= [S6.10.9.2-1 '04] [S6.10.9.3.2-2 '04] Vn Vp C 0.87 1 C− ( )⋅ 1 do D 2 + + ⋅ 2 D⋅ tw.n⋅ bf.t.n tf.t.n⋅ bf.b.n tf.b.n⋅ +( ) 2.5≤if C Vp⋅( ) otherwise := [S6.10.9.3.2-1 '04] C 0.63= [S6.10.9.3.2-6 '04] [S6.10.9.3.2-5 '04] [S6.10.9.3.2-4 '04]C 1.0 D tw.n 1.12 Es k⋅ Fyw.n ⋅<if 1.12 D tw.n Es k⋅ Fyw.n ⋅ 1.12 Es k⋅ Fyw.n ⋅ D tw.n ≤ 1.40 Es k⋅ Fyw.n ⋅≤if 1.57 D tw.n 2 Es k⋅ Fyw.n ⋅ D tw.n 1.40 Es k⋅ Fyw.n ⋅>if := [S6.10.9.3.2-7 '04]k 5.9=k 5 5 do D 2 +:= do 3 m⋅:=Stiffener spacing from 1st cross frame stiffener: Vu_StrengthI 1922 kN⋅ :=Shear from factored loads at 6 m from pier: [S6.10.9.3.2 '04]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. 2nd Interior Panel From Pier: ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎞⎟⎠ ⎞⎟ ⎠ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦ ⎤ ⎦

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

O-63 -6000 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 0 5 10 15 20 25 30 35 40 Distance (m) 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. -800 -600 -400 -200 0 200 400 600 0 5 10 15 20 25 30 35 40 Distance (m) Sh ea r (k N ) . DC1 DC2 DW Point of maximum (+) moment Point of maximum (-) moment Figure O-6 Shears calculated from unfactored permanent dead loads.

O-64 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 0 5 10 15 20 25 30 35 40 Distance (m) M o m en t ( kN - m ) . Design Tandem Design Truck Dual Truck Train Fatigue Truck Figure O-7 Moments calculated from unfactored live loads excluding girder distribution factors. -800 -600 -400 -200 0 200 400 600 800 0 5 10 15 20 25 30 35 40 Distance (m) Sh ea r (k N ) Design Tandem Design Truck Fatigue Truck Figure O-8 Shears calculated from unfactored live loads excluding girder distribution factors.

O-65 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 0 5 10 15 20 25 30 35 40 Distance (m) M o m en t ( kN - m ) . Maximum Live Load Moments (Including GDF) Fatigue Moments (Includes GDF) Figure O-9 Maximum moments calculated from unfactored live loads including girder distribution factors. -1000 -800 -600 -400 -200 0 200 400 600 800 0 5 10 15 20 25 30 35 40 Distance (m) Sh e ar (k N ) Maximum Live Load Shears (Includes GDF) Fatgiue Shear (Includes GDF) Figure O-10 Maximum shears calculated from unfactored live loads including girder distribution factors.