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OCR for page 89
O-1
APPENDIX O
DESIGN EXAMPLES
Appendix O has not been edited by TRB.
OCR for page 90
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.
1200mm
480mm 3 Lanes @ 3600mm=10800mm 3000mm 480mm
2
FWS (122.5 kg/m )
240mm w/ 40mm IWS
50mm Haunch
600mm 4 @ 3690mm=14760mm 600mm
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.
OCR for page 91
O-3
End Field Pier
Bearing Splice Bearing
18°
4 at 7000 mm spacing = 28000 mm
30000 mm
40000 mm
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 485W (Fy = 485 MPa)
Grade 345W (Fy = 345 MPa)
Figure O-3 Hybrid Configuration
OCR for page 92
O-4
O.5 Girder Elevation Description
The elevation view of the interior girder is provided in Figure O-4.
End Bolted Pier
bearing field splice bearing
30000 mm 10000 mm
4 at 7000 mm = 28000 mm
intermediate cross frame
cross frame stiffeners connection plate
connection plates
Figure O-4. Elevation View of Interior Girder
OCR for page 93
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.
OCR for page 94
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.
OCR for page 95
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.
OCR for page 96
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
OCR for page 97
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
OCR for page 98
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
OCR for page 99
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.
OCR for page 143
O-55
Hybrid factor: [S6.10.1.10.1 '04]
Fyw.n
:= min 1.0 = 0.71
Fyc.n
Myt.n := Fyt.n STop_Steel_Comp.n Myc.n := Fyc.n SBot_Steel_Comp.n
Dn := (dTop_Steel_Comp.n - tf.t.n ) if Myt.n Myc.n
(dBot_Steel_Comp.n - tf.b.n ) otherwise
Dn = 728.3 mm
2
Afn := Af.t.n if Dn dBot_Steel_Comp.n - tf.t.n Afn = 18000.0 mm
Af.b.n otherwise
2 Dn tw.n
:= = 1.133
Afn
Rh :=
(
12 + 3 -
3 ) Rh = 0.98
12 + 2
Nominal flexural resistance of the flange to local buckling: [S6.10.8.2 '04]
Fyr.n := ( 0.7 Fyc.n ) if 0.7 Fyc.n Fyw.n [S6.10.8.2.2-6 '04]
Fyw.n otherwise
Fyr.n = 339.5 MPa [S6.10.8.2.2-1 '04]
[S6.10.8.2.2-2 '04]
Fnc.FLB.n := ( Rb Rh Fyc.n ) if f.n pf.n
1 - 1 -
Fyr.n f.n - pf.n
Rh Fyc.n rf.n - pf.n
Rb Rh Fyc.n otherwise
Fnc.FLB.n = 476.3 MPa
OCR for page 144
O-56
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 = 728.3 mm
Radius of gyration about vertical axis:
bf.b.n
rt.n := rt.n = 144.9 mm [S6.10.8.2.3-10 '04]
12
1 + 1 Dc.n tw.n
3 bf.b.n tf.b.n
Limiting unbraced lengths:
Es
Lp.n := rt.n Lp.n = 2942 mm [S6.10.8.2.3-4 '04]
Fyc.n
Es
Lr.n := rt.n Lr.n = 9244.1 mm [S6.10.8.2.3-5 '04]
Fyc.n
Moment gradient factor:
moment at middle largest moment at moment at brace
of unbraced length: either brace point: 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:
1.25 ( MDC1mid.n + MDC2mid.n) + 1.5 ( MDWmid.n) 1.75 ( MLL_IMmid.n)
fmid.n := +
SBot_Steel_NC.n SBot_Steel_Comp.n
fmid.n = 329.7 MPa
largest stress at either brace point:
1.25 ( MDC12.n + MDC22.n) + 1.5 ( MDW2.n) 1.75 ( MLL_IM2.n )
f2.n := +
SBot_Steel_NC.n SBot_Steel_Comp.n
f2.n = 467.2 MPa
OCR for page 145
O-57
Moment gradient factor:
:
stress at brace point opposite of2f
1.25 ( MDC1o.n + MDC2o.n) + 1.5 ( MDWo.n) 1.75 ( MLL_IMo.n )
fo.n := +
SBot_Steel_NC.n SBot_Steel_Comp.n
fo.n = 192.2 MPa
f1.n := max ( ( 2 fmid.n - f2.n fo.n ) ) f1.n = 192.2 MPa [S6.10.8.2.3-11 '04]
Cb := 1.0 if f2.n 0 MPa [S6.10.8.2.3-6 '04]
fmid.n
1.0
f2.n
2
f1.n f1.n
1.75 - 1.05 + 0.3 otherwise
f2.n f2.n [S6.10.8.2.3-7 '04]
Cb = 1.4
Elastic lateral torsional buckling stress:
2
Cb Rb Es
Fcr.n := Fcr.n = 1575.8 MPa [S6.10.8.2.3-8 '04]
2
Lb.n
rt.n
Nominal flexural resistance of the flange to lateral torsional buckling:
1. compact unbraced length:
Fnc_1.n := ( Rb Rh Fyc.n )
Fnc_1.n = 476.3 MPa
2. non compact unbraced length:
Fyr.n Lb.n - Lp.n
Fnc_2.n := min Cb 1 -
1 -
R
h yc.n r.n
F L - Lp.n
Rb Rh Fyc.n
Rb Rh Fyc.n
Fnc_2.n = 476.3 MPa
3. slender unbraced length:
Fcr.n
Fnc_3.n := min
Rb Rh Fyc.n
Fnc_3.n = 476.3 MPa
OCR for page 146
O-58
Nominal flexural resistance of the flange to lateral torsional buckling:
Fnc.LTB.n := Fnc_1.n if Lb.n Lp.n
Fnc_2.n if ( Lp.n < Lb.n ) ( Lb.n Lr.n )
Fnc_3.n if Lb.n > Lr.n
Fnc.LTB.n = 476.3 MPa
Fnc.FLB.n
Fnc.n := min Fnc.n = 476.3 MPa
Fnc.LTB.n
Resistance factor for flexure:
f := 1.0 [S6.5.4.2 '04]
Check compression flange buckling:
1
Check_Comp_Flange_StrIn := "OK" if fstrI_cf.n + fl f Fnc.n [S6.10.3.2.1-2 '04]
3
"Flexural resistance failure" otherwise
Check_Comp_Flange_StrI n = "OK"
1
fstrI_cf.n + fl.n
3
PR_Comp_Flange_StrI n :=
f Fnc.n
PR_Comp_Flange_StrI n = 95.8 %
Discretely Braced Flanges in Tension: [S6.10.3.2.2 '04]
Check flange nominal yielding: fbu + fl f Rh Fyt [S6.10.3.2.1-1 '04]
Check_Ten_Flange_Yield_Str1n:= "OK" if fstrI_tf.n + fl.n f Rh Fyt.n
"Tension flange yield occurs" otherwise
Check_Ten_Flange_Yield_Str1n = "OK"
fstrI_tf.n + fl.n
PR_Ten_Flange_Yield_Str1n :=
f Rh Fyt.n
PR_Ten_Flange_Yield_Str1n = 92.3 %
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O-59
Negative Moment Region: [S6.10.7 '04]
Shear: The provisions of Article 6.10.9 shall apply. [S6.10.6.3 '04]
Shear Resistance: Vr v Vn [S6.10.9 '04]
Resistance of unstiffened web in negative moment region: [S6.10.9.2 '04]
Plastic shear force:
Vp := 0.58 Fyw.n Dtw.n Vp = 3641.8 kN [S6.10.9.2-2 '04]
Shear buckling coefficient for unstiffened condition:
k := 5 [S6.10.9.2 '04]
D Es k
C := 1.0 if < 1.12 [S6.10.9.3.2-4 '04]
tw.n Fyw.n
1.12 Es k Es k D Es k
if 1.12 1.40
D Fyw.n Fyw.n tw.n Fyw.n [S6.10.9.3.2-5 '04]
tw.n
Es k Es k
1.57 D
if > 1.40
2 Fyw.n tw.n Fyw.n
D
[S6.10.9.3.2-6 '04]
tw.n
C = 0.53
Shear bucking resistance:
Vcr := C Vp Vcr = 1922.1 kN [S6.10.9.3.3-1 '04]
Shear resistance of unstiffened web:
Vr_unstiffened := v Vcr Vr_unstiffened = 1922.1 kN
OCR for page 148
O-60
1st Interior Panel From Pier: [S6.10.9.3.2 '04]
Shear from factored loads at pier: Vu_StrengthI := 2377 kN
Check_Shearn := "OK-Unstiffened Design"if Vu_StrengthI Vr_unstiffened
"Increase shear resistance" otherwise
Check_Shearn = "Increase shear resistance"
Therefore, add a stiffener between pier and 1st cross frame:
Stiffener spacing from pier stiffener: do := 3 m
5
k := 5 + k = 5.9 [S6.10.9.3.2-7 '04]
2
do
D
D Es k
C := 1.0 if < 1.12 [S6.10.9.3.2-4 '04]
tw.n Fyw.n
Es k Es k Es k
1.12 D
if 1.12 1.40
D Fyw.n Fyw.n tw.n Fyw.n [S6.10.9.3.2-5 '04]
tw.n
Es k Es k
1.57 D
if > 1.40
2 Fyw.n tw.n Fyw.n
D
[S6.10.9.3.2-6 '04]
tw.n
C = 0.63
0.87 ( 1 - C) 2 Dtw.n [S6.10.9.3.2-1 '04]
Vn := Vp C + if 2.5
do
2 ( bf.t.n tf.t.n + bf.b.n tf.b.n ) [S6.10.9.3.2-2 '04]
1+
D
( C Vp) otherwise
[S6.10.9.2-1 '04]
Vn = 2753.0 kN
Check_Shear_1st_Int_Panel_Str_In := "OK" if Vu_StrengthI v Vn
"Increase shear resistance" otherwise
Check_Shear_1st_Int_Panel_Str_In = "OK"
Vu_StrengthI
PR_Shear_1st_Int_Panel_Str_In :=
v Vn
PR_Shear_1st_Int_Panel_Str_In = 86.3 %
OCR for page 149
O-61
2nd 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.
3rd Interior Panel From Pier: [S6.10.9.3.2 '04]
Shear from factored loads at 6 m from pier: Vu_StrengthI := 1922 kN
Stiffener spacing from 1st cross frame stiffener: do := 3 m
5
k := 5 + k = 5.9 [S6.10.9.3.2-7 '04]
2
do
D
D Es k
C := 1.0 if < 1.12 [S6.10.9.3.2-4 '04]
tw.n Fyw.n
Es k Es k Es k
1.12 D
if 1.12 1.40
D Fyw.n Fyw.n tw.n Fyw.n [S6.10.9.3.2-5 '04]
t
w.n
1.57 Es k D Es k
D
t
2 Fyw.n
if
tw.n
> 1.40
Fyw.n
[S6.10.9.3.2-6 '04]
w.n
C = 0.63
0.87 ( 1 - C) 2 Dtw.n [S6.10.9.3.2-1 '04]
Vn := Vp C + 2.5
if
do
2 ( bf.t.n tf.t.n + bf.b.n tf.b.n ) [S6.10.9.3.2-2 '04]
1+
D
( C Vp) otherwise
[S6.10.9.2-1 '04]
Vn = 2753.0 kN
Check_Shear_3rd_Int_Panel_Str_In := "OK" if Vu_StrengthI v Vn
"Increase shear resistance" otherwise
Check_Shear_3rd_Int_Panel_Str_In = "OK"
Vu_StrengthI
PR_Shear_3rd_Int_Panel_Str_In :=
v Vn
PR_Shear_3rd_Int_Panel_Str_In = 69.8 %
OCR for page 150
O-62
O.9 Summary
400mm 450mm
25mm 40mm
14mm 14mm
1300mm 1300mm
25mm 400mm 40mm 540mm
Positive Moment Regions Negative Moment Regions
O.10 Shears and Moments Diagrams
OCR for page 151
O-63
-6000
DC1
-5000 DC2
-4000 DW
-3000
-2000
Moment (kN-m)
-1000
0
1000 Dead load
inflection point
2000
CL
3000
Bearing
4000
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-5 Moments calculated from unfactored permanent dead loads.
-800
DC1
-600 DC2
DW
-400
.
-200
Shear (kN)
0
Point of Point of
200
maximum maximum
(+) moment (-) moment
400
600
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-6 Shears calculated from unfactored permanent dead loads.
OCR for page 152
O-64
-5000
Design Tandem
-4000 Design Truck
-3000 Dual Truck Train
Fatigue Truck
-2000
Moment (kN-m) .
-1000
0
1000
2000
3000
4000
5000
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-7 Moments calculated from unfactored live loads excluding girder
distribution factors.
-800
Design Tandem
-600 Design Truck
Fatigue Truck
-400
-200
Shear (kN)
0
200
400
600
800
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-8 Shears calculated from unfactored live loads excluding girder distribution
factors.
OCR for page 153
O-65
-4000
Maximum Live Load Moments (Including GDF)
-3000 Fatigue Moments (Includes GDF)
-2000
Moment (kN-m) .
-1000
0
1000
2000
3000
4000
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-9 Maximum moments calculated from unfactored live loads including girder
distribution factors.
-1000
Maximum Live Load Shears (Includes GDF)
-800
Fatgiue Shear (Includes GDF)
-600
-400
Shear (kN)
-200
0
200
400
600
800
0 5 10 15 20 25 30 35 40
Distance (m)
Figure O-10 Maximum shears calculated from unfactored live loads including girder
distribution factors.
