APPENDIX CB - COMPOSITE BRIDGE, 24 M SPAN, 7.32 m Width

Appendix CBBridge Design Manual - 2002 Composite Bridge Design

Ethiopian Roads Authority Page CB-1

APPENDIX CB - COMPOSITE BRIDGE, 24 M SPAN, 7.32 m Width

The following calculations is an example of a documentation for a composite bridge with aspan of 24m and a width of 7.32m. The principle dimensions of the bridge are shown in thefigures below.

Figure Longitudinal section

Figure Typical cross section

Four design conditions are checked:

• Strength I• Service I• Fatigue• Construction stage

Appendix CBComposite Bridge Design Bridge Design Manual - 2002

Page CB-2 Ethiopian Roads Authority

CB.1 DESIGN CONSIDERATIONS

The calculations are based on: ERA BRIDGE DESIGN MANUAL-2002AASHTO LRFD BRIDGE DESIGN MANUAL-1996

Resistance factors – steel (Table 10-2)

Plate girders, transverse beams: φf =φc = 1.0 (both flexure and shear)Shear connectors: φsc = 0.85Bearing: φb = 1.0Axial compression: φc = 0.9

Resistance factors – concrete (Table 9-7)

Flexure of reinforced concrete φ = 0.9

Material - Steel

E- modulus: 200 000 Mpa Section 10.1Poisson ratio: 0.3Density: γs = 7850 kg/m3 Table 3-4Thermal expansion: 11.7E-6/deg C Section 10.1

Yield strength

Rolled plates

AASHTO Designation: M270 -Grade 345 Table 10-1Equivalent to European steel S355

Fy = 345 MPa

Rolled profiles

AASHTO Designation: M270 -Grade 250 Table 10-1Equivalent to European steel S275

Fy = 250 MPa

Shear connectors

Shear connectors shall be made from cold-drawn bars, Grades 1015, 1018 or 1020, eithersemi- or fully killed, conforming to AASHTO M169.

Fy = 345 MPa (minimum yield strength)Fu = 400 MPa (minimum tensile strength)



Reinforcement bars

fy = 350 Mpa

Material - Concrete:

Poisson ratio: 0.2 Section 9.3Thermal expansion: 10.8E-6/°C Section 9.3

Grade: C25

fc' = 20 Mpa Table 9-1

Density: γc = 2400 kg/m3 Section 9.3

Ec = 0.043*γc1.5*SQR(fc') Equation 9.3

Ec = 22600 Mpa

Concrete cross section area transferred to equivalent steel area.

The equivalent steel area can be calculated by a modular ratio factor for C25 concrete of:(see AASHTO 6.10.5.1.b)n=10 Short term loadsn=30 Long term loads

CB.2 COMPUTER PROGRAMS

Following PC-programs have been used:

• Main analysis: STAAD3, ver 22.0• Cross section program: SECTION, ver 3.0

SECTION is a general cross section program for calculation of section properties (seesection CB-8:Appendix A)



CB.3 STRUCTURAL CROSS SECTIONS

Steel cross section

The steel cross section has a shape as shown in the figure below.

Figure Steel cross section

Concrete slab - Effective flange width

The gross section for one girder is shown in the figure below.

*) exclusive edge beam**) exclusive cover at top surface (50 mm)

The effective flange width shall be taken as the minimum of:(ref AASHTO ch. 4.6.2.6.1-interior beam)

1. ¼*24=6m2. 12*0.23+0.5*0.325=2.923. 1.41+2.25=3.66This means that the effective width is 2.92m.

22501410*)

230**)

325

Web 1345x15

Topflange 325x20

Bottom flange 400x35



For this exampe, the effective width is reduced to 2.0 m for the strength loadcase. This givesthe plastic neutral axis in the web.

Cross section for Strength loadcase

The capacity for the section is based on the plastic moment capacity. This can be calculatedaccording to AASHTO ch 6.10.5.1.3.The forces in the longitudinal reinforcement isconservatively neglected.

Cross section for Service and Fatigue loadcase

For calculating deflection for the Service loadcase and fatigue stresses, the concrete width isreduced with a factor of n according to AASHTO ch 6.10.5.1.1.b. This represents the shortterm composite section. With n=10 for concrete with fc'=20, this gives a concrete effectivewidth of:

W = 2910/10=291 mm

CB.4 BASIC LOADS

Dead load - DC

Steel

Dead load of steel is 79 kN/m3 Table 3-4

For one beam, the dead load is assumed to be

DCs = 4 kN/m.

Concrete

The following is calculated for one girder.

Overhang slab

The railing including posts is estimated to 2.75 kN/m.

Edge beam including slab to c/l of girder has a cross section of:

A = 1.81*0.258 + 0.4*(0.4-0.24)= 0.531 m2

Slab between girders.

The slab has a thickness of 0.28 m



A = 2.25*0.28 =0.63 m2

Total load from concrete:

DCc = 2.75 + 24*(0.531+0.632)= 30.7 kN/m

Wearing surface - DW

The wearing surface is estimated to have a thickness of 50 mm. With a density of 22.5kN/m2, this gives a load of:

DW = 0.05*22.5= 1.125 kN/m2

Or for one girder

DW = 1.125*7.32/2 = 4.1 kN/m

Live load - LL

Strength and service load combinations

Number of lanes: 7.32/3=2 Section 3.8

Lane load: (Section 3.8)

LL = 9.3 kN/m (per lane; design lane=3.0m)

With the lever arm method, the load for one girder can be calculated to:

Moment @ A

Rb = 2*LL*(4.5+1.41-3)/4.5 =LL*1.293LL= 9.3*1.293 = 12.028 kN/m

4500

A

1410

3000

LL

B

3000



Truck load (Section 3.8)

Reacton force on one girder is the total truckload multiplied with a lever arm factor of 1.293.This means that following truck load is acting on one girder

P1 =145*1.293 = 188 kNP2 =35*1.293 = 45 kN

Tandem load (Section 3.8)

Reacton force on one girder is the total tandem load multiplied with a lever arm factor of0.647. This load will not be governing for this bridge.

Fatigue load combination

Number of lanes: 1 (Section 3.8)

With the lever arm method, the load for one girder can be calculated to:

Moment @ A

Rb = Q*(4.5+1.41-1.5)/4.5 =Q*0.98

Truck load (Section 3.8)

Reaction force on one girder is the truckload multiplied with a lever arm factor of 0.98. Thismeans that following truck load is acting on one girder.

P1P2 P1a = 4300-90004300

P1P2 P1a = 90004300

4500

A

1410

3000Q

B



P1 =145*0.98=142 kNP2 =35*0.98= 34 kN

Note: a is 9000 for fatigue load Section 3.8

Dynamic Load Allowance - IM

The dynamic load allowance is 33%, ref. Section 3.13, which means a load factor of 1.33.This load factor is only valid for truck loads and tandem loads.

Wind on Vehicles -WL

Wind on vehicles results in an additional vertical load to be considered in the SERVICE Iloadcase. The wind pressure is 1.5 kN/m acting 1.8m above the road. This gives followingadditional vertical load for one beam.

The reaction force at beam B is then

Rb=P*2.8/4.5= 1 kN/m

Temperature

Since the bridge can elongate freely and the thermal expansion coefficent is nearly the samefor concrete and steel, the temperature differnace has no influence on the bridge.

Fatigue load

The average daily number (ADT=average daily traffic) of vehicles is estimated to 300. Thisresults in an ADDT (number of trucks per day) in one direction of

ADDT = 0.4 * ADT= 120

Based on an rural highway (Section 3.8).

The ADDTSL (number of trucks per day in a single-lane averaged over the design life) canthen be calculated to:

4500

A

1800

1000

P=1.5 kN/m

B



ADDTSL = 0.85* ADDT = 102

corresponding to a P=0.85 (two lanes, Section 3.8).

Number of cycles can then be calculated to:

N = 365*75*n*ADDTSL = 365*75*1*102 = 2.8E6 according to AASHTO ch 6.6.1.2.4

Based on

n = 1 (number of stress ranges per truck; l>12m)life time = 75 year

Calculations are made with the computer program STAAD in section CB-9:Appendix B.

CB.5 LOAD COMBINATIONS

STRENGTH I - Construction stage

SECTION/LoadfactorLoads STEELSteel 1.25Concrete 1.25Wearing surface 1.25

STRENGTH I - Normal stage

SECTION/LoadfactorLoads STEEL COMPOSITSteel 1.25Concrete 1.25Wearing surface 1.25Live load – lane load 1.75Live load – truck load 1.75*1.33

SERVICE I - Camber

SECTION/LoadfactorLoads STEELSteel 1.0Concrete 1.0Wearing surface 1.0



SERVICE I - Normal stage

Loads Load factorsWearing surface 1.0Wind load 1.0Live load – lane load 1.0Live load – truck load 1.0*1.33

FATIGUELoadfactor

Loads COMPOSITLive load – truck load 0.75*1.33=1.0

CB.6 STEEL

STRENGTH - I

Construction stage – ref AASHTO ch 6.10.10

Prior to the concrete hardening, the member is a non-composite beam section, ref figurebelow.

Figure. Section during construction stage

Following cross section values have been calculated by the PC-program SECTION, refsection CB-8: Appendix A.

Dc = 801 mm (Depth of the web in compression in the elastic range)Dcp = 923 mm (Depth of the web in compression in the plastic range)Ix = 1.207E10 mm4 (Moment of inertia)Sx1 = 1.470E7 mm3 (Section modulus for top flange)Sx2 = 2.084E7 mm3 (Section modulus for top flange)J = 8.096E6 mm4 (S.T Venant torsional constant)

Web 1345x15

Topflange 325x20

Bottom flange 450x35



Moment:

The beam shall carry the dead load from the steel beam, the concrete slab and the wearingsurface. Even if the wearing surface not is applied, this load is also representing the deckform load during the construction stage.

Total load on the beam is :

Q = 4.1 + 30.7 + 4 = 38.8 kN/m

The beam is a simply supported beam with a span of 24m.

This gives a moment including a loadfactor of 1.25 of:

M = 1.25*ql2/8 = 1.25*38.8*242/8 = 3492 kNm

The stress in the top flange is then

Sigx= 3492E6/1.470E7= 238Mpa

The reaction force can be calculated to:

RA = 1.25*38.8*24/2=582 kN

Control if the section is a compact section according to AASHTO ch 6.10.5.2.2.c

Requirement for a compact section is

2*Dcp/tw<=3.76*Sqr(E/Fyc)

Dcp <= 15/2*3.76*Sqr(2E5/345) = 679

Not fulfilled

Control if the section is a non-compact section according to AASHTO ch 6.10.5.3.2.b

Q=38.8 kN/m

24000A



The web slenderness is checked

2*Dc/tw<=6.77*Sqr(E/fc)

with fc = 238 MPa, this gives

Dc<=1472 mm

With Dc= 801, this requirement is fulfilled.

Compression flange slenderness according to AASHTO ch 6.10.5.3.3.c

Bf/(2*tf)<=1.38*Sqr(E/(fc*Sqr(2*Dc/tw))

This gives

Bf <= 2*20*1.38*Sqr(2E5/(238*Sqr(2*824/15)) = 494

With bf=325, this requirement is fulfilled

Compression flange bracing according to AASHTO ch 6.10.5.3.3.d and 6.10.6.4

Lb<=1.76*rt*Sqr(E/Fyc)

rt = Sqr(1/12*(20*3253+801/3*153)/(20*325+15*801/3) = 73.85

Lb<= 1.76*73.85*Sqr(2E5/345) = 3129 mm

With Lb= 6000 mm, this requirement is not fulfilled.

Moment capacity is then calculated according to AASHTO ch 6.10.6.4

If 2*Dc/tw<=λb*Sqr(E/Fyc)

then

Mn=3.14*E*Cb*Rh*(Iyc/Lb)*Sqr(0.772*(J/Iyc)+9.87*(d/Lb)2)

λb = 4.64 according to AASHTO ch 6.10.5.4.2.aCb= 1.0Rh=1.0Iyc=1/12*20*3253=57.2E6Lb=6000J=8.811E6d=1400



Dc<=4.64*15/2*Sqr(2E5/345)= 838

With Dc=801, the moment capacity can be calculated to:

Mr=Mn= 4850 MNm

With the acual moment of 3492 kNm , the capacity of the beam is fulfilled.

Distance between braces = 6000 mm

Operating stage

After the concrete has hardened, the member has a composite cross section as shown in thefigure below.

First the section is controlled if it’s a compact according to AASHTO ch 6.10.5.2 or non-compact section according to AASHTO ch 6.10.5.3.

Requirement for a compact section is

2*Dcp/tw<=3.76*Sqr(E/Fyc)

Dcp <= 14/2*3.76*Sqr(E/Fyc) = 633

Dcp (assumed to be placed in the web) can be calculated as according to AASHTO ch6.10.5.1.4.b:

25 theor. clearance

2000

230

325



Dcp =D/2*((Fyt*At-Fyc*Ac-0.85*fc’*As-Fyr*Ar)/(Fyw*Aw) + 1)

With

Fyt=Fyc=Fyw=345Ar = 0At = 400*35=14000Ac=325*20=6500Aw=15*1345=20175fc’=20As = 2000*230=460000D = 1345

Dcp= 167

This means that the member fulfills the requirement for a compact section.

Since the concrete supports the compression flange, there is no other requirements to thesection.

The moment capacity can then be calculated to:

Mp=Pw/2/D*(Dcp2+(D-Dcp)2)+Ps*ds+Pc*dc+Pt*dtaccording to AASHTO Appendix A6.1

(Note reinforcement forces are neglected according to AASHTO ch 6.10.5.1.3)

with

Pc=325*20*345=2.245E6Pt=400*35*345=4.83E6Pw=1345*15*345=6.96E6Ps=2000*230*0.85*20=7.82E6ds=230/2+25+20+Dcp=327dt=1400-20-Dcp-35/2=1195dc=Dcp+20/2=177

Moment capacity is:

Mr=Mn=Mp=3662+2557+397+5772=12389 kNm

The shear capacity can be calculated as: (according to AASHTO ch 6.10.7.2)



If D> tw*3.07*Sqr(E/Fyw)

Then

Vn=4.55*tw3*E/D

With

tw=15E=2E5Fyw=345D=1345

D>1108

Vr=Vn=4.55*153*2E5/1345 = 2283 kN

Actual moment and shearforces are calculated based on following factored loads:

Uniform load

Q= 1.25*38.8=49 kN/m (dead load)Q=1.75*12=21 kN/m (lane load)

Totally: Q = 70 kN/m

Point loads

P1 =1.75*1.33*188=438 kNP2 =1.75*1.33*45=105 kN

To get max moment and shear at support points, a shall be 4.3m, i.e. the pointloads shall beas close as possible.

In Section CB-9: Appendix B, the simple beam model has been run to calculate maxmoments and shear forces.

P1P2 P1a = 4300-90004300



Two controls are done, one at the support and one in the midspan.

Support

Max reaction force is:

V=1697 kN <Vrd = 2282 kN OK!

Midspan:

Max moment is:

M=9769 kN <Mr = 12389 kN OK!

SERVICE - I

Camber

The steel-beams shall be fabricated with a camber so the beams in principle not have anydeflection without traffic load. The camber is calculated based on that the steel sectioncarries the deadload before the concrete has hardened. This means that the moment of inertiafor this section can be calculated to:

Ix = 1.207E10 mm4 (ref section CB-8)

Total load on the beam is:

Q = 4.1 + 30.7 + 4 = 38.8 kN/m

The beam is a simply supported beam with a span of 24m. This gives a deflection of

D=5ql4/(384EI)= 5*38.8*240004/(384*2E5*1.207E10) = 69 mm

Choose an overheigth of the beam of 80 mm

Deflection by traffic

This loadcase is covered by the SERVICE I loadcombination according to Section 3.3. Thedeflection limit is l/500 (Section 2.5).



The member section in this case is a composite section according the figure below.

The concrete area can be transferred to an equivalent steel area by reducing the width with afactor of 10 accounting for a short term composite section. This means that the moment ofinertia and shear area i vertical direction for this section can be calculated to:

Ix = 3.572E10 mm4

Ref also section CB-8 Appendix A for cross section calculations with the PC-programSECTION.

Since STAAD takes into account shear deformations, also the shear area is required. This iscalculated only from the steel beam.

Ay = 1345*15= 20175 mm2 (ref CB-8: Appendix A)

Deflection of the composite section is based on following factored loads:

Uniform load

Q= 1.0 kN/m (wind load)Q=12 kN/m (lane load)

Totally: Q = 13 kN/m

Point loads

P1 =1.33*188 = 250 kNP2 =1.33*45 = 60 kN

25 theor. clearance

2910

230

P1P2 P1a = 4300-90004300



To get max deflection, a is chosen to 4.3m.

In Section CB-9: Appendix B, the simple beam model has been run to calculate maxdeflection.

Max deflection is calculated to 29.2 mm. This means a deflection ration of 24000/29.2l/822.

Max allowable is 1/500 according to Section 2.3.

OK

FATIGUE

Fatigue requirements for web

Flexure

Requirement to webs without longitudinal stiffeners shall satisfy according to AASHTO ch6.10.4.3

Dcp <= 15/2*5.76*Sqr(2E5/345) = 1040

Calculated Dcp from the construction stage (prior ro composite section) is Dcp= 923 mm.After the concrete has hardened the composite section results in a Dcp of much less than923mm. This menas that the allowable elastic flexural stress in the compression flange fcf is:

fcf = Rh*Fyk= 345 MPa

no reduction to capacity

DETAIL DESIGN

Shear connectors

The pitch of shear connectors is calculated based on:

• Pitch at fatigue loading• Pitch at fatigue loading• Minimum 6 times the stud diameter

Pitch at fatigue loading according to AASHTO ch 6.10.7.4.1.b

The pitch for the shear connectors can be calcualted as:

P = n*Zr*I/(Vsr*Q)



Where

P = pitch in longitudinal direction in mmn = number of shear connnectors transverseI = moment of inertia of short-term compositeQ = first moment of the transformed area about the neutral axis of the short-term compositeVsr = shear force range under LL+I determined for the fatigue limit stateZr = shear fatigue resistance of an individual shear connector

Zr can be calculated as .

Zr = α*d2>=38*d2

With

d = 20 (diameter of stud)

α = 238 – 29.5*logN = 238-29.5*log(2.8E6)=47.8

Zr = 47.8*202 = 19.12 kN

I= 3.572E10 mm4 (ref Section CB-8: Appendix A)

Q = 291*230*(1425+230/2-1176.8.)=24.308E6

In Section CB-9: Appendix B, the shear forces are calculated for the beam with followingtruckload:

P1 =142 kNP2 = 34 kN

Max shear at support is 245 kN

Vsr = 245 kN

P = 229 mm

Pitch at strength loading according to AASHTO ch 6.10.7.4.4.a

Qr = φsc*Qn

φsc = 0.85

P1P2 P1a = 90004300



Qn = 0.5*Asc*Sqr(fc’*Ec)<=Asc*Fu

fc’ = 20 MpaEc = 22600 MpaAsc = π*202/4=314 mm2Fu = 400 Mpa (minimum)

Qn = 0.5*314*Sqr(20*22600) = 105 kN <= 314*400 =125 kN

Qr = 0.85*105 = 89 kN

The nominal horizontal shear force Vh is then calculated as the minimum of:

Vhc = 0.85*fc’*b*tsOr

Vhs = Fyw*D*tw + Fyt*bt*tt + Fyc*bc*tc

fc’=20 Mpab = 2000 mmbc = 325 mmbt = 400 mmts =230 mmtt = 35 mmtc = 20 mmtw = 15 mmD = 1345 mmFyw = Fyc = Fyt = 345 Mpa

Vhc = 0.85*20*2000*230 = 7820 k N

Vhs = 345*(1345*15 +325*20 + 400*35) = 14032 kN

Vh = 7820 kN

Minimum number of shear connectors (n) between mid point of beam to endsupport is then

n = 7820 / 89 = 87

With two shear connnectors in transverse direction, this gives a pitch of

p = 12000/(87/2) = 275 mm



Minimum required pitch according to AASHTO ch 6.10.7.4.1.b

p >= 6*D= 6*20 =120 mm

The pitch distance is thus decided to be c/c 120 mm

Stud φ20 c/c 120mm

Bearing stiffeners

The bearing stiffeners are controlled for the strength load combination. This menas that themaximum reaction force is 1697 kN.

It’s assumed that the bearing stiffners are connected to the bottom flange with a full contact,thus all vertical force is tranferred by contact between the bottom flange and the bearingstiffener.

The following calculations follws in principle the requirements from AASHTO ch 6.10.8.2.

Projecting width according to AASHTO ch 6.10.8.2.2

Each stiffener shall have a width limited to:

bf <= 0.48*tp*Sqr(E/Fys)

E = 2E5 MpaFys = 345 Mpatp = 20 mm

bf <= 231 mm

Since the bottom flange is 400 mm, this requirement is fulfilled.

Bearing resistance according to AASHTO ch 6.10.8.2.3

Br = φb*Apn*Fys

With

φb = 1.0Apn = 20*(400-3*15-2*10) =6700 (compenstaed for web to flange weld)Fys = 345 MPa



Br = 1.0*6700*345=2311 kNBr > V = 1697 kN OK!

Axial resistance of bearing resistance

The cross section as shown in the figures below is checked for axial compression

d = 20+2*9*tw = 20+2*9*15 =290 mmh= 2*178 + 15 = 371 mm

400

d

Pl 20

178

130

h

II



As = 290*15+20*(371-15) =11470 mm2Is = 20*3713/12+(290-20)*153/12 = 85.18 E6 mm4

radius of gyration of the cross section is

rs = Sqr(Is/As)= 86 mm

buckling length is 0.75*D=0.75*1345=1009mm

λ = (1009/86/π)2*Fy/E = 0.023

Pn = 0.66λ*Fy*As= 3975 kN

Pr = 0.9*Pn = 3578 kN

Pr >> Vr =1697 kN OK

The stiffener and the web shall fit to the bottom flange so the vertical force can betransferred by direct contact.

End beam at support

A transverse endbeam is located at each support. This beams can be if the bearings need tobe changed. Lift points are located 500mm from each main girder, see figure below.

Figure. End beam at support for lifting the bridge

Reaction force for one beam is (ref Section 10.2) 582 kN including a loadfactor of 1.25.Moment and sherforce for the beam is thus

Ms = 582*0.5=291 kNm

500 P

HEB400

P

4500500



Vs = 582 kN

HEB 400 has following capacities:

Mrd = 250*2.884E6=721 kNm>Ms (elastic)

Since D < 2.46*tw*Sqr(E/Fyk), then

Vrd = 0.58*250*D*tw=0.58*250*(400-2*24)*13.5=689kN > Vs

The profile is thus OK!

Construction stage

During the construction stage, lateral torsional buckling is prevented by transverse beamsevery 6 m along the beams, as shown in the figure below.

Max flange force in the top flange is, (ref Section 10.1)

F =238*325*20=1547 kN

The horizontal force Pu is estimated to be 0.02*P, i.e.:

Pu = 0.02* 1547 = 31 kN

Additional moments from top flange to center of beam:

M = 31*0.6 = 18.6 kNm

The moment is transferred through the flange welds, see figure below.

Max600

+-Pu

HEA 300

+-Pu

4500



F = 18.6/0.3 = 62 kN

Tau = 62E3/(2*120*5)=55 Mpa < (Fyk/Sqr3) OK

The axial stress in the HEA 300 member can be calculated to

Sig = 31E3/11250 = 3 MPa

no buckling problem

If the beam is used as support for the formwork during casting of the slab, the beam can bechecked for following load case:

q = 0.3*24*6 + 6 (formwork)= 49.2 kN/m

M = q*4.52/8= 125 kNm

W(HEA300) =1.259E6 mm3

Siq = 125E6/1.259E6 = 99 Mpa > Fyk = 250 MPa

The beam can act as support for formwork during construction stage.

F

F

120300

q

4500



CB.7 CONCRETE

Overhang

Load and moments:

Dead load

Railing: The railing including posts is estimated to 2.75 kN/m.

Concrete: Edge beam including slab to c/l of girder has a cross section of:

A1= 1.81*0.258 = 0.467 m2 (slab)A2= 0.4*(0.4-0.24)= 0.064 m2 (edge beam)

DCc1 = 24*0.467 = 11.208 kN/mDCc2 = 24*0.064 = 1.536 kN/m

Wearing surface: The wearing surface is estimated to have a thickness of 50 mm. Witha density of 22.5 kN/m2, this gives a load of:

D = 0.05*22.5= 1.125 kN/m2

DW = 1.125*1.81 = 2.036 kN/m

Total load: DD = 2.75 + 11.208 + 1.536 + 2.036 = 17.5 kN/m

Moment: MDL = 2.75*1.61 + 11.208*1.81/2 + 1.536*1.61 + 2.036*1.81/2 =18.886 kNm

Rail load

P = 44.51 kN (Ref Art 2.7 AASHTO 1996)

400

cL girder

1810



Mi = 44.51*1.14=50.741 kNm

Effective length for moment:

E = 1140 + 0.833X according to AASHTO ch 4.6.2.1.3

X = 1610

E = 1140 + 0.833*1610= 2.481 m

MRL = 50.741/2.481=20.451 kNm/m

Truck load: (145kN axle)

P = 145/2 = 72.5 kN (one wheel)

M = 72.5*1.11=80.5 kNm


E = 1140 + 0.833X

X = 1.11

300

900+280/2=1140

P

I

1610

P I

1110



E = 1.14+0.833*1.11 = 2.065

MLT = 80.5/2.065 = 39 kNm/m

Lane load: (3.1 kN/m)

MLL = 3.1*1.412/2= 3.08 kNm/m

Total moment:

Loadcase a) – Deadload+railload:

M = 1.25*MDL + 1.75*MRL = 1.25*18.89 + 1.75*20.45 = 59.4 kNm/m

Loadcase b) – Deadload+truck + lane load:

M = 1.25*MDL + 1.75*1.33*MLT + 1.75*MLL = 1.25*18.89 + 1.75*1.33*39 + 1.75*3.08 =

= 119.8 kNm/m

Design for flexure:

Top layer reinforcement

Assume reinforcement bars: φ = 20 mmCover – top surface: 50 mmCover – bottom surface: 25 mmSlab gross thickness: D = 280 mm

d = 280 - φ/2 – top cover = 280 –10-50 = 220 mm

c = As*Fy/(0.85*fc’*b) according to AASHTO ch 5.7.3.1.1withfc’ = 20 Mpa

Q I

1410



b = 1000 mmfy = 350 MpaAs = 2000 mm2 (assumed)

c = 2000*350/(0.85*20*1000) = 41.17 mm

a = c*β1 = 41.17*0.85= 35mm

As = M /(φ*Fy*(d-a/2)=119.8E6/(0.9*350*(220-35/2))= 1878 mmaccording to AASHTO ch 5.7.3.2

φ 20 c/c 165 mm or alternative

φ 12 c/c 160 mm + φ 16 c/c 160 mm

Bottom layer reinforcement

Minimum reinforcement according to AASHTO ch 5.7.3.3.2

δmin > 0.03*fc’/fy = 0.03*20/350=0.002

As = 0.002*280*1000=560mm2

φ 12 c/c 200 mm (bottom minimum reinforcement)

Slab between girders - transverse

400

cL bridge

1810 2250



Max positive moment:

Max positive moment is by placing one lane in the mid of the bridge.

Dead load moment from overhang

Moment has been calculated for the overhang as: MDL = -18.9 kNm/m

Dead load moment from slab between girder

Concrete: DCc = 24*0.28 = 6.72 kN/m

Wearing surface: D = 0.05*22.5= 1.125 kN/m

Total dead load: D = 6.72+1.125 = 7.845 kN/m

Moment: M = 7.845*4.52/8 = +19.9 kNm/m


P = 145/2 = 72.5 kN (one wheel)

M = 72.5*1.35=98 kNm


E = 660 + 0.55S according to AASHTO ch 4.6.2.1.3

With S=4.5

E = 3.13

MLT = 98/3.13 = +31.3 kNm/m

P

1350

PCL girder

4500

1800



Lane load: (3.1 kN/m)

Q = 3.1 kN/m

MLL = 3.1*3/2*(0.75+3/4) = +7 kNm/m

Total moment:

Deadload+truck + lane load:

M = 1.25*MDL + 1.75*1.33*MLT + 1.75*MLL = 1.25*(19.9-18.9) + 1.75*1.33*31.2 + 1.75*7

= 86.1 kNm/mMax negative moment:

Max negative moment is by placing two lanes as far out as possible to the railings.

Dead load moment

From earlier calculations: MDL = 19.9-18.9 = +1.0 kNm/m


P = 145/2 = 72.5 kN (one wheel)

M = 72.5*0.81 = -59 kNm (exterior wheel)

M = 72.5*0.99 = +72 kNm (interior wheel)

MLT = 72-59 = 13 kNm/m


E = 1220 + 0.25S AASHTO ch 4.6.2.1.3

600 *)

P

810

P

CL girder4500

990



With S=4.5

E = 2345

MLT = 13/2.345 = +5.5 kNm/m

As can be seen from the dead load moment and the truck load moment, there will not be anynegative moment for this bridge.

Design for flexure – positive moment:

Assume reinforcement bars: φ = 16 mmCover – top surface: 50 mmCover – bottom surface: 25 mmSlab gross thickness: D = 280 mm

d = 280 - φ/2 – top cover = 280 –8-50 = 222 mm

c = As*Fy/(0.85*fc’*b) according to AASHTO ch 5.7.3.1.1with

fc’ = 20 Mpab = 1000 mmFy = 350 MpaAs = 1500 mm2 (assumed) according to AASHTO ch 5.7.3.2

c = 1500*350/(0.85*20*1000) = 30.82 mm

a = c*β1 = 30.82*0.85= 26.25mm

As = M /(φ*Fy*(d-a/2)=86.1E6/(0.9*350*(220-26/2))= 1321 mm

φ 16 c/c 150 mm (bottom reinforcement)


δmin > 0.03*fc’/fy = 0.03*20/350=0.002

As = 0.002*280*1000=560 mm2

φ 12 c/c 200 mm (top minimum reinforcement)



Distribution reinforcement – longitudinal direction

The amount of distribution reinforcement in the bottom of the slab shall be a percantage ofthe primary reinforcement in transverse direction for positive moment according toAASHTO ch 5.7.3.3.2:

As = 3840/Sqr(S) <= 67%

With S =4500As = 3840/Sqr(4500) = 57%

Asreq = 0.57*1321 = 752 mm2

φ 12 c/c 150 mm (bottom longitudinal reinforcement)


φ 12 c/c 200 mm (top longitudinal minimum reinforcement)



CB.8 APPENDIX A CROSS SECTION CALCULATIONS

CB.8.1 Calculations with SECTION 3.0





CB.8.2 Formulas for manual calculations

In the following tables, formulas in bold are the outputs given by SECTION 3.0

CB.8.2.1 I-shaped Steel section characteristics

Flange 1 Flange 2 Web Complete SectionThickness tf1 tf2 tw

Width b1 b2 hw = h-b1-b2

Area A1 = tf1 b1 A2 = tf2 b2 Aw = tw hw A=A1+A2+Aw

Ordinate ofcenter ofgravity

Zg1 = tf1/2 Zg2= h-tf2/2 Zgw=tf2 + hw/2 ezel=(Zg1A1+Zg2A2+ZgwAw)

A1+A2+Aw

Moment ofInertia / Gi / yaxis 1

Igy1 = b1 tf13/12 Igy2 = b2 tf2

3/12 Igyw = tw hw3/12

Moment of In./G/y axis

Iy1=Igy1 +A1 (Zg1-ezel)2

Iy2=Igy2 +A2 (Zg2-ezel)2

Iyw=Igyw +Aw (Zgw-ezel)2

Iy=Iy1+Iy2+Iyw

Moment ofInertia / z axis

Iz1 = tf1 b13/12 Iz2 = tf2 b2

3/12 Izw = hw tw3/12 Iz = Igz1 + Igz2 + Igzw

Sec. modulus /y axis

Wey1 = Iy _h-ezel

Wey2 = Iy _ezel

Sec. modulus /z axis

Wez1 = 2Iz /b1 Wez1 = 2Iz /b2

TorsionalConstant2

Ix1= b1 x ft13/3 Ix2= b2 x tf2

3/3 Ixw=hw tw3/3 Ix = Ix1 + Ix2 + Ixw

Ordinate of the neutral axis inthe plastic range.

ezpl =A1-A2+h-tf1+tf2

2tw 21 In this formulas, Gi is the Center of Gravity of the considered component ( web or Flanges )2 This formula is an approximation valid only for section made of thin plates ( like most of I shaped section). Thecondition is that ai/bi < 10 for each of the component of the section ( web and flanges) where ai is the thickness andbi the width of one component.

tf1

tf2

h

b1

b2

y

z

ezel

G

flange 1

flange 2

web

tw

Z



CB.8.2.2 Calculation of compostite sections characteristics

Characteristics(Steel

equivalent)

Concrete Steel Section( Calculated as per

previous table)

Composite Section

Thickness tc

Width bc /nArea Ac=tcbc /n As A=A1+A2+Aw

Ordinate ofcenter of gravity

Zgc = h+ tc/2 Zgs ezel=ZgcAc+ZgsAs

Ac+As

Moment ofInertia / Gi / yaxis 1

Igyc = bc tc3/12n Igys

Moment ofInertia / Centerof Gravity/yaxis

Iyc=Igyc +Ac (Zgc-ezel)2

Iys=Igys +As (Zgs-ezel)2

Iy=Iyc+Iys

Moment ofInertia / z axis

Izc = tfc bc3/12n Izs Iz =Igz1+Igz2 +Igzw

Section modulus/ y axis

Weyc =Iy /(h+tc-ezel) Wey1 = Iy/ (h-ezel)Wey2 = Iy/ ezel

1 In this formulas, Gi is the Center of Gravity of the considered component ( Concrete stab or steelbeam )

tc

tf2

h

bc (Effective width, see paragraph CB3)

b2

y

z

ezel

G

flange 1

flange 2

web

tw

concrete

Z



CB.9 APPENDIX B - Calculations by STAAD

STRENGTH

On the following page, moment and sheardiagram are shown. Therafter, the computer run isattached.



PAGE NO. 1



�*************************************************** ** S T A A D - III ** Revision 22.3 ** Proprietary Program of ** Research Engineers, Inc. ** Date= DEC 14, 1999 ** Time= 16:15:57 ** ** USER ID: Research Engineers ***************************************************

�

1. STAAD SPACE STRENGTH2. INPUT WIDTH 723. UNIT MMS NEWTON4. JOINT COORDINATES5. 1 .000 .000 .0006. 2 500.000 .000 .0007. 3 1000.000 .000 .0008. 4 1500.000 .000 .0009. 5 2000.000 .000 .00010. 6 2500.000 .000 .00011. 7 3000.000 .000 .00012. 8 3500.000 .000 .00013. 9 4000.000 .000 .00014. 10 4500.000 .000 .00015. 11 5000.000 .000 .00016. 12 5500.000 .000 .00017. 13 6000.000 .000 .00018. 14 6500.000 .000 .00019. 15 7000.000 .000 .00020. 16 7500.000 .000 .00021. 17 8000.000 .000 .00022. 18 8500.000 .000 .00023. 19 9000.001 .000 .00024. 20 9500.001 .000 .00025. 21 10000.000 .000 .00026. 22 10500.000 .000 .00027. 23 11000.000 .000 .00028. 24 11500.000 .000 .00029. 25 12000.000 .000 .00030. 26 12500.000 .000 .00031. 27 13000.000 .000 .00032. 28 13500.000 .000 .00033. 29 14000.000 .000 .00034. 30 14500.000 .000 .00035. 31 15000.000 .000 .00036. 32 15500.000 .000 .00037. 33 16000.000 .000 .00038. 34 16500.000 .000 .00039. 35 17000.000 .000 .00040. 36 17500.000 .000 .00041. 37 18000.000 .000 .000STRENGTH -- PAGE NO. 2

42. 38 18500.000 .000 .00043. 39 19000.000 .000 .00044. 40 19500.000 .000 .00045. 41 20000.000 .000 .00046. 42 20500.000 .000 .00047. 43 21000.000 .000 .00048. 44 21500.000 .000 .00049. 45 22000.000 .000 .00050. 46 22500.000 .000 .00051. 47 23000.000 .000 .00052. 48 23500.000 .000 .000



53. 49 24000.000 .000 .00054. MEMBER INCIDENCES55. 1 1 256. 2 2 357. 3 3 458. 4 4 559. 5 5 660. 6 6 761. 7 7 862. 8 8 963. 9 9 1064. 10 10 1165. 11 11 1266. 12 12 1367. 13 13 1468. 14 14 1569. 15 15 1670. 16 16 1771. 17 17 1872. 18 18 1973. 19 19 2074. 20 20 2175. 21 21 2276. 22 22 2377. 23 23 2478. 24 24 2579. 25 25 2680. 26 26 2781. 27 27 2882. 28 28 2983. 29 29 3084. 30 30 3185. 31 31 3286. 32 32 3387. 33 33 3488. 34 34 3589. 35 35 3690. 36 36 3791. 37 37 3892. 38 38 3993. 39 39 4094. 40 40 4195. 41 41 4296. 42 42 4397. 43 43 44STRENGTH -- PAGE NO. 3

98. 44 44 4599. 45 45 46100. 46 46 47101. 47 47 48102. 48 48 49103. MEMBER PROPERTY AMERICAN104. 1 TO 48 PRI YD 500. ZD 100.105. CONSTANT106. E STEEL ALL107. DENSITY STEEL ALL108. POISSON STEEL ALL109. SUPPORT110. 1 PINNED111. 49 FIXED BUT FX MX MY MZ112. UNITS KNS MET113. DEF MOV LOAD114. * TRUCK LOAD115. TYPE 1 LOAD 105. 438. 438. DIS 4.3 4.3116. *117. LOAD 1 DEADLOAD118. MEMBER LOAD119. 1 TO 48 UNI GY -70.120. *121. LOAD GENERATION 100 ADD LOAD 1



122. TYPE 1 0.0 0.0 0.0 XINC 0.2123. PERFORM ANALYSIS

�

P R O B L E M S T A T I S T I C S-----------------------------------

NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 49/ 48/ 2ORIGINAL/FINAL BAND-WIDTH = 1/ 1TOTAL PRIMARY LOAD CASES = 101, TOTAL DEGREES OF FREEDOM = 289SIZE OF STIFFNESS MATRIX = 3468 DOUBLE PREC. WORDSREQRD/AVAIL. DISK SPACE = 12.61/ 989.6 MB, EXMEM = 1967.5 MB

�++ Processing Element Stiffness Matrix. 16:16: 0++ Processing Global Stiffness Matrix. 16:16: 0++ Processing Triangular Factorization. 16:16: 0

***WARNING - IMPROPER LOAD WILL CAUSE INSTABILITY AT JOINT 49DIRECTION = MX PROBABLE CAUSE MODELING PROBLEM -.320E-09

++ Calculating Joint Displacements. 16:16: 0++ Calculating Member Forces. 16:16: 1

124. PLOT BEND FILE125. PRINT MAX FORCE ENVSTRENGTH -- PAGE NO. 4

MEMBER FORCE ENVELOPE---------------------

ALL UNITS ARE KNS MET

MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS

MEMB FY/ DIST LD MZ/ DIST LDFZ DIST LD MY DIST LD FX DIST LD

1 MAX 1585.62 .00 2 .02 .00 57.00 .00 1 .00 .00 1 .00 .00 1

MIN 805.01 .50 1 -771.76 .50 5.00 .50 101 .00 .50 101 .00 .50 101

2 MAX 1526.01 .00 5 -411.24 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 770.02 .50 1 -1509.69 .50 7.00 .50 101 .00 .50 101 .00 .50 101

3 MAX 1466.56 .00 8 -804.98 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 735.03 .50 1 -2203.33 .50 9.00 .50 101 .00 .50 101 .00 .50 101

4 MAX 1415.25 .00 10 -1181.26 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 700.00 .50 1 -2867.68 .50 12.00 .50 101 .00 .50 101 .00 .50 101

5 MAX 1355.40 .00 13 -1540.00 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 664.96 .50 1 -3489.43 .50 14.00 .50 101 .00 .50 101 .00 .50 101

6 MAX 1305.75 .00 2 -1881.19 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 630.13 .50 1 -4126.71 .50 2.00 .50 101 .00 .50 101 .00 .50 101



7 MAX 1270.37 .00 2 -2204.99 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 595.07 .50 1 -4753.20 .50 2.00 .50 101 .00 .50 101 .00 .50 101

8 MAX 1235.59 .00 2 -2511.22 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 559.96 .50 1 -5362.27 .50 2.00 .50 101 .00 .50 101 .00 .50 101

9 MAX 1200.15 .00 2 -2799.98 .00 1.00 .00 1 .00 .00 1 .00 .00 1

STRENGTH -- PAGE NO. 5

MIN 524.99 .50 1 -5938.06 .50 3.00 .50 101 .00 .50 101 .00 .50 101

10 MAX 1148.73 .00 4 -3071.35 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 489.39 .50 1 -6448.33 .50 6.00 .50 101 .00 .50 101 .00 .50 101

11 MAX 1098.41 .00 6 -3325.03 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 455.47 .50 1 -6940.66 .50 8.00 .50 101 .00 .50 101 .00 .50 101

12 MAX 1037.72 .00 9 -3561.32 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 420.33 .50 1 -7370.90 .50 11.00 .50 101 .00 .50 101 .00 .50 101

13 MAX 986.68 .00 11 -3779.88 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 385.19 .50 1 -7791.46 .50 13.00 .50 101 .00 .50 101 .00 .50 101

14 MAX 927.23 .00 14 -3981.17 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 350.19 .50 1 -8141.66 .50 16.00 .50 101 .00 .50 101 .00 .50 101

15 MAX 876.16 .00 16 -4164.99 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 314.94 .50 1 -8490.63 .50 18.00 .50 101 .00 .50 101 .00 .50 101

16 MAX 816.90 .00 19 -4331.37 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 280.13 .50 1 -8761.79 .50 20.00 .50 101 .00 .50 101 .00 .50 101

17 MAX 765.05 .00 21 -4479.89 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN 245.36 .50 1 -9037.92 .50 23.00 .50 101 .00 .50 101 .00 .50 101

18 MAX 704.42 .00 24 -4611.38 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -42.34 .50 4 -9236.94 .50 25.00 .50 101 .00 .50 101 .00 .50 101

19 MAX 653.75 .00 26 -4725.09 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -92.57 .50 6 -9433.43 .50 28.00 .50 101 .00 .50 101 .00 .50 101

20 MAX 594.94 .00 29 -4821.22 .00 1.00 .00 1 .00 .00 1 .00 .00 1




MIN -152.53 .50 9 -9561.12 .50 30.00 .50 101 .00 .50 101 .00 .50 101

21 MAX 543.45 .00 31 -4900.07 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -203.36 .50 11 -9677.43 .50 33.00 .50 101 .00 .50 101 .00 .50 101

22 MAX 484.28 .00 34 -4961.20 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -263.73 .50 14 -9733.13 .50 35.00 .50 101 .00 .50 101 .00 .50 101

23 MAX 432.33 .00 36 -5004.94 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -315.77 .50 16 -9769.53 .50 38.00 .50 101 .00 .50 101 .00 .50 101

24 MAX 372.71 .00 39 -5031.41 .00 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -375.64 .50 19 -9769.45 .00 38.00 .50 101 .00 .50 101 .00 .50 101

25 MAX 322.07 .00 41 -5031.22 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -426.13 .50 21 -9753.16 .00 40.00 .50 101 .00 .50 101 .00 .50 101

26 MAX 262.12 .00 44 -5005.02 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -486.01 .50 24 -9709.81 .00 43.00 .50 101 .00 .50 101 .00 .50 101

27 MAX 209.18 .00 46 -4961.37 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -536.89 .50 26 -9621.68 .00 45.00 .50 101 .00 .50 101 .00 .50 101

28 MAX 150.90 .00 49 -4900.00 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -595.62 .50 29 -9535.26 .00 27.00 .50 101 .00 .50 101 .00 .50 101

29 MAX 98.89 .00 51 -4821.12 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -646.79 .50 31 -9461.49 .00 29.00 .50 101 .00 .50 101 .00 .50 101

30 MAX 40.98 .00 54 -4724.82 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -707.08 .50 34 -9343.67 .00 32.00 .50 101 .00 .50 101 .00 .50 101

31 MAX -10.59 .00 56 -4611.31 .50 1.00 .00 1 .00 .00 1 .00 .00 1


MIN -758.55 .50 36 -9198.19 .00 34.00 .50 101 .00 .50 101 .00 .50 101

32 MAX -70.23 .00 59 -4479.99 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -818.59 .50 39 -9000.54 .00 37.00 .50 101 .00 .50 101 .00 .50 101

33 MAX -121.71 .00 61 -4331.35 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -868.15 .50 41 -8783.27 .00 39.00 .50 101 .00 .50 101 .00 .50 101



34 MAX -181.86 .00 64 -4164.98 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -928.77 .50 44 -8505.69 .00 42.00 .50 101 .00 .50 101 .00 .50 101

35 MAX -232.68 .00 66 -3981.32 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -980.85 .50 46 -8216.54 .00 44.00 .50 101 .00 .50 101 .00 .50 101

36 MAX -292.83 .00 69 -3780.12 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1040.12 .50 49 -7858.90 .00 47.00 .50 101 .00 .50 101 .00 .50 101

37 MAX -343.37 .00 71 -3561.27 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1091.31 .50 51 -7498.15 .00 49.00 .50 101 .00 .50 101 .00 .50 101

38 MAX -402.99 .00 74 -3324.91 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1150.63 .50 54 -7060.38 .00 52.00 .50 101 .00 .50 101 .00 .50 101

39 MAX -454.51 .00 76 -3071.18 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1202.00 .50 56 -6627.85 .00 54.00 .50 101 .00 .50 101 .00 .50 101

40 MAX -504.18 .00 100 -2799.82 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1261.57 .50 59 -6117.08 .00 56.00 .50 101 .00 .50 101 .00 .50 101

41 MAX -558.00 .00 81 -2511.20 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1312.53 .50 61 -5605.56 .00 59.00 .50 101 .00 .50 101 .00 .50 101

42 MAX -595.19 .00 1 -2205.02 .50 1.00 .00 1 .00 .00 1 .00 .00 1


MIN -1372.31 .50 64 -5023.52 .00 61.00 .50 101 .00 .50 101 .00 .50 101

43 MAX -630.19 .00 1 -1881.19 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1423.17 .50 66 -4431.72 .00 64.00 .50 101 .00 .50 101 .00 .50 101

44 MAX -664.91 .00 1 -1540.06 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1483.17 .50 69 -3777.78 .00 66.00 .50 101 .00 .50 101 .00 .50 101

45 MAX -700.11 .00 1 -1181.22 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1534.73 .50 71 -3106.28 .00 69.00 .50 101 .00 .50 101 .00 .50 101

46 MAX -735.11 .00 1 -804.99 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1593.90 .50 74 -2380.46 .00 71.00 .50 101 .00 .50 101 .00 .50 101

47 MAX -769.94 .00 1 -411.27 .50 1.00 .00 1 .00 .00 1 .00 .00 1

MIN -1645.34 .50 76 -1628.99 .00 74.00 .50 101 .00 .50 101 .00 .50 101



48 MAX -804.97 .00 1 .03 .50 28.00 .00 1 .00 .00 1 .00 .00 1

MIN -1696.69 .50 78 -831.43 .00 76.00 .50 101 .00 .50 101 .00 .50 101

********** END OF FORCE ENVELOPE FROM INTERNAL STORAGE **********

126. FINISH

*************** END OF STAAD-III ***************

**** DATE= DEC 14,1999 TIME= 16:16:19 ****

********************************************************** For questions on STAAD-III, contact: ** Research Engineers, Inc at ** West Coast: Ph- (714) 974-2500 Fax- (714) 921-2543 ** East Coast: Ph- (508) 688-3626 Fax- (508) 685-7230 **********************************************************

SERVICE - Deflection

On the next page, the max deflection is plotted. Therafter, the computer run is attached.





PAGE NO. 1


�

1. STAAD SPACE SERVICE2. INPUT WIDTH 723. UNIT MMS NEWTON4. JOINT COORDINATES5. 1 .000 .000 .0006. 2 500.000 .000 .0007. 3 1000.000 .000 .0008. 4 1500.000 .000 .0009. 5 2000.000 .000 .00010. 6 2500.000 .000 .00011. 7 3000.000 .000 .00012. 8 3500.000 .000 .00013. 9 4000.000 .000 .00014. 10 4500.000 .000 .00015. 11 5000.000 .000 .00016. 12 5500.000 .000 .00017. 13 6000.000 .000 .00018. 14 6500.000 .000 .00019. 15 7000.000 .000 .00020. 16 7500.000 .000 .00021. 17 8000.000 .000 .00022. 18 8500.000 .000 .00023. 19 9000.001 .000 .00024. 20 9500.001 .000 .00025. 21 10000.000 .000 .00026. 22 10500.000 .000 .00027. 23 11000.000 .000 .00028. 24 11500.000 .000 .00029. 25 12000.000 .000 .00030. 26 12500.000 .000 .00031. 27 13000.000 .000 .00032. 28 13500.000 .000 .00033. 29 14000.000 .000 .00034. 30 14500.000 .000 .00035. 31 15000.000 .000 .00036. 32 15500.000 .000 .00037. 33 16000.000 .000 .00038. 34 16500.000 .000 .00039. 35 17000.000 .000 .00040. 36 17500.000 .000 .00041. 37 18000.000 .000 .000SERVICE -- PAGE NO. 2

42. 38 18500.000 .000 .00043. 39 19000.000 .000 .00044. 40 19500.000 .000 .00045. 41 20000.000 .000 .00046. 42 20500.000 .000 .00047. 43 21000.000 .000 .00048. 44 21500.000 .000 .00049. 45 22000.000 .000 .00050. 46 22500.000 .000 .000



51. 47 23000.000 .000 .00052. 48 23500.000 .000 .00053. 49 24000.000 .000 .00054. MEMBER INCIDENCES55. 1 1 256. 2 2 357. 3 3 458. 4 4 559. 5 5 660. 6 6 761. 7 7 862. 8 8 963. 9 9 1064. 10 10 1165. 11 11 1266. 12 12 1367. 13 13 1468. 14 14 1569. 15 15 1670. 16 16 1771. 17 17 1872. 18 18 1973. 19 19 2074. 20 20 2175. 21 21 2276. 22 22 2377. 23 23 2478. 24 24 2579. 25 25 2680. 26 26 2781. 27 27 2882. 28 28 2983. 29 29 3084. 30 30 3185. 31 31 3286. 32 32 3387. 33 33 3488. 34 34 3589. 35 35 3690. 36 36 3791. 37 37 3892. 38 38 3993. 39 39 4094. 40 40 4195. 41 41 4296. 42 42 4397. 43 43 44SERVICE -- PAGE NO. 3

98. 44 44 4599. 45 45 46100. 46 46 47101. 47 47 48102. 48 48 49103. MEMBER PROPERTY104. 1 TO 48 PRI AX 1E5 IX 1E8 IY 1E8 IZ 3.572E10 AY 1E5 AZ 20175105. CONSTANT106. E STEEL ALL107. DENSITY STEEL ALL108. POISSON STEEL ALL109. SUPPORT110. 1 PINNED111. 49 FIXED BUT FX MX MY MZ112. UNITS KNS MET113. DEF MOV LOAD114. * TRUCK LOAD - SERVICE115. TYP 1 LOA 60 250 250 DIS 4.3 4.3116. *117. LOAD 1 DEADLOAD118. MEMBER LOAD119. 1 TO 48 UNI GY -13.



120. *121. LOAD GENERATION 20 ADD LOAD 1122. TYPE 1 5.0 0.0 0.0 XINC 0.2123. PERFORM ANALYSIS

�



�++ Processing Element Stiffness Matrix. 9:29:42++ Processing Global Stiffness Matrix. 9:29:42++ Processing Triangular Factorization. 9:29:42

***WARNING - IMPROPER LOAD WILL CAUSE INSTABILITY AT JOINT 49DIRECTION = MX PROBABLE CAUSE MODELING PROBLEM .000E+00

++ Calculating Joint Displacements. 9:29:42++ Calculating Member Forces. 9:29:42

124. UNITS MMS NEWS125. PLOT DISP FILE126. PRINT JOINT DISPL LIST 20 TO 30SERVICE -- PAGE NO. 4

�

JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN

�20 1 .0000 -.7573 .0000 .0000 .0000 -.0003

2 .0000 -2.7578 .0000 .0000 .0000 -.00123 .0000 -2.7621 .0000 .0000 .0000 -.00124 .0000 -2.7645 .0000 .0000 .0000 -.00125 .0000 -2.7653 .0000 .0000 .0000 -.00126 .0000 -2.7648 .0000 .0000 .0000 -.00127 .0000 -2.7628 .0000 .0000 .0000 -.00128 .0000 -2.7594 .0000 .0000 .0000 -.00139 .0000 -2.7547 .0000 .0000 .0000 -.001310 .0000 -2.7485 .0000 .0000 .0000 -.001311 .0000 -2.7411 .0000 .0000 .0000 -.001312 .0000 -2.7323 .0000 .0000 .0000 -.001313 .0000 -2.7221 .0000 .0000 .0000 -.001314 .0000 -2.7108 .0000 .0000 .0000 -.001315 .0000 -2.6980 .0000 .0000 .0000 -.001316 .0000 -2.6841 .0000 .0000 .0000 -.001317 .0000 -2.6690 .0000 .0000 .0000 -.001318 .0000 -2.6525 .0000 .0000 .0000 -.001319 .0000 -2.6350 .0000 .0000 .0000 -.001320 .0000 -2.6161 .0000 .0000 .0000 -.001321 .0000 -2.5962 .0000 .0000 .0000 -.0013

21 1 .0000 -.7721 .0000 .0000 .0000 -.00032 .0000 -2.8100 .0000 .0000 .0000 -.00093 .0000 -2.8151 .0000 .0000 .0000 -.00094 .0000 -2.8190 .0000 .0000 .0000 -.00105 .0000 -2.8214 .0000 .0000 .0000 -.00106 .0000 -2.8218 .0000 .0000 .0000 -.00107 .0000 -2.8206 .0000 .0000 .0000 -.00108 .0000 -2.8177 .0000 .0000 .0000 -.00109 .0000 -2.8136 .0000 .0000 .0000 -.0010



10 .0000 -2.8079 .0000 .0000 .0000 -.001011 .0000 -2.8009 .0000 .0000 .0000 -.001012 .0000 -2.7925 .0000 .0000 .0000 -.001113 .0000 -2.7826 .0000 .0000 .0000 -.001114 .0000 -2.7716 .0000 .0000 .0000 -.001115 .0000 -2.7590 .0000 .0000 .0000 -.001116 .0000 -2.7453 .0000 .0000 .0000 -.001117 .0000 -2.7303 .0000 .0000 .0000 -.001118 .0000 -2.7138 .0000 .0000 .0000 -.001119 .0000 -2.6963 .0000 .0000 .0000 -.001120 .0000 -2.6774 .0000 .0000 .0000 -.001121 .0000 -2.6574 .0000 .0000 .0000 -.0011

22 1 .0000 -.7836 .0000 .0000 .0000 -.00022 .0000 -2.8498 .0000 .0000 .0000 -.00073 .0000 -2.8557 .0000 .0000 .0000 -.00074 .0000 -2.8603 .0000 .0000 .0000 -.00075 .0000 -2.8636 .0000 .0000 .0000 -.00076 .0000 -2.8649 .0000 .0000 .0000 -.0007

SERVICE -- PAGE NO. 5

�



�7 .0000 -2.8653 .0000 .0000 .0000 -.00078 .0000 -2.8638 .0000 .0000 .0000 -.00089 .0000 -2.8604 .0000 .0000 .0000 -.000810 .0000 -2.8553 .0000 .0000 .0000 -.000811 .0000 -2.8489 .0000 .0000 .0000 -.000812 .0000 -2.8410 .0000 .0000 .0000 -.000813 .0000 -2.8315 .0000 .0000 .0000 -.000814 .0000 -2.8209 .0000 .0000 .0000 -.000815 .0000 -2.8086 .0000 .0000 .0000 -.000816 .0000 -2.7952 .0000 .0000 .0000 -.000917 .0000 -2.7804 .0000 .0000 .0000 -.000918 .0000 -2.7641 .0000 .0000 .0000 -.000919 .0000 -2.7468 .0000 .0000 .0000 -.000920 .0000 -2.7279 .0000 .0000 .0000 -.000921 .0000 -2.7080 .0000 .0000 .0000 -.0009

23 1 .0000 -.7919 .0000 .0000 .0000 -.00012 .0000 -2.8773 .0000 .0000 .0000 -.00043 .0000 -2.8839 .0000 .0000 .0000 -.00044 .0000 -2.8892 .0000 .0000 .0000 -.00055 .0000 -2.8932 .0000 .0000 .0000 -.00056 .0000 -2.8953 .0000 .0000 .0000 -.00057 .0000 -2.8964 .0000 .0000 .0000 -.00058 .0000 -2.8956 .0000 .0000 .0000 -.00059 .0000 -2.8935 .0000 .0000 .0000 -.000510 .0000 -2.8900 .0000 .0000 .0000 -.000511 .0000 -2.8845 .0000 .0000 .0000 -.000612 .0000 -2.8772 .0000 .0000 .0000 -.000613 .0000 -2.8684 .0000 .0000 .0000 -.000614 .0000 -2.8582 .0000 .0000 .0000 -.000615 .0000 -2.8465 .0000 .0000 .0000 -.000616 .0000 -2.8334 .0000 .0000 .0000 -.000617 .0000 -2.8190 .0000 .0000 .0000 -.000618 .0000 -2.8030 .0000 .0000 .0000 -.000619 .0000 -2.7860 .0000 .0000 .0000 -.000620 .0000 -2.7673 .0000 .0000 .0000 -.000721 .0000 -2.7475 .0000 .0000 .0000 -.0007

24 1 .0000 -.7968 .0000 .0000 .0000 -.00012 .0000 -2.8922 .0000 .0000 .0000 -.00023 .0000 -2.8995 .0000 .0000 .0000 -.00024 .0000 -2.9056 .0000 .0000 .0000 -.00025 .0000 -2.9102 .0000 .0000 .0000 -.00026 .0000 -2.9130 .0000 .0000 .0000 -.0002



7 .0000 -2.9149 .0000 .0000 .0000 -.00028 .0000 -2.9148 .0000 .0000 .0000 -.00039 .0000 -2.9134 .0000 .0000 .0000 -.000310 .0000 -2.9107 .0000 .0000 .0000 -.000311 .0000 -2.9060 .0000 .0000 .0000 -.000312 .0000 -2.9004 .0000 .0000 .0000 -.0003


�



�13 .0000 -2.8928 .0000 .0000 .0000 -.000314 .0000 -2.8833 .0000 .0000 .0000 -.000415 .0000 -2.8721 .0000 .0000 .0000 -.000416 .0000 -2.8597 .0000 .0000 .0000 -.000417 .0000 -2.8457 .0000 .0000 .0000 -.000418 .0000 -2.8302 .0000 .0000 .0000 -.000419 .0000 -2.8135 .0000 .0000 .0000 -.000420 .0000 -2.7952 .0000 .0000 .0000 -.000421 .0000 -2.7758 .0000 .0000 .0000 -.0004

25 1 .0000 -.7985 .0000 .0000 .0000 .00002 .0000 -2.8948 .0000 .0000 .0000 .00013 .0000 -2.9027 .0000 .0000 .0000 .00014 .0000 -2.9094 .0000 .0000 .0000 .00005 .0000 -2.9147 .0000 .0000 .0000 .00006 .0000 -2.9182 .0000 .0000 .0000 .00007 .0000 -2.9207 .0000 .0000 .0000 .00008 .0000 -2.9213 .0000 .0000 .0000 .00009 .0000 -2.9207 .0000 .0000 .0000 .000010 .0000 -2.9186 .0000 .0000 .0000 .000011 .0000 -2.9146 .0000 .0000 .0000 -.000112 .0000 -2.9097 .0000 .0000 .0000 -.000113 .0000 -2.9029 .0000 .0000 .0000 -.000114 .0000 -2.8947 .0000 .0000 .0000 -.000115 .0000 -2.8852 .0000 .0000 .0000 -.000116 .0000 -2.8736 .0000 .0000 .0000 -.000117 .0000 -2.8603 .0000 .0000 .0000 -.000118 .0000 -2.8454 .0000 .0000 .0000 -.000219 .0000 -2.8292 .0000 .0000 .0000 -.000220 .0000 -2.8114 .0000 .0000 .0000 -.000221 .0000 -2.7924 .0000 .0000 .0000 -.0002

26 1 .0000 -.7968 .0000 .0000 .0000 .00012 .0000 -2.8848 .0000 .0000 .0000 .00033 .0000 -2.8934 .0000 .0000 .0000 .00034 .0000 -2.9008 .0000 .0000 .0000 .00035 .0000 -2.9067 .0000 .0000 .0000 .00036 .0000 -2.9109 .0000 .0000 .0000 .00037 .0000 -2.9140 .0000 .0000 .0000 .00038 .0000 -2.9153 .0000 .0000 .0000 .00029 .0000 -2.9153 .0000 .0000 .0000 .000210 .0000 -2.9139 .0000 .0000 .0000 .000211 .0000 -2.9106 .0000 .0000 .0000 .000212 .0000 -2.9064 .0000 .0000 .0000 .000213 .0000 -2.9003 .0000 .0000 .0000 .000214 .0000 -2.8929 .0000 .0000 .0000 .000215 .0000 -2.8840 .0000 .0000 .0000 .000116 .0000 -2.8734 .0000 .0000 .0000 .000117 .0000 -2.8617 .0000 .0000 .0000 .000118 .0000 -2.8481 .0000 .0000 .0000 .0001


�

JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE



------------------


�19 .0000 -2.8327 .0000 .0000 .0000 .000120 .0000 -2.8156 .0000 .0000 .0000 .000121 .0000 -2.7971 .0000 .0000 .0000 .0000

27 1 .0000 -.7919 .0000 .0000 .0000 .00012 .0000 -2.8624 .0000 .0000 .0000 .00063 .0000 -2.8716 .0000 .0000 .0000 .00064 .0000 -2.8796 .0000 .0000 .0000 .00055 .0000 -2.8862 .0000 .0000 .0000 .00056 .0000 -2.8910 .0000 .0000 .0000 .00057 .0000 -2.8948 .0000 .0000 .0000 .00058 .0000 -2.8967 .0000 .0000 .0000 .00059 .0000 -2.8973 .0000 .0000 .0000 .000510 .0000 -2.8966 .0000 .0000 .0000 .000511 .0000 -2.8940 .0000 .0000 .0000 .000412 .0000 -2.8905 .0000 .0000 .0000 .000413 .0000 -2.8851 .0000 .0000 .0000 .000414 .0000 -2.8784 .0000 .0000 .0000 .000415 .0000 -2.8703 .0000 .0000 .0000 .000416 .0000 -2.8604 .0000 .0000 .0000 .000417 .0000 -2.8495 .0000 .0000 .0000 .000418 .0000 -2.8367 .0000 .0000 .0000 .000319 .0000 -2.8226 .0000 .0000 .0000 .000320 .0000 -2.8072 .0000 .0000 .0000 .000321 .0000 -2.7897 .0000 .0000 .0000 .0003

28 1 .0000 -.7836 .0000 .0000 .0000 .00022 .0000 -2.8276 .0000 .0000 .0000 .00083 .0000 -2.8374 .0000 .0000 .0000 .00084 .0000 -2.8460 .0000 .0000 .0000 .00085 .0000 -2.8533 .0000 .0000 .0000 .00086 .0000 -2.8587 .0000 .0000 .0000 .00087 .0000 -2.8631 .0000 .0000 .0000 .00088 .0000 -2.8657 .0000 .0000 .0000 .00079 .0000 -2.8670 .0000 .0000 .0000 .000710 .0000 -2.8669 .0000 .0000 .0000 .000711 .0000 -2.8650 .0000 .0000 .0000 .000712 .0000 -2.8621 .0000 .0000 .0000 .000713 .0000 -2.8574 .0000 .0000 .0000 .000714 .0000 -2.8514 .0000 .0000 .0000 .000715 .0000 -2.8440 .0000 .0000 .0000 .000616 .0000 -2.8349 .0000 .0000 .0000 .000617 .0000 -2.8248 .0000 .0000 .0000 .000618 .0000 -2.8127 .0000 .0000 .0000 .000619 .0000 -2.7995 .0000 .0000 .0000 .000620 .0000 -2.7849 .0000 .0000 .0000 .000621 .0000 -2.7684 .0000 .0000 .0000 .0005

29 1 .0000 -.7721 .0000 .0000 .0000 .00032 .0000 -2.7789 .0000 .0000 .0000 .00113 .0000 -2.7903 .0000 .0000 .0000 .0011


�



�4 .0000 -2.8000 .0000 .0000 .0000 .00105 .0000 -2.8079 .0000 .0000 .0000 .00106 .0000 -2.8139 .0000 .0000 .0000 .00107 .0000 -2.8190 .0000 .0000 .0000 .00108 .0000 -2.8222 .0000 .0000 .0000 .00109 .0000 -2.8242 .0000 .0000 .0000 .001010 .0000 -2.8248 .0000 .0000 .0000 .0010



11 .0000 -2.8235 .0000 .0000 .0000 .000912 .0000 -2.8214 .0000 .0000 .0000 .000913 .0000 -2.8173 .0000 .0000 .0000 .000914 .0000 -2.8121 .0000 .0000 .0000 .000915 .0000 -2.8054 .0000 .0000 .0000 .000916 .0000 -2.7970 .0000 .0000 .0000 .000917 .0000 -2.7877 .0000 .0000 .0000 .000918 .0000 -2.7764 .0000 .0000 .0000 .000819 .0000 -2.7640 .0000 .0000 .0000 .000820 .0000 -2.7502 .0000 .0000 .0000 .000821 .0000 -2.7346 .0000 .0000 .0000 .0008

30 1 .0000 -.7573 .0000 .0000 .0000 .00032 .0000 -2.7181 .0000 .0000 .0000 .00133 .0000 -2.7299 .0000 .0000 .0000 .00134 .0000 -2.7402 .0000 .0000 .0000 .00135 .0000 -2.7492 .0000 .0000 .0000 .00136 .0000 -2.7567 .0000 .0000 .0000 .00137 .0000 -2.7626 .0000 .0000 .0000 .00128 .0000 -2.7665 .0000 .0000 .0000 .00129 .0000 -2.7691 .0000 .0000 .0000 .001210 .0000 -2.7704 .0000 .0000 .0000 .001211 .0000 -2.7698 .0000 .0000 .0000 .001212 .0000 -2.7684 .0000 .0000 .0000 .001213 .0000 -2.7651 .0000 .0000 .0000 .001214 .0000 -2.7605 .0000 .0000 .0000 .001115 .0000 -2.7546 .0000 .0000 .0000 .001116 .0000 -2.7470 .0000 .0000 .0000 .001117 .0000 -2.7384 .0000 .0000 .0000 .001118 .0000 -2.7280 .0000 .0000 .0000 .001119 .0000 -2.7163 .0000 .0000 .0000 .001120 .0000 -2.7034 .0000 .0000 .0000 .001021 .0000 -2.6887 .0000 .0000 .0000 .0010

************** END OF LATEST ANALYSIS RESULT **************

127. FINISH

*************** END OF STAAD-III ***************

**** DATE= DEC 13,1999 TIME= 9:29:43 ****




FATIGUE

On the following page, sheardiagram is shown. Therafter, the computer run is attached.





PAGE NO. 1


�

1. STAAD SPACE FATIGUE2. INPUT WIDTH 723. UNIT MMS NEWTON4. JOINT COORDINATES5. 1 .000 .000 .0006. 2 500.000 .000 .0007. 3 1000.000 .000 .0008. 4 1500.000 .000 .0009. 5 2000.000 .000 .00010. 6 2500.000 .000 .00011. 7 3000.000 .000 .00012. 8 3500.000 .000 .00013. 9 4000.000 .000 .00014. 10 4500.000 .000 .00015. 11 5000.000 .000 .00016. 12 5500.000 .000 .00017. 13 6000.000 .000 .00018. 14 6500.000 .000 .00019. 15 7000.000 .000 .00020. 16 7500.000 .000 .00021. 17 8000.000 .000 .00022. 18 8500.000 .000 .00023. 19 9000.001 .000 .00024. 20 9500.001 .000 .00025. 21 10000.000 .000 .00026. 22 10500.000 .000 .00027. 23 11000.000 .000 .00028. 24 11500.000 .000 .00029. 25 12000.000 .000 .00030. 26 12500.000 .000 .00031. 27 13000.000 .000 .00032. 28 13500.000 .000 .00033. 29 14000.000 .000 .00034. 30 14500.000 .000 .00035. 31 15000.000 .000 .00036. 32 15500.000 .000 .00037. 33 16000.000 .000 .00038. 34 16500.000 .000 .00039. 35 17000.000 .000 .00040. 36 17500.000 .000 .00041. 37 18000.000 .000 .000FATIGUE -- PAGE NO. 2

42. 38 18500.000 .000 .00043. 39 19000.000 .000 .00044. 40 19500.000 .000 .00045. 41 20000.000 .000 .00046. 42 20500.000 .000 .00047. 43 21000.000 .000 .00048. 44 21500.000 .000 .00049. 45 22000.000 .000 .00050. 46 22500.000 .000 .00051. 47 23000.000 .000 .000



52. 48 23500.000 .000 .00053. 49 24000.000 .000 .00054. MEMBER INCIDENCES55. 1 1 256. 2 2 357. 3 3 458. 4 4 559. 5 5 660. 6 6 761. 7 7 862. 8 8 963. 9 9 1064. 10 10 1165. 11 11 1266. 12 12 1367. 13 13 1468. 14 14 1569. 15 15 1670. 16 16 1771. 17 17 1872. 18 18 1973. 19 19 2074. 20 20 2175. 21 21 2276. 22 22 2377. 23 23 2478. 24 24 2579. 25 25 2680. 26 26 2781. 27 27 2882. 28 28 2983. 29 29 3084. 30 30 3185. 31 31 3286. 32 32 3387. 33 33 3488. 34 34 3589. 35 35 3690. 36 36 3791. 37 37 3892. 38 38 3993. 39 39 4094. 40 40 4195. 41 41 4296. 42 42 4397. 43 43 44FATIGUE -- PAGE NO. 3

98. 44 44 4599. 45 45 46100. 46 46 47101. 47 47 48102. 48 48 49103. MEMBER PROPERTY AMERICAN104. 1 TO 48 PRI YD 500. ZD 100.105. CONSTANT106. E STEEL ALL107. DENSITY STEEL ALL108. POISSON STEEL ALL109. SUPPORT110. 1 PINNED111. 49 FIXED BUT FX MX MY MZ112. UNITS KNS MET113. DEF MOV LOAD114. * TRUCK LOAD115. TYPE 1 LOAD 34 142 142 DIS 4.3 9.116. *117. LOAD GENERATION 100118. TYPE 1 0.0 0.0 0.0 XINC 0.2119. PERFORM ANALYSIS

�





�++ Processing Element Stiffness Matrix. 16:30:28++ Processing Global Stiffness Matrix. 16:30:28++ Processing Triangular Factorization. 16:30:28

***WARNING - IMPROPER LOAD WILL CAUSE INSTABILITY AT JOINT 49DIRECTION = MX PROBABLE CAUSE MODELING PROBLEM -.320E-09

++ Calculating Joint Displacements. 16:30:28++ Calculating Member Forces. 16:30:29

120. PLOT BEND FILE121. PRINT MAX FORCE ENVFATIGUE -- PAGE NO. 4

MEMBER FORCE ENVELOPE---------------------

ALL UNITS ARE KNS MET

MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS

MEMB FY/ DIST LD MZ/ DIST LDFZ DIST LD MY DIST LD FX DIST LD

1 MAX 213.86 .00 1 .00 .00 15.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -102.96 .50 4.00 .50 100 .00 .50 100 .00 .50 100

2 MAX 205.92 .00 4 -2.97 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -200.61 .50 6.00 .50 100 .00 .50 100 .00 .50 100

3 MAX 197.98 .00 7 -5.95 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -289.57 .50 8.00 .50 100 .00 .50 100 .00 .50 100

4 MAX 192.67 .00 9 -8.93 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -374.73 .50 11.00 .50 100 .00 .50 100 .00 .50 100

5 MAX 184.72 .00 12 -11.90 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -451.77 .50 13.00 .50 100 .00 .50 100 .00 .50 100

6 MAX 179.84 .00 1 -14.87 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -539.60 .50 1.00 .50 100 .00 .50 100 .00 .50 100

7 MAX 179.91 .00 1 -17.85 .00 100.00 .00 1 .00 .00 1 .00 .00 1



MIN 5.95 .50 100 -629.54 .50 1.00 .50 100 .00 .50 100 .00 .50 100

8 MAX 179.80 .00 1 -20.83 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -719.46 .50 1.00 .50 100 .00 .50 100 .00 .50 100

9 MAX 179.86 .00 1 -23.80 .00 100.00 .00 1 .00 .00 1 .00 .00 1

FATIGUE -- PAGE NO. 5

MIN 5.95 .50 100 -804.26 .50 2.00 .50 100 .00 .50 100 .00 .50 100

10 MAX 174.52 .00 3 -26.77 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.96 .50 100 -873.52 .50 5.00 .50 100 .00 .50 100 .00 .50 100

11 MAX 169.28 .00 5 -29.75 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.96 .50 100 -942.63 .50 7.00 .50 100 .00 .50 100 .00 .50 100

12 MAX 161.25 .00 8 -32.72 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -997.32 .50 10.00 .50 100 .00 .50 100 .00 .50 100

13 MAX 156.11 .00 10 -35.70 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 5.95 .50 100 -1054.44 .50 12.00 .50 100 .00 .50 100 .00 .50 100

14 MAX 148.10 .00 13 -38.68 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN 3.48 .50 14 -1094.56 .50 15.00 .50 100 .00 .50 100 .00 .50 100

15 MAX 142.72 .00 15 -41.65 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -4.64 .50 17 -1139.80 .50 17.00 .50 100 .00 .50 100 .00 .50 100

16 MAX 134.91 .00 18 -44.63 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -9.70 .46 19 -1166.40 .42 19.00 .50 100 .00 .50 100 .00 .50 100

17 MAX 129.52 .00 20 -47.60 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -17.75 .50 22 -1198.66 .50 22.00 .50 100 .00 .50 100 .00 .50 100

18 MAX 121.45 .00 23 -50.57 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -23.02 .50 24 -1214.40 .42 24.00 .50 100 .00 .50 100 .00 .50 100

19 MAX 116.20 .00 25 -53.55 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -31.08 .50 27 -1230.98 .50 27.00 .50 100 .00 .50 100 .00 .50 100

20 MAX 108.29 .00 28 -56.52 .00 100.00 .00 1 .00 .00 1 .00 .00 1


MIN -36.37 .50 29 -1235.89 .42 29.00 .50 100 .00 .50 100 .00 .50 100



21 MAX 103.05 .00 30 -59.50 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -44.26 .50 32 -1236.92 .29 31.00 .50 100 .00 .50 100 .00 .50 100

22 MAX 95.06 .00 33 -62.47 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -49.52 .46 34 -1236.85 .00 32.00 .50 100 .00 .50 100 .00 .50 100

23 MAX 89.61 .00 35 -65.45 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -57.45 .50 37 -1226.78 .00 34.00 .50 100 .00 .50 100 .00 .50 100

24 MAX 81.89 .00 38 -68.42 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -62.79 .46 39 -1216.17 .00 37.00 .50 100 .00 .50 100 .00 .50 100

25 MAX 76.34 .00 40 -71.40 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -70.85 .50 42 -1194.19 .00 39.00 .50 100 .00 .50 100 .00 .50 100

26 MAX 68.60 .00 43 -74.38 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -75.99 .46 44 -1169.02 .00 42.00 .50 100 .00 .50 100 .00 .50 100

27 MAX 63.32 .00 45 -77.35 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -106.83 .50 2 -1135.15 .00 44.00 .50 100 .00 .50 100 .00 .50 100

28 MAX 55.38 .00 48 -80.32 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -112.01 .50 4 -1133.15 .50 5.00 .50 100 .00 .50 100 .00 .50 100

29 MAX 49.88 .00 50 -83.30 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -119.89 .50 7 -1140.33 .50 7.00 .50 100 .00 .50 100 .00 .50 100

30 MAX 43.48 .00 74 -86.28 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -125.31 .50 9 -1140.32 .17 8.00 .50 100 .00 .50 100 .00 .50 100

31 MAX 39.10 .00 77 -89.25 .00 100.00 .00 1 .00 .00 1 .00 .00 1


MIN -133.39 .50 12 -1138.82 .08 10.00 .50 100 .00 .50 100 .00 .50 100

32 MAX 36.18 .00 79 -92.23 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -138.67 .50 14 -1132.90 .00 12.00 .50 100 .00 .50 100 .00 .50 100

33 MAX 31.75 .00 82 -95.20 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -146.42 .50 17 -1115.71 .08 15.00 .50 100 .00 .50 100 .00 .50 100

34 MAX 28.79 .00 84 -98.18 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -151.87 .50 19 -1099.00 .00 17



.00 .50 100 .00 .50 100 .00 .50 100

35 MAX 24.45 .00 87 -101.15 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -159.75 .50 22 -1067.17 .00 20.00 .50 100 .00 .50 100 .00 .50 100

36 MAX 21.50 .00 89 -104.12 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -165.01 .50 24 -1038.61 .00 22.00 .50 100 .00 .50 100 .00 .50 100

37 MAX 17.07 .00 92 -107.10 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -173.10 .50 27 -992.21 .00 25.00 .50 100 .00 .50 100 .00 .50 100

38 MAX 14.16 .00 94 -110.07 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -178.30 .50 29 -951.66 .00 27.00 .50 100 .00 .50 100 .00 .50 100

39 MAX 9.76 .00 97 -113.05 .00 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -186.33 .50 32 -891.66 .00 29.00 .50 100 .00 .50 100 .00 .50 100

40 MAX 6.82 .00 99 -112.20 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -191.58 .50 34 -838.28 .00 32.00 .50 100 .00 .50 100 .00 .50 100

41 MAX .69 .00 80 -98.17 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -199.51 .50 37 -766.34 .00 34.00 .50 100 .00 .50 100 .00 .50 100

42 MAX -3.74 .00 83 -84.15 .50 100.00 .00 1 .00 .00 1 .00 .00 1


MIN -204.86 .50 39 -698.36 .00 37.00 .50 100 .00 .50 100 .00 .50 100

43 MAX -6.62 .00 85 -70.12 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -212.74 .50 42 -614.51 .00 39.00 .50 100 .00 .50 100 .00 .50 100

44 MAX -11.04 .00 88 -56.10 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -218.11 .50 44 -531.95 .00 42.00 .50 100 .00 .50 100 .00 .50 100

45 MAX -13.98 .00 90 -42.08 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -226.04 .50 47 -436.16 .00 44.00 .50 100 .00 .50 100 .00 .50 100

46 MAX -18.37 .00 93 -28.05 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -231.36 .50 49 -339.05 .00 47.00 .50 100 .00 .50 100 .00 .50 100

47 MAX -21.30 .00 95 -14.02 .50 100.00 .00 1 .00 .00 1 .00 .00 1

MIN -239.29 .50 52 -231.33 .00 49.00 .50 100 .00 .50 100 .00 .50 100

48 MAX -25.71 .00 98 .00 .50 29.00 .00 1 .00 .00 1 .00 .00 1



MIN -244.58 .50 54 -119.64 .00 52.00 .50 100 .00 .50 100 .00 .50 100

********** END OF FORCE ENVELOPE FROM INTERNAL STORAGE **********

122. FINISH

*************** END OF STAAD-III ***************

**** DATE= DEC 14,1999 TIME= 16:30:45 ****


Documents

APPENDIX CB - COMPOSITE BRIDGE, 24 M SPAN, 7.32 m Width