ATV-Snowmobile Bridge Design Calcs_100.pdf

June 2021 djanda.com

Bridge Design Calculations –

ATV/Snowmobile Bridge

U.S. Department of Transportation Federal Highway Administration

ATV/Snowmobile Bridge

Yale-Kilgore Road

Prepared By: DJ&A, P.C.

2000 Maple Street Missoula, MT 59808 T 406.721.4320 F 406.549.6371

Structural Design Calculations

Design Loads

Idaho Ground Snow Loads

Seismic Parameters from USGS

Snow Groomer (Basis of Design)

Superstructure Design

Girder Design

Visual Analysis Results – 70’ Span

Bearing Pad Design

Substructure Design

Abutment Design

Backwall Design

Wingwall Design

Wingwall Base Connection & Development Length

Pile Analysis

Pile Cap Design

Pile Cap Reinforcement

Live Load Distribution for Strut & Tie Model

Strut & Tie Model

Pier

Pile Analysis

Pile Cap Design

Pile Cap Reinforcement

Strut & Tie Model

Lateral Analysis

Lateral Pile Load Summary

Seismic Analysis

Wind Analysis

Design Loads

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USGS Seismic Design Parameters

Technical data PistenBully 400 / 400 W

Engine 400 400 W

Type Cummins QSL 9

No. of cylinders 6

Displacement 8.9 l / 2.4 gal 8,900 ccm / 543 cu.in

Power output (ECE) 272 kW / 370 hp

Exhaust emissions standard Euro 3A, EPA TIER 3

Max. torque 1,519 Nm / 1,120 ft lbs at 1,500 rpm

Tank capacity 260 l / 69 gal

Tank capacity from 19 l/h / 5 gal

Drive pump 140 ccm / 8.5 cu.in

Driving characteristics 400 400 W

Speed 0 – 23 km/h / 0 – 14 mph continuously variable

0 – 20 km/h / 0 – 12 mph continuously variable

Speed with winch in action 0 – 17 km/h / 0 – 11 mph

Gradeability up to 100 %

Turning radius on-the-spot

Electrics 400 400 W

Low-voltage system 24 V

Alternator 24 V / 140 A

Batteries 2 x 12 V / 135 Ah

Cold start rating 900 A

Lightning 400 400 W

Front 2 H7 front-headlights and 2 H11 working headlight

Rear 2 H11 rear-headlights

Lateral optional

Search headlight Twin searchlights

Additional headlight – 2 x LED 2,200 lm on winch boom

Cabin 400 400 W

ROPS certificat yes

Driver’s seat adjustable

Operating elements display with touchscreen

Glazing Front, rear and side windows heated

Rear mirrors heated

Wipers cooling-water heated

Options 400 400 W

Hydraulically foldable sideflaps optional

Front high pressure connection optional

Xenon set optional

Solid tires optional series

Magnum sprocket optional

Hydraulic oil pre-heating optional

Trailer hitch optional

Cableway emergency operation optional

Foldable galery optional

Rear camera optional series

Harness belt optional series

Winch superstructure 400 W

Rope pull continuously variable 40 kN / 4,080 kp

Rope diameter 11 mm / 0.4"

Rope length 1,050 m / 1,148 yd

Usable rope length 1,000 m / 1,094 yd

Rope breaking strain 130 kN / 13,256 kp

Drive rating at 40 kN pull 110 kW / 150 PS

Weight (winch, rope and superstructure) 1,900 kg / 4,189 lbs

Weights 400 400 W

Tare weight with combined tracks 7,340 kg / 16,182 lbs

9,270 kg / 20,437 lbs with steel tracks 8,020 kg / 17,681 lbs

9,950 kg / 21,936 lbs

Gross weight limit 11,800 kg / 26,015 lbs

11,800 kg / 26,015 lbs

Payload on platform 1,500 kg / 3,307 lbs

2,500 kg / 5,512 lbs

Dimensions 400 / 400 W

Width without tracks 2,500 mm / 98.4" over combined tracks / steel tracks 4,206 mm / 165.6" over tiller with intermediate flaps 5,500 mm / 216.5" over tiller and foldable sideflaps 6,400 mm / 252"

Blade width open 5,260 mm / 207" width wide 4,420 mm / 174"

Height 1,000 mm / 39.4"

Height above everything 2,830 mm / 111.4"

400 W above winch ready for operation

3,280 mm / 129.1" when driver’s cabin tilted 3,250 mm / 128"

Ground clearance 350 mm / 13.8"

Length with blade and tiller 9,010 mm / 354.7" with blade, tiller and track-setters 10,310 mm / 405.9"

Load area Length 2,120 mm / 83.5"

Width 1,920 mm / 75.6"

Suggested garage dimensions

Length 11,000 mm / 433"

Width 6,000 mm / 236"

Height 3,500 mm / 138"

Superstructure Design

STEEL GIRDER DESIGN & LOAD RATING Steel Trail Bridge

Calculations are in accordance with AASHTO LRFD Bridge Design Specifications, 8th Ed. & AASHTO Manual for Bridge Evaluation, 3rd Ed.

References to the Design Specifications are shown in [ ] brackets, references to the

Bridge Evaluation Manual are shown in { } brackets.

GENERAL COMMENTS AND ASSUMPTIONS

LRFD Bridge Design methodology is used. USFS Manual for Trail Bridge Design referenced for loads and live load factors (FSH 7709.56b, Chapter 80).

Load Resistance Factor Rating (LRFR) methodology is used.

Load rating calculations are completed for superstructure elements only.

Live load distribution by approximate method.

GENERAL INFORMATION

The following unit weights are used:

Concrete, γc 150 pcf:= pcf = pounds per cubic foot

Asphalt, γws 140 pcf:= [Table 3.5.1-1]

Steel, γs 490 pcf:=

Wood, γw 50 pcf:=

Load Modifiers are as follows:

Ductility ηD 1.0:= For Conventional Designs [1.3.3]

Redundancy ηR 1.0:= For Conventional Redundancy [1.3.4]

Importance ηI 1.0:= For Typical Bridges [1.3.5] ηi = ηD ηR ηI 0.95 [1.3.2.1] therefore, ηi max ηD ηR ηI 0.95, ( ) 1.00=:= (maximum load factors)

Load Factors are as follows:

STRENGTH SERVICE

DC: γDC 1.25:= γDCS 1.00:= Dead Load of Components

DW: γDW 1.50:= γDWS 1.00:= Dead Load of Wearing Surface {6A.4.2.2-1 Notes}

Pedestrian LL: γPL 1.75:= γPLS 1.30:= Pedestrian Live Load

Load Combinations per

USFS Manual:

[FSH 7709.56b, Chapter 80]

Snow: γSLmax 1.75:= γSLmax.S 1.30:= Dead + Snow Load Cases Only γSLmin 0.50:= Snow in Combination with Live Load

Snowmobile: γSmax 1.75:= γSmax.S 1.30:= Dead + Live Load Cases Only γSmin 1.0:= Dead + Snow + Live Load Case (Skiier or Over-Snow Vehicle)

Design LL: γLL 1.75:= γLLS 1.30:= H10 & Snow Groomer Design Vehicle

Wind: γWSIII 1.0:= Wind Load on Structure - STRENGTH III

Resistance Factors are as follows:

Resistance Factor: ϕf 1.0:= Steel Flexure or Shear [6.5.4.2] ϕv 1.0:=

Condition Factor: ϕc 1.0:= ** New Construction ** {Table 6A.4.2.3-1}

System Factor: ϕsf 0.85:= For 4 Girder Bridge {Table 6A.4.2.4-1} ϕsv 1.0:=

W30x108_70' Span.xmcd 1 of 32 Designed: ASG Checked: MJ

BRIDGE GEOMETRY:

Note: Plans show timber running planks. Asphalt conservatively used for possible future paving.

Roadway Width, Wr 16 ft:= Skew, Skew 0 deg:=

Out-to-Out Deck Width, Wd 16.5 ft:= Girder Span, Span 70 ft:= CL Brg. to

CL Brg.

Exterior Girder Spacing, Sext 4.3333 ft:= Number of Lanes, NL 1:=

Interior Girder Spacing, Sint 4.3333 ft:= Number of Girders, N 4:=

Overhang, Sover

Wd N 2-( ) Sext- Sint-

1.750 ft=:=

MATERIAL PROPERTIES

Corrugated Steel Deck: 4-1/4 x 12 Corrugated Steel Deck Panel dD 4.25 in:= Deck Depth

Steel Girder: W30x108

Tension Flange bfT.G 10.50 in= Flange Width Ag.G 31.7 in

= Gross Area tfT.G 0.760 in= Flange Thickness Ix.G 4470 in

= Moment of Inertia

At.G bfT.G tfT.G 7.98 in

Sxc.G 299 in

= Section Modulus - Top

Sxt.G Sxc.G:= Section Modulus - Bottom

Iyt.G tfT.G bfT.G

73.32 in rx.G

Ix.G

Ag.G

11.87 in=:= Radius of Gyration

Compression Flange bfC.G bfT.G:= Flange Width E 29000 ksi:= Modulus of Elasticity tfC.G tfT.G:= Flange Thickness Fy.G 50 ksi:= Yield Stress - A588 Steel

Ac.G bfC.G tfC.G 7.98 in

=:= Fyt.G Fy.G:= Fyc.G Fy.G:= Fyw.G Fy.G:=

Rh.G 1:= Girder is homogeneous

Iyc.G tfC.G bfC.G

73.32 in

W30x108_70' Span.xmcd 2 of 32 Designed: ASG

Web Lu.G 1 ft:= Unbraced Length dG 29.8 in= Girder Depth ** Top Flange Supported by Metal Deck ** tw.G 0.545 in= Web Thickness

DG dG tfT.G- tfC.G- 28.28 in=:=

Aw.G DG tw.G 15.41 in

Neutral Axis Location with respect to bottom of Girder Yb.G

At.G 0.5 tfT.G Ac.G tfT.G DG+ 0.5 tfC.G+( )+ Aw.G tfT.G 0.5 DG+( )+ At.G Ac.G+ Aw.G+( )

14.90 in=:=

Torsional Constant

J DG tw.G bfC.G tfC.G

1 0.63 tfC.G bfC.G bfT.G tfT.G

1 0.63 tfT.G bfT.G

+ 4.46 in

=:= [A6.3.3]

W30x108_70' Span.xmcd 3 of 32 Designed: ASG

STEEL GIRDER DESIGN:

GIRDER CROSS-SECTION PROPORTION LIMITS: [6.10.2]

Web Proportion Limits:

For Webs Without Longitudinal Stiffeners:

Limit Web_checkG "OK"

DG

tw.G

150if

"No GOOD" otherwise

"OK"=:=DG

tw.G

51.89= < 150

Flange Proportion Limits:

Limit Flange_check1G "OK" bfC.G

2 min tfT.G tfC.G, ( ) 12if

"No GOOD" otherwise

"OK"=:=bfT.G

2 tfT.G 6.91= bfC.G

2 tfC.G 6.91= < 12.0

Minimum bfT.G 10.50 in= Flange_check2G "OK" min bfT.G bfC.G, ( )

DG

if

"No GOOD" otherwise

"OK"=:=

DG

4.71 in= bfC.G 10.50 in=

Minimum tfT.G 0.76 in= Flange_check3G "OK" min tfT.G tfC.G, ( ) 1.1 tw.Gif

"No GOOD" otherwise

"OK"=:=

> 1.1 tw.G 0.60 in= tfC.G 0.76 in=

0.1 < Iyc.G

Iyt.G

1.00= < 10 Iy_check "OK" 0.1 Iyc.G

Iyt.G

10if

"No GOOD" otherwise

"OK"=:=

GIRDER COMPACT SECTION REQUIREMENTS: [6.10.6.2.3]

Appendix A6 is only applicable to sections in straight bridges whose supports are not skewed more than 20 degrees, with intermediate diaphragms or cross-frames placed in contiguous lines parallel to the supports, and meet the following criteria.

Dc = Web depth in compression Dc.G dG tfC.G- Yb.G- 14.14 in=:=

IF Fyt & Fyc < 70 ksi slender "Web is Not Slender" 2 Dc.G tw.G

5.7 E

Fyc.G

<if

"Web is Slender" otherwise

:=2 Dc.G tw.G

51.89= < 5.7 E

Fyc.G

137.27=

AND

AND

Iyc.G

Iyt.G

1.00= >= 0.3 slender "Web is Not Slender"=

If all conditions are met, design per Section 6, Appendix A Non-composite I-Section with compact or noncompact webs. IF NOT, design per Section 6.10.8.

Code "Design per SECTION 6.10.8" Fyt.G 70 ksi>

Fyc.G 70 ksi>

Iyc.G

Iyt.G

0.3<

2 Dc.G tw.G

5.7 E

Fyc.G if

"Design per SECTION 6 APPENDIX A" otherwise

Code "Design per SECTION 6 APPENDIX A"=

W30x108_70' Span.xmcd 4 of 32 Designed: ASG

COMPACT SECTION CRITERIA

Web is Compact if: [A6.2.1] λpwDcp = Limiting slenderness ratio for compact web sections2Dcp tw < λpwDcp < λrw

Dcp

Dc λrw = Limiting slenderness ratio for a non-compact web λrw.G 5.7

E

Fyc.G

Dcp for Non-Composite Sections:

Dcp = Web depth in compression at plastic moment IF Fyw.G Aw.G 771 kip= > Fyc.G Ac.G Fyt.G At.G- 0.00 kip=

Dcp

DG

2 Aw.G Fyw.G Fyt.G At.G Fyw.G Aw.G+ Fyc.G Ac.G-( ) Fyw.G Aw.G Fyc.G Ac.G Fyt.G At.G->if

DG otherwise

14.14 in=:=

[D6.3.2]

Plastic Moment, Mp for Non-composite Section: [Table D6.1-1]

Pw Fyw.G DG tw.G 771 kip=:= Web P = Plastic force

Pc Fyc.G bfC.G tfC.G 399 kip=:= Compression flange

Pt Fyt.G bfT.G tfT.G 399 kip=:= Tension flange

Pcheck "OK" Pc Pt Pw+if

"No GOOD" otherwise

:= Pcheck "OK"= [Table D6.1-1 condition]

Y = Dist. from N.A. to bottom of top flange Y

DG

Pt Pc-

Pw 1+

14.14 in=:= d = Dist. from N.A. to center of compression or tension flange dc Y tfC.G

+ 14.52 in=:= dt DG Y-tfT.G

+ 14.52 in=:=

Mp Pw

2DG

Y

DG Y-( )2

Pc dc Pt dt+( )+ 1420 kip ft=:= Plastic Moment

Yield Moment, My

Myc Fyc.G Sxc.G 14950 kip in=:= with respect to compression flange

Myt Fyt.G Sxt.G 14950 kip in=:= with respect to tension flange

My min Myc Myt, ( ) 14950 kip in=:=

Compactness Check:

[A6.2.1] λpwDcp

E

Fyc.G

0.54 Mp

Rh.G My 0.09-

87.3=:= λw

2 Dc.G tw.G

51.89=:=

Web is Compact if the conditions are met:

Compact1 "Compact" Fyc.G 70 ksi<

Fyt.G 70 ksi<

DG

tw.G if

"Non-Compact" otherwise

"Compact"=:=

D tw limit for unstiffened webs

W30x108_70' Span.xmcd 5 of 32 Designed: ASG

Web is Compact if the conditions are met:

Compact2 "Compact"

2Dcp tw.G λpwDcpif

"Non-Compact" otherwise

Compact2 "Compact"=

SL_limit "Web not Slender" λpwDcp λrw.G

Dcp

Dc.G if

"Slender Web" otherwise

SL_limit "Web not Slender"=

Web Plastification Factor Compression Flange, Rpc

Rpc Mp

Myc

2Dcp tw.G λpwDcpif

1 1 Rh.G Myc

Mp λw λpwDcp-λrw.G λpwDcp-

Myc otherwise

:= For Compact

For Non-Compact Rpc 1.14=

Web Plastification Factor Tension Flange, Rpt

Rpt Mp

Myt

2Dcp tw.G λpwDcpif

1 1 Rh.G Myt λw λpwDcp-λrw.G λpwDcp-

Myt otherwise

For Non-Compact Rpt 1.14=

GIRDER FLEXURAL RESISTANCE

COMPRESSION FLANGE [A6.3]

The nominal flexural resistance is the smaller of the local bucking resistance and the lateral torsional buckling resistance [A6.3.1] Mnc = minimum of Mnc_local and Mnc_LTB

Local Buckling Resistance [A6.3.2]

IF λf λpf< Mnc_local = Rpc Myc otherwise Mnc_local = 1 1 Fyr Sxc

Rpc Myc λf λpf-λrf λpf-λf = compression flange slenderness ratio λrf = limiting slenderness ratio for non-compact flangeλpf = limiting slenderness ratio for compact flange

D tw kc = flange local buckling coeff. = for built-up sections

OR kc 0.76:= for rolled shapes

Fyr max 0.5 Fyc.G min 0.7 Fyc.G Rh.G Fyt.G Sxt.G

Sxc.G

, Fyw.G,

35.00 ksi=:= compression flange stress at onset of nominal yielding λf bfC.G

2tfC.G

6.91=:= λpf 0.38 E

Fyc.G

9.15=:= λrf 0.95 E kc

Fyr 23.84=:=

Mnc_local 0 λpf λrf>if

Rpc Myc( ) λf λpf<if

1 1 Fyr Sxc.G λf λpf-λrf λpf-

Rpc Myc otherwise

Mnc_local 1420 kip ft=

W30x108_70' Span.xmcd 6 of 32 Designed: ASG

Lateral Torsional Buckling Resistance [A6.3.3]

IF Lb Lp Mnc= Rpc Myc

Lp Lb< Lr Mnc= Cb 1 1 Fyr Sxc

Lb Lp-

Lr Lp-

Rpc Myc < Rpc Myc

Lb Lr> Mnc= Fcr Sxc < Rpc Myc

Lb Lu.G 12 in=:= = unbraced length Lr= limiting unbraced length for yielding

Lp = limiting unbraced length for nom. flexural resistance rt bfC.G

12 1 Dc.G tw.G

3 bfC.G tfC.G

2.64 in=:= = effective radius of gyration for lat. tors.

buckling Lp 1.0 rt

E

Fyc.G

63.5 in=:= h = depth between centerline flanges h dG 0.5 tfC.G- 0.5 tfT.G- 29.04 in=:= Lr 1.95 rt

E

Fyr

J

Sxc.G h 1 1 6.76

Fyr Sxc.G h

E J

++ 259 in=:=

Cb = moment gradient modifier = 1.0 for members where Mmid/M2 > 1 USE: Cb 1:= [C6.4.10]

If the Lb > Lr is met, Fcr needs to be defined, otherwise, Fcr Cb π

E

Lb rt

1 0.078

J

Sxc.G h

Lb rt

+ 13820.19 ksi=:=

Lp 5.29 ft= Lb 1.00 ft= Lr 21.57 ft= Rpc Myc 1420 kip ft=

Mnc_LTB Rpc Myc Lb Lpif min Cb 1 1 Fyr Sxc.G

Lb Lp-

Lr Lp-

Rpc Myc Rpc Myc, Lp Lb< Lrif min Fcr Sxc.G Rpc Myc, ( ) otherwise

Mnc_LTB 1420 kip ft=

Mnc.G min Mnc_local Mnc_LTB, ( ):= Mnc.G 1420 kip ft= Compression Flange Moment Resistance

TENSION FLANGE [A6.4]

Mnt.G Rpt Myt:= Mnt.G 1420 kip ft= Tension Flange Moment Resistance

CONTROLLING MOMENT RESISTANCE

Mn.G min Mnc.G Mnt.G, ( ):= Mn.G 1420 kip ft= Girder Moment Resistance

W30x108_70' Span.xmcd 7 of 32 Designed: ASG

GIRDER SHEAR RESISTANCE: [6.10.9.2]

kG 5:= Shear-Buckling Coefficient for Unstiffened Sections

Ratio of Shear-Buckling Resistance to the Shear Yield Strength

CG 1.0

DG

tw.G

1.12 E kG

Fyw.G if

1.12

DG

tw.G

E kG

Fyw.G

1.12

< 1.40 E kG

Fyw.G if

1.57 otherwise

1.00=:= [6.10.9.3.2-4]

[6.10.9.3.2-5]

[6.10.9.3.2-6]

Vp.G 0.58 Fy.G DG tw.G 446.97 kip=:= [6.10.9.2-2]

Vn.G CG Vp.G 446.97 kip=:= [6.10.9.2-1]

DEAD LOADS

Component Dead Load, DC:

Railing, Each Side of Deck

(Distribute Equally to All Girders)wrail 75 plf:= DCRail.G

2 wrail

N

0.038 klf=:=

Corrugated Steel Deck Self Weight, dD.DL 11.5 psf:= DCD.G dD.DL Wd

N

0.047 klf=:=

Diaphragms, wdia 20 plf:= DCDia wdia 0.020 klf=:=

Girder Self Weight, DCGirder Ag.G γs 0.108 klf=:=

Total:

DCG DCRail.G DCD.G+ DCDia+ DCGirder+ 0.213 klf=:=

Wearing Surface Dead Load, DW:

Asphalt Wearing Surface, Note: Conservatively used for potential future paving.

tws dD

2 in+ 4.13 in=:= Avg. Thickness DWG tws Wd γws

N

0.199 klf=:=

LIVE LOADS

Multiple Presence

Factor:

Multiple Presence Factor for live loads is included per [3.6.1.1.2].

Multiple Presence Factor may be reduced to 95% of given value for ADTT 1000 m1 1.2:= Multiple Presence Factor for Single Lane Bridge [Table 3.6.1.1.2-1]

Adjust m for Low ADTT? Adjust_m1 1:= 1 for "Yes", 0 for "No" m1adjusted 0.95 m1( ) Adjust_m1 1=if m1 Adjust_m1 0=if m1adjusted 1.14=

W30x108_70' Span.xmcd 8 of 32 Designed: ASG

Add Dynamic Load Allowance per {6A.4.4.3} IMG 0.33:=

Pedestrian Load:

wPL 90 psf:= LLPL wPL Wr

N

0.360 klf=:=

Snow Load:

Ground (Uniform Snow Load at Full Snow Load), wSL 157 psf:= Ground Snow Load - From

Idaho Ground Snow Load

Finder

LLSL

wSL Wd

N

0.648 klf=:=

Snow Depth (Uniform Snow Load at Depth), γsnow min 0.13 wSL psf 14+ 30, pcf 30.00 pcf=:= (ASCE 7-16, 7.7-1) dSL 2 ft:= Snow Depth - Used in

Combination with

Snowmobile or Snow

Groomer

LLSL.2

dSL Wd γsnow

N

0.248 klf=:=

Snowmobile:

wmobile 500 lbf:= Weight of Snowmobile wperson 300 lbf:= Weight of Person

NS 12:= Assumed Number of

Snowmobiles on Span wMobile

NS wmobile wperson+( )

Wr Span

0.009 ksf=:=

LLS

wMobile Wr

N

0.034 klf=:=

MOMENT SHEAR

DC MDC

DCG Span

130.34 kip ft=:= VDC

DCG Span

7.45 kip=:=

DW MDW

DWG Span

121.59 kip ft=:= VDW

DWG Span

6.95 kip=:=

Pedestrian MPL

LLPL Span

220.50 kip ft=:= VPL

LLPL Span

12.60 kip=:=

Snow MSL

LLSL Span

396.67 kip ft=:= VSL

LLSL Span

22.67 kip=:=

Snow -

Depth

MSL2

LLSL.2 Span

151.59 kip ft=:= VSL2

LLSL.2 Span

8.66 kip=:=

Snowmobile MS

LLS Span

21.00 kip ft=:= VS

LLS Span

1.20 kip=:=

W30x108_70' Span.xmcd 9 of 32 Designed: ASG

Vehicle Loads:

Vehicle live loads were calculated in Visual Analysis.

H10 MH10 321 kip ft:= VH10 19 kip:=

Snow

Groomer

MUnit.Groomer 16 kip ft:= VUnit.Groomer 0.93 kip:= Unit Truck - 7' Long

Track with a 10.5'

Track Gauge WGroomer 26 kip:= Total Load of Groomer

MG MUnit.Groomer

WGroomer

1 kip

416.00 kip ft=:= VG VUnit.Groomer

WGroomer

1 kip

24.18 kip=:=

LIVE LOAD DISTRIBUTION FACTORS:

Lane Live Load distribution per [3.6.1.1.2]

Live Load Distribution for 6' Wheel Gauge (For H10):

Distribution Factor for Interior Girders:

Moment: DFint.M

Sint

9.2 ft m1adjusted m1

Sint 5.5 ft dD 2 inif

0.5 max 0 0.5 Sint 6 ft-

Sint m1adjusted otherwise

:= [Table 4.6.2.2.2c-1]

DFint.M 0.45=

Shear: DFintV 0.5 max 0 0.5 Sint 6 ft-m1adjusted 0.57=:= Lever Rule

Distribution Factor for Exterior Girders:

Lever Rule:

Moment & Shear xO= Distance from wheel line 2' off rail face to exterior girder per [3.6.1.3.1] xO 6- in:= (negative number indicates wheel on interior of girder)

Distribution by lever rule with 6' axle spacing DFExtLR

Sext xO+

Sext

0.5 m1adjusted:=

DFExtLR 0.50=

Rigid X-section:

Moment & Shear

[4.6.2.2.2d] x1 78 in:= x2 26 in:= Dist. From CL Structure to CL of Each Girder

Xext x1 6.50 ft=:= Dist. From Centerline Structure to Exterior Girder

Σx_sq 2x1

2 x2

+ 94 ft

=:= Sum of x2 * Number of Girders At Ea. Location

Dist. From Centerline Structure to Center of Gravity of Design Truck e1

Wr

2 ft- 3 ft- 3.00 ft=:=

DFRigid

NL

N

Xext e1

Σx_sq m1adjusted 0.52=:=

W30x108_70' Span.xmcd 10 of 32 Designed: ASG

Final Distribution Factors:

Interior Girder: DFIntM DFint.M 0.45=:=

DFIntV DFintV 0.57=:=

Exterior Girder: DFextM max DFExtLR DFRigid, ( ) 0.52=:=

DFextV max DFExtLR DFRigid, ( ) 0.52=:=

Final Factor: DFM max DFIntM DFextM, ( ) 0.52=:=

DFV max DFIntV DFextV, ( ) 0.57=:=

Live Load Distribution for 10.5' Wheel Gauge (For Snow Groomer):

Distribution Factor for Interior Girders:

Moment: DFint.M2 0.5 max 0 0.5 Sint 10.5 ft-m1adjusted:= Lever Rule

DFint.M2 0.57=

Shear: DFint.V2 DFint.M2 0.57=:=

Distribution Factor for Exterior Girders:

Lever Rule:

Moment & Shear xO= Distance from wheel line 2' off rail face to exterior girder per [3.6.1.3.1] xO 6.00- in= (negative number indicates wheel on interior of girder)

Distribution by lever rule with 10.5' axle spacing DFExtLR.2

Sext xO+

Sext

0.5 m1adjusted:=

DFExtLR.2 0.50=

Rigid X-section:

Moment & Shear

[4.6.2.2.2d] x1 78.00 in= x2 26.00 in= Dist. From CL Structure to CL of Each Girder

Xext 78.00 in= Dist. From Centerline Structure to Exterior Girder

Σx_sq 94 ft

= Sum of x2 * Number of Girders At Ea. Location

Dist. From Centerline Structure to Center of Gravity of Design Truck e1.2

Wr

2 ft- 5.25 ft- 0.75 ft=:=

DFRigid.2

NL

N

Xext e1.2

Σx_sq m1adjusted 0.34=:=

Final Distribution Factors:

Interior Girder: DFIntM2 DFint.M2 0.57=:=

DFIntV2 DFint.V2 0.57=:=

Exterior Girder: DFextM2 max DFExtLR.2 DFRigid.2, ( ) 0.50=:=

DFextV2 max DFExtLR.2 DFRigid.2, ( ) 0.50=:=

Final Factor: DFM2 max DFIntM2 DFextM2, ( ) 0.57=:=

DFV2 max DFIntV2 DFextV2, ( ) 0.57=:=

W30x108_70' Span.xmcd 11 of 32 Designed: ASG

DESIGN LOADS

STRENGTH Factored Force Effects:

Dead

Load

Mu.DL.G ηi γDC MDC γDW MDW+( ) 345.32 kip ft=:=

Vu.DL.G ηi γDC VDC γDW VDW+( ) 19.73 kip=:=

Pedestrian Mu.PL ηi γPL MPL 385.88 kip ft=:=

Vu.PL ηi γPL VPL 22.05 kip=:=

Snow Mu.SL.max ηi γSLmax MSL 694.17 kip ft=:=

Vu.SL.max ηi γSLmax VSL 39.67 kip=:=

Mu.SL.min ηi γSLmin MSL 198.34 kip ft=:=

Vu.SL.min ηi γSLmin VSL 11.33 kip=:=

Mu.SL.G ηi γSLmax MSL2 265.29 kip ft=:= Snow -

Depth Vu.SL.G ηi γSLmax VSL2 15.16 kip=:=

Snowmobile Mu.S.max ηi γSmax MS 36.75 kip ft=:=

Vu.S.max ηi γSmax VS 2.10 kip=:=

Mu.S.min ηi γSmin MS 21.00 kip ft=:=

Vu.S.min ηi γSmin VS 1.20 kip=:=

H10 Mu.H10 ηi γLL DFM 1 IMG+( ) MH10 389.83 kip ft=:=

Vu.H10 ηi γLL DFV 1 IMG+( ) VH10 25.21 kip=:=

Mu.Groomer ηi γLL DFM2 1 IMG+( ) MG 551.90 kip ft=:= Snow

Groomer Vu.Groomer ηi γLL DFV2 1 IMG+( ) VG 32.08 kip=:=

SERVICE II Factored Force Effects:

η ηi is equal to 1.0 for the Service Limit State. All values are equal to 1.0. [1.3.2.1]

Dead

Load fDL.C.G γDCS MDC γDWS MDW+

Sxc.G

10.11 ksi=:= Compression Flange - Top fDL.T.G γDCS MDC γDWS MDW+

Sxt.G

10.11 ksi=:= Tension Flange - Bottom

Pedestrian fPL.C.G γPLS MPL

Sxc.G

11.50 ksi=:= fPL.T.G γPLS MPL

Sxt.G

11.50 ksi=:=

Snow fSL.C.G γSLmax.S MSL

Sxc.G

20.70 ksi=:= fSL.T.G γSLmax.S MSL

Sxt.G

20.70 ksi=:=

W30x108_70' Span.xmcd 12 of 32 Designed: ASG

Snow -

Depth fSL2.C.G γSLmax.S MSL2

Sxc.G

7.91 ksi=:= fSL2.T.G γSLmax.S MSL2

Sxt.G

7.91 ksi=:=

Snowmobile fS.C.G γSmax.S MS

Sxc.G

1.10 ksi=:= fS.T.G γSmax.S MS

Sxt.G

1.10 ksi=:=

H10 fH10.C.G γLLS DFM 1 IMG+( ) MH10

Sxc.G

11.62 ksi=:= fH10.T.G γLLS DFM 1 IMG+( ) MH10

Sxt.G

11.62 ksi=:=

Snow

Groomer fGroom.C.G γLLS DFM2 1 IMG+( ) MG

Sxc.G

16.45 ksi=:= fGroom.T.G γLLS DFM2 1 IMG+( ) MG

Sxt.G

16.45 ksi=:=

WIND LOADS

Wind Loads calculated per [3.8.1.1] & [3.8.1.2]. Analysis perfomed for Strength III & V Cases.

VIII 115:= mph Design 3-Second gust Wind Speed [Figure 3.8.1.1.2-1]

Wind Exposure Category Shall be Determined Perpendicular to Bridge [3.8.1.1.3]

Exposure "C":= Wind Exposure Category [3.8.1.1.4 & 5]

ZActual 8:= ft Assumed Maxium Height of Bridge [3.8.1.2.1]

ZEffective 33 ZActual 33<if

ZActual otherwise

33.00=:= Maximum Effective Height of Bridge

Pressure Exposure & Elevation Coefficient, Kz:

Kz.III

2.5 ln ZEffective

0.9834

6.87+

345.6 Exposure "B"=if

2.5 ln

0.0984

7.35+

478.4 Exposure "C"=if

2.5 ln

0.0164

7.65+

616.1 otherwise

1.00=:= [3.8.1.2.1-2]

[3.8.1.2.1-3]

[3.8.1.2.1-4]

W30x108_70' Span.xmcd 13 of 32 Designed: ASG

GIII 1.0:= Gust Effect Factor - Strength III [Table 3.8.1.2.1-1]

CD 1.3:= Drag Coefficient [Table 3.8.1.2.1-2]

Wind Pressures:

Pz.III 2.56 10 6-

VIII

Kz.III GIII CD ksf 0.044 ksf=:= [3.8.1.2.1-1]

Apply Wind Load on Superstructure per [3.8.1.2.2], Transverse Wind Event Controls.

Contributory Area:

Hrail 21 in:= From Top of Deck

Hcontrib Hrail dD+ tws+ dG+ 4.93 ft=:= Contributing Height

Applied Uniform Wind Loads:

WSIII Hcontrib Pz.III 0.217 klf=:=

Flange Section Modulus:

Syc tfC.G bfC.G

13.96 in

=:= Compression Flange

Syt tfT.G bfT.G

13.96 in

=:= Tension Flange

Sy Syc Syt+ DG tw.G

+ 29.33 in

=:= Girder

Wind Force to Flange:

WSCIII

Syc

Sy

WSIII 0.10 klf=:= Wind Load Proportioned to Flanges

Based on Relative Lateral Stiffness.

WSTIII

Syt

Sy

WSIII 0.10 klf=:=

Calculate the wind force based on fixed-fixed condition for entire span. The girders will be braced at the abutments and piers to create the fixed condition. Moment in each girder flange will be total moment divided by the number of girders.

Span.wind Span:= Design Span for Wind Calculations is from Braced End Bay to Braced End Bay

Wind Moments:

MwindC.III

WSCIII Span.wind

N 24

5.28 kip ft=:= Compression (Top) Flange

MwindT.III

WSTIII Span.wind

N 24

5.28 kip ft=:= Tension (Bottom) Flange

W30x108_70' Span.xmcd 14 of 32 Designed: ASG

MEMBER ADEQUACY:

VERTICAL LOADS

The lateral bending stresses in discretely braced flanges must satisfy: fL 0.6 Fyf [Eq. 6.10.1.6-1]

For Discretely Braced Flanges in Compression, fbu fL+ ϕf Fnc [Eq. 6.10.8.1.1-1 & A6.1.1-1]

Mu fL Sxc+ ϕf Mnc fbu fL+ ϕf Rh Fyc [Eq. 6.10.3.2.1-1] fbu ϕf Fcrw [Eq. 6.10.3.2.1-3]

For Discretely Braced Flanges in Tension, fbu fL+ .ϕf Fnt [Eq. 6.10.8.1.2-1 & A6.1.2-1]

Mu fL Sxt+ ϕf Mnt fbu fL+ ϕf Rh Fyt [Eq. 6.10.3.2.2-1] fbu = flange bending stress calculated w/o consideration of flange lateral bending fL = flange lateral bending stressed as determined by [6.10.1.6]

Fnc = nominal flexural resistance of the compression flange

Fnt = nominal flexural resistance of the tension flange

Fcrw = nominal bend-buckling resistance for webs

Fnc Rh.G

Mnc.G

Sxc.G

56.97 ksi=:=

Fnt Rh.G

Mnt.G

Sxt.G

56.97 ksi=:=

Web Bend Buckling Resistance, {6A.6.4.2.2}

For Webs Without Longitudinal Stiffeners kG.S

Dc.G

36.00=:=

[6.10.1.9.1-2]

Fcrw.G min

0.9 E kG.S

Rh.G Fyc.G, Fyw.G

0.7

50.00 ksi=:= [6.10.1.9.1-1]

Note: The SERVICE II checks are done in the load rating portion of the design.

W30x108_70' Span.xmcd 15 of 32 Designed: ASG

DESIGN CHECK:

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 PL+( ) Pedestrian

Mu.G1 Mu.DL.G Mu.PL+ 731.19 kip ft=:=

Vu.G1 Vu.DL.G Vu.PL+ 41.78 kip=:=

FlexureG1 "OK" Mu.G1 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG1 "OK"= Mu.G1 ϕf Mn.G 0.52=

ShearG1 "OK" Vu.G1 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG1 "OK"= Vu.G1 ϕv Vn.G 0.09=

Compression Flange: Tension Flange:

Flange Stresses: fbu1.C

Mu.G1

Sxc.G

29.35 ksi=:= fbu1.T

Mu.G1

Sxt.G

29.35 ksi=:= fL1 0:= No lateral loads during for

STRENGTH I Case Lat1 "OK" fL1 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat1 "OK"= fbu1.C fL1+ 29.35 ksi=

Flex1a "OK" fbu1.C fL1+ ϕf Fncif

"FAIL" otherwise

:= Flex1a "OK"= ϕf Fnc 56.97 ksi= fbu1.C fL1+ 29.35 ksi= Flex1b "OK" fbu1.C fL1+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex1b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex1c "OK" fbu1.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex1c "OK"= ϕf Fcrw.G 50.00 ksi= fbu1.T fL1+ 29.35 ksi= Flex1d "OK" fbu1.T fL1+ ϕf Fntif

"FAIL" otherwise

Flex1d "OK"= ϕf Fnt 56.97 ksi= fbu1.T fL1+ 29.35 ksi= Flex1e "OK" fbu1.T fL1+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

Flex1e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 16 of 32 Designed: ASG

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 SL+( ) Uniform Snow Load Snow

Mu.G2 Mu.DL.G Mu.SL.max+ 1039.49 kip ft=:=

Vu.G2 Vu.DL.G Vu.SL.max+ 59.40 kip=:=

FlexureG2 "OK" Mu.G2 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG2 "OK"= Mu.G2 ϕf Mn.G 0.73=

ShearG2 "OK" Vu.G2 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG2 "OK"= Vu.G2 ϕv Vn.G 0.13=

Compression Flange: Tension Flange:

Flange Stresses: fbu2.C

Mu.G2

Sxc.G

41.72 ksi=:= fbu2.T

Mu.G2

Sxt.G

41.72 ksi=:= fL2 0:= No lateral loads during for

STRENGTH I Case Lat2 "OK" fL2 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat2 "OK"= fbu2.C fL2+ 41.72 ksi=

Flex2a "OK" fbu2.C fL2+ ϕf Fncif

"FAIL" otherwise

:= Flex2a "OK"= ϕf Fnc 56.97 ksi= fbu2.C fL2+ 41.72 ksi= Flex2b "OK" fbu2.C fL2+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex2b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex2c "OK" fbu2.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex2c "OK"= ϕf Fcrw.G 50.00 ksi= fbu2.T fL2+ 41.72 ksi=

Flex2d "OK" fbu2.T fL2+ ϕf Fntif

"FAIL" otherwise

:= Flex2d "OK"= ϕf Fnt 56.97 ksi= fbu2.T fL2+ 41.72 ksi= Flex2e "OK" fbu2.T fL2+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex2e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 17 of 32 Designed: ASG

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 S+( ) Snowmobile

Mu.G3 Mu.DL.G Mu.S.max+ 382.07 kip ft=:=

Vu.G3 Vu.DL.G Vu.S.max+ 21.83 kip=:=

FlexureG3 "OK" Mu.G3 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG3 "OK"= Mu.G3 ϕf Mn.G 0.27=

ShearG3 "OK" Vu.G3 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG3 "OK"= Vu.G3 ϕv Vn.G 0.05=

Compression Flange: Tension Flange:

Flange Stresses: fbu3.C

Mu.G3

Sxc.G

15.33 ksi=:= fbu3.T

Mu.G3

Sxt.G

15.33 ksi=:= fL3 0:= No lateral loads during for

STRENGTH I Case Lat3 "OK" fL3 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat3 "OK"= fbu3.C fL3+ 15.33 ksi=

Flex3a "OK" fbu3.C fL3+ ϕf Fncif

"FAIL" otherwise

:= Flex3a "OK"= ϕf Fnc 56.97 ksi= fbu3.C fL3+ 15.33 ksi= Flex3b "OK" fbu3.C fL3+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex3b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex3c "OK" fbu3.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex3c "OK"= ϕf Fcrw.G 50.00 ksi= fbu3.T fL3+ 15.33 ksi=

Flex3d "OK" fbu3.T fL3+ ϕf Fntif

"FAIL" otherwise

:= Flex3d "OK"= ϕf Fnt 56.97 ksi= fbu3.T fL3+ 15.33 ksi= Flex3e "OK" fbu3.T fL3+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex3e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 18 of 32 Designed: ASG

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 LL+( ) H10

Mu.G4 Mu.DL.G Mu.H10+ 735.14 kip ft=:=

Vu.G4 Vu.DL.G Vu.H10+ 44.94 kip=:=

FlexureG4 "OK" Mu.G4 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG4 "OK"= Mu.G4 ϕf Mn.G 0.52=

ShearG4 "OK" Vu.G4 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG4 "OK"= Vu.G4 ϕv Vn.G 0.10=

Compression Flange: Tension Flange:

Flange Stresses: fbu4.C

Mu.G4

Sxc.G

29.50 ksi=:= fbu4.T

Mu.G4

Sxt.G

29.50 ksi=:= fL4 0:= No lateral loads during for

STRENGTH I Case Lat4 "OK" fL4 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat4 "OK"= fbu4.C fL4+ 29.50 ksi=

Flex4a "OK" fbu4.C fL4+ ϕf Fncif

"FAIL" otherwise

:= Flex4a "OK"= ϕf Fnc 56.97 ksi= fbu4.C fL4+ 29.50 ksi= Flex4b "OK" fbu4.C fL4+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex4b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex4c "OK" fbu4.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex4c "OK"= ϕf Fcrw.G 50.00 ksi= fbu4.T fL4+ 29.50 ksi=

Flex4d "OK" fbu4.T fL4+ ϕf Fntif

"FAIL" otherwise

:= Flex4d "OK"= ϕf Fnt 56.97 ksi= fbu4.T fL4+ 29.50 ksi= Flex4e "OK" fbu4.T fL4+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex4e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 19 of 32 Designed: ASG

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 LL+( ) Snow Groomer

Mu.G5 Mu.DL.G Mu.Groomer+ 897.21 kip ft=:=

Vu.G5 Vu.DL.G Vu.Groomer+ 51.81 kip=:=

FlexureG5 "OK" Mu.G5 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG5 "OK"= Mu.G5 ϕf Mn.G 0.63=

ShearG5 "OK" Vu.G5 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG5 "OK"= Vu.G5 ϕv Vn.G 0.12=

Compression Flange: Tension Flange:

Flange Stresses: fbu5.C

Mu.G5

Sxc.G

36.01 ksi=:= fbu5.T

Mu.G5

Sxt.G

36.01 ksi=:= fL5 0:= No lateral loads during for

STRENGTH I Case Lat5 "OK" fL5 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat5 "OK"= fbu5.C fL5+ 36.01 ksi=

Flex5a "OK" fbu5.C fL5+ ϕf Fncif

"FAIL" otherwise

:= Flex5a "OK"= ϕf Fnc 56.97 ksi= fbu5.C fL5+ 36.01 ksi= Flex5b "OK" fbu5.C fL5+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex5b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex5c "OK" fbu5.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex5c "OK"= ϕf Fcrw.G 50.00 ksi= fbu5.T fL5+ 36.01 ksi=

Flex5d "OK" fbu5.T fL5+ ϕf Fntif

"FAIL" otherwise

:= Flex5d "OK"= ϕf Fnt 56.97 ksi= fbu5.T fL5+ 36.01 ksi= Flex5e "OK" fbu5.T fL5+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex5e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 20 of 32 Designed: ASG

STRENGTH I Limit State: Snowmobile With Uniform Snow Load Snow & Snowmobile

Mu.G6a Mu.DL.G Mu.S.max+ Mu.SL.min+ 580.40 kip ft=:= ηi 1.25 DC 1.50 DW+ 1.75 S+ 0.5 SL+( )

Vu.G6a Vu.DL.G Vu.S.max+ Vu.SL.min+ 33.17 kip=:=

Mu.G6b Mu.DL.G Mu.S.min+ Mu.SL.max+ 1060.49 kip ft=:= ηi 1.25 DC 1.50 DW+ 1.0 S+ 1.75 SL+( )

Vu.G6b Vu.DL.G Vu.S.min+ Vu.SL.max+ 60.60 kip=:=

Mu.G6 max Mu.G6a Mu.G6b, ( ) 1060.49 kip ft=:=

Vu.G6 max Vu.G6a Vu.G6b, ( ) 60.60 kip=:=

FlexureG6 "OK" Mu.G6 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG6 "OK"= Mu.G6 ϕf Mn.G 0.75=

ShearG6 "OK" Vu.G6 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG6 "OK"= Vu.G6 ϕv Vn.G 0.14=

Compression Flange: Tension Flange:

Flange Stresses: fbu6.C

Mu.G6

Sxc.G

42.56 ksi=:= fbu6.T

Mu.G6

Sxt.G

42.56 ksi=:= fL6 0:= No lateral loads during for

STRENGTH I Case Lat6 "OK" fL6 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat6 "OK"= fbu6.C fL6+ 42.56 ksi=

Flex6a "OK" fbu6.C fL6+ ϕf Fncif

"FAIL" otherwise

:= Flex6a "OK"= ϕf Fnc 56.97 ksi= fbu6.C fL6+ 42.56 ksi= Flex6b "OK" fbu6.C fL6+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex6b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex6c "OK" fbu6.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex6c "OK"= ϕf Fcrw.G 50.00 ksi= fbu6.T fL6+ 42.56 ksi=

Flex6d "OK" fbu6.T fL6+ ϕf Fntif

"FAIL" otherwise

:= Flex6d "OK"= ϕf Fnt 56.97 ksi= fbu6.T fL6+ 42.56 ksi= Flex6e "OK" fbu6.T fL6+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex6e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 21 of 32 Designed: ASG

STRENGTH I Limit State: ηi 1.25 DC 1.50 DW+ 1.75 LL+ 1.75 SL+( ) Snow & Snow Groomer

Mu.G7 Mu.DL.G Mu.Groomer+ Mu.SL.G+ 1162.50 kip ft=:= Snow Groomer with Uniform Snow Load at 2' Depth Vu.G7 Vu.DL.G Vu.Groomer+ Vu.SL.G+ 66.97 kip=:=

FlexureG7 "OK" Mu.G7 ϕf Mn.G 1.0if

"FAIL" otherwise

:= FlexureG7 "OK"= Mu.G7 ϕf Mn.G 0.82=

ShearG7 "OK" Vu.G7 ϕv Vn.G 1.0if

"FAIL" otherwise

:= ShearG7 "OK"= Vu.G7 ϕv Vn.G 0.15=

Compression Flange: Tension Flange:

Flange Stresses: fbu7.C

Mu.G7

Sxc.G

46.66 ksi=:= fbu7.T

Mu.G7

Sxt.G

46.66 ksi=:= fL7 0:= No lateral loads during for

STRENGTH I Case Lat7 "OK" fL7 0.6 min Fyc.G Fyt.G, ( )if

"FAIL" otherwise

:= Lat7 "OK"= fbu7.C fL7+ 46.66 ksi=

Flex7a "OK" fbu7.C fL7+ ϕf Fncif

"FAIL" otherwise

:= Flex7a "OK"= ϕf Fnc 56.97 ksi= fbu7.C fL7+ 46.66 ksi= Flex7b "OK" fbu7.C fL7+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

:= Flex7b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex7c "OK" fbu7.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex7c "OK"= ϕf Fcrw.G 50.00 ksi= fbu7.T fL7+ 46.66 ksi=

Flex7d "OK" fbu7.T fL7+ ϕf Fntif

"FAIL" otherwise

:= Flex7d "OK"= ϕf Fnt 56.97 ksi= fbu7.T fL7+ 46.66 ksi= Flex7e "OK" fbu7.T fL7+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex7e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 22 of 32 Designed: ASG

STRENGTH III Limit State: ηi 1.25 DC 1.50 DW+ 1.0 WS+( ) Wind

Mu8.C Mu.DL.G ηi γWSIII MwindC.III+ 350.60 kip ft=:= Compression (Top) Flange

Mu8.T Mu.DL.G ηi γWSIII MwindT.III+ 350.60 kip ft=:= Tension (Bottom) Flange

Use Amplified Flange Bending Stresses Per [Eq. 6.10.1.6-4]

Web Load-Shedding Factor, Rb: Rb 1.0:= For Section 6, Appendix A designs

COMPRESSION FLANGE STRESS TENSION FLANGE STRESS

Vertical Loads: fbu8.C

Mu8.C

Sxc.G

14.07 ksi=:= fbu8.T

Mu8.T

Sxt.G

14.07 ksi=:=

Lateral Loads: fL8.C γWSIII

MwindC.III

Syc

4.54 ksi=:= fL8.T γWSIII

MwindT.III

Syt

4.54 ksi=:=

FINAL LATERAL BENDING STRESSES

fL8.C1 fL8.C Lb 1.2 Lp Cb Rb fbu8.C

Fyc.G if

0.85 fbu8.C

Fcr fL8.C otherwise

:= fL8.T1 fL8.T Lb 1.2 Lp Cb Rb fbu8.T

Fyt.G if

0.85 fbu8.T

Fcr fL8.C otherwise

4.54 ksi=:= fL8.C1 4.54 ksi= fL8.T1 4.54 ksi=

Lat8a "OK" fL8.C1 0.6 Fyc.Gif

"FAIL" otherwise

:= Lat8a "OK"=

Lat8b "OK" fL8.T1 0.6 Fyt.Gif

"FAIL" otherwise

:= Lat8b "OK"= fbu8.C fL8.C1+ 15.58 ksi=

Flex8a "OK" fbu8.C fL8.C1+ ϕf Fncif

"FAIL" otherwise

:= Flex8a "OK"= ϕf Fnc 56.97 ksi= fbu8.C fL8.C1+ 18.61 ksi= Flex8b "OK" fbu8.C fL8.C1+ ϕf Rh.G Fyc.Gif

"FAIL" otherwise

Flex8b "OK"= ϕf Rh.G Fyc.G 50.00 ksi=

Flex8c "OK" fbu8.C ϕf Fcrw.Gif

"FAIL" otherwise

:= Flex8c "OK"= ϕf Fcrw.G 50.00 ksi= fbu8.T fL8.T1+ 15.58 ksi=

Flex8d "OK" fbu8.T fL8.T1+ ϕf Fntif

"FAIL" otherwise

:= Flex8d "OK"= ϕf Fnt 56.97 ksi= fbu8.T fL8.T1+ 18.61 ksi= Flex8e "OK" fbu8.T fL8.T1+ ϕf Rh.G Fyt.Gif

"FAIL" otherwise

:= Flex8e "OK"= ϕf Rh.G Fyt.G 50.00 ksi=

W30x108_70' Span.xmcd 23 of 32 Designed: ASG

SERVICE LIMIT STATE DESIGN CHECKS:

Member Live Load Deflection checked for SERVICE I Limit State

When investigating absolute maximum deflection, all design lanes are loaded and all supporting elements are considered to deflect equally. For multiple girder bridges, the distribution factor for deflection is therefore the number of lanes divided by the number of girders. The dynamic load allowance and multiple presence factor must be included.

[2.5.2.6.2]

SERVICE I Limit State

Distribution Factor for Deflection:

DF∆

N m1adjusted 0.29=:= For Single Lane Bridge [2.5.2.6.2]

Maximum Live Load Deflection:

IM∆ 1.33:= Use 33% dynamic load allowance for deflection calcs.

Pedestrian ∆PL

5 LLPL( ) Span

384 E Ix.G

1.50 in=:=

Snow ∆SL

5 LLSL( ) Span

2.70 in=:=

Snow -

Depth

∆SL.2

5 LLSL.2( ) Span

1.03 in=:=

Snowmobile ∆S

5 LLS( ) Span

0.14 in=:=

Deflections calculated by structural analysis program with vehicle loads applied to a single girder.

H10 ∆H10.truck 1.8 in:= Two Truck Axles

∆H10 DF∆ IM∆ ∆H10.truck 0.68 in=:=

Deflections calculated by structural analysis program with vehicle loads applied to a single girder.

Snow

Groomer

∆Groomer.truck 0.09 in:= Two Truck Axles

∆Groomer DF∆ IM∆ ∆Groomer.truck WGroomer

1 kip

0.89 in=:= [3.6.1.3.2]

Deflection Span Ratios are shown below for the various loading conditions. Deflection criteria taken from

AASHTO and ASCE if not defined in AASHTO.

Pedestrian Snow Snow - Depth Snowmobile H10 Snow Groomer

Span

∆PL

560= Span

∆SL

311= Span

∆SL.2

814= Span

∆S

5879= Span

∆H10

1231= Span

∆Groomer

947=

Snow + Snowmobile Snow + Snow Groomer

Span

0.75 ∆SL ∆S+( )

394=

Span

0.75 ∆SL ∆Groomer+( ) 312=

W30x108_70' Span.xmcd 24 of 32 Designed: ASG

∆Ped "OK" Span

∆PL

360if

"No GOOD" otherwise

∆Ped "OK"=

∆Snow "OK" Span

∆SL

240if

"No GOOD" otherwise

∆Snow "OK"=

∆Snowmobile "OK" Span

∆S

360if

"No GOOD" otherwise

"OK"=:=

∆Snowmobile "OK"=

∆H10.Truck "OK" Span

∆H10

800if

"No GOOD" otherwise

"OK"=:=

∆H10.Truck "OK"=

∆Groomer.Truck "OK" Span

∆Groomer

800if

"No GOOD" otherwise

"OK"=:=

∆Groomer.Truck "OK"=

∆Snow.Snowmobile "OK" Span

0.75 ∆SL ∆S+( )

240if

"No GOOD" otherwise

"OK"=:=

∆Snow.Snowmobile "OK"=

∆Snow.Groomer "OK" Span

0.75 ∆SL ∆Groomer+( ) 240if

"No GOOD" otherwise

"OK"=:=

∆Snow.Groomer "OK"=

CAMBER REQUIREMENTS Provide camber equal to 1.5*DL deflection at service limit state u= distance from support u 0.1 Span 0.2 Span, 0.5 Span..:= u

Span

0.10

0.20

0.30

0.40

0.50

DCG DWG+( ) u

24 E Ix.G Span( )

2 Span( ) u

- u

+ 1.5

0.8072

1.5271

2.0907

2.4486

2.5712 in u

7.00

14.00

21.00

28.00

35.00 ft

Points along Span

Span fraction

DL deflection

(inches)

W30x108_70' Span.xmcd 25 of 32 Designed: ASG

SERVICE II Limit State:

Both Steel Flanges of Non-Composite Sections, [6.10.4.2.2] fR.G 0.8 Rh.G Fy.G 40.00 ksi=:= Top Flange & Bottom Flanges [6.10.4.2.2-3]

Web, {6A.6.4.2.2}

For Webs Without Longitudinal Stiffeners kG.S 36.00= [6.10.1.9.1-2]

Fcrw.G 50.00 ksi= [6.10.1.9.1-1] fR.Web.G Fcrw.G 50.00 ksi=:= [6.10.4.2.2-4]

SERVICE II Checks:

Vertical Load Stress:

ffC.G max fPL.C.G fSL.C.G, fS.C.G, fH10.C.G, fGroom.C.G, fSL.C.G fS.C.G+, fSL2.C.G fGroom.C.G+, ( ) 24.36 ksi=:= ffT.G max fPL.T.G fSL.T.G, fS.T.G, fH10.T.G, fGroom.T.G, fSL.T.G fS.T.G+, fSL2.T.G fGroom.T.G+, ( ) 24.36 ksi=:= fL.G 0 ksi:= Lateral Load Stress

CompFlangeStress.G "OK" ffC.G fL.G

+ 0.8 Rh.G Fy.Gif

"FAIL" otherwise

:= CompFlangeStress.G "OK"= [6.10.4.2.2-3]

TenFlangeStress.G "OK" ffT.G fL.G

+ 0.8 Rh.G Fy.Gif

"FAIL" otherwise

:= TenFlangeStress.G "OK"= [6.10.4.2.2-3]

WebStress.G "OK" ffC.G Fcrw.Gif

"FAIL" otherwise

:= WebStress.G "OK"= [6.10.4.2.2-4]

W30x108_70' Span.xmcd 26 of 32 Designed: ASG

STEEL GIRDER RATING FACTOR ANALYSIS:

The girders are rated for moment and shear.

RATING FACTOR GENERAL EQUATION

Member Capacity - Factored DL effects {6A.4.2.1}

{Eq. 6A.4.2.1-1} Rating Factor, RF =

Factored LL effects

Member Capacity, C = Nominal_Capacity ϕc ϕs ϕ {Eq. 6A.4.2.1-2} ϕc 1.00= ϕsf 0.85= ϕc ϕsf 0.85=

Girder Capacities: ϕsv 1.00= ϕc ϕsv 1.00= {Table 6A.4.2.2-1}

STRENGTH I:

CM.G max ϕc ϕsf 0.85, ( ) ϕf Mn.G 1206.67 kip ft=:=

CV.G max ϕc ϕsv 0.85, ( ) ϕv Vn.G 446.97 kip=:=

SERVICE II Limit State:

Both Steel Flanges of Non-Composite Sections, [6.10.4.2.2] fR.G 40.00 ksi= Top Flange & Bottom Flanges [6.10.4.2.2-3]

GIRDER RATING FACTORS

Pedestrian RFPL.M.G

CM.G Mu.DL.G-

Mu.PL

2.23=:=

RFPL.V.G

CV.G Vu.DL.G-

Vu.PL

19.38=:=

RFPL.CFL.G

fR.G fDL.C.G-fPL.C.G

2.60=:=

RFPL.TFL.G

fR.G fDL.T.G-fPL.T.G

2.60=:=

RFPL.Web.G fR.Web.G fDL.C.G-fPL.C.G

3.47=:=

Snow RFSL.M.G

CM.G Mu.DL.G-

Mu.SL.max

1.24=:=

RFSL.V.G

CV.G Vu.DL.G-

Vu.SL.max

10.77=:=

RFSL.CFL.G

fR.G fDL.C.G-fSL.C.G

1.44=:=

RFSL.TFL.G

fR.G fDL.T.G-fSL.T.G

1.44=:=

RFSL.Web.G fR.Web.G fDL.C.G-fSL.C.G

1.93=:=

W30x108_70' Span.xmcd 27 of 32 Designed: ASG

Snowmobile RFS.M.G

CM.G Mu.DL.G-

Mu.S.max

23.44=:=

RFS.V.G

CV.G Vu.DL.G-

Vu.S.max

203.44=:=

RFS.CFL.G

fR.G fDL.C.G-fS.C.G

27.28=:=

RFS.TFL.G

fR.G fDL.T.G-fS.T.G

27.28=:=

RFS.Web.G fR.Web.G fDL.C.G-fS.C.G

36.41=:=

W30x108_70' Span.xmcd 28 of 32 Designed: ASG

H10 RFH10.M.G

CM.G Mu.DL.G-

Mu.H10

2.21=:=

RFH10.V.G

CV.G Vu.DL.G-

Vu.H10

16.95=:=

RFH10.CFL.G

fR.G fDL.C.G-fH10.C.G

2.57=:=

RFH10.TFL.G

fR.G fDL.T.G-fH10.T.G

2.57=:=

RFH10.Web.G fR.Web.G fDL.C.G-fH10.C.G

3.43=:=

Snow

Groomer RFGroomer.M.G

CM.G Mu.DL.G-

Mu.Groomer

1.56=:=

RFGroomer.V.G

CV.G Vu.DL.G-

Vu.Groomer

13.32=:=

RFGroomer.CFL.G fR.G fDL.C.G-fGroom.C.G

1.82=:=

RFGroomer.TFL.G fR.G fDL.T.G-fGroom.T.G

1.82=:=

RFGroomer.Web.G fR.Web.G fDL.C.G-fGroom.C.G

2.42=:=

Snow &

Snowmobile

RFSS.M.G

CM.G Mu.DL.G-max Mu.S.max Mu.SL.min+ Mu.S.min Mu.SL.max+, ( ) 1.20=:=

RFSS.V.G

CV.G Vu.DL.G-max Vu.S.max Vu.SL.min+ Vu.S.min Vu.SL.max+, ( ) 10.45=:=

RFSS.CFL.G

fR.G fDL.C.G-fSL.C.G fS.C.G+ 1.37=:=

RFSS.TFL.G

fR.G fDL.T.G-fSL.T.G fS.T.G+ 1.37=:=

RFSS.Web.G fR.Web.G fDL.C.G-fSL.C.G fS.C.G+ 1.83=:=

W30x108_70' Span.xmcd 29 of 32 Designed: ASG

Snow &

Snow

Groomer

RFSG.M.G

CM.G Mu.DL.G-

Mu.Groomer Mu.SL.G+ 1.05=:=

RFSG.V.G

CV.G Vu.DL.G-

Vu.Groomer Vu.SL.G+ 9.04=:=

RFSG.CFL.G

fR.G fDL.C.G-fGroom.C.G fSL2.C.G+ 1.23=:=

RFSG.TFL.G

fR.G fDL.T.G-fGroom.T.G fSL2.T.G+ 1.23=:=

RFSG.Web.G fR.Web.G fDL.C.G-fGroom.C.G fSL2.C.G+ 1.64=:=

GIRDER RATING FACTOR SUMMARY:

Pedestrian RFPL.G min RFPL.M.G RFPL.V.G, RFPL.CFL.G, RFPL.TFL.G, RFPL.Web.G, ( ) 2.23=:=

Snow RFSL.G min RFSL.M.G RFSL.V.G, RFSL.CFL.G, RFSL.TFL.G, RFSL.Web.G, ( ) 1.24=:=

Snowmobile RFS.G min RFS.M.G RFS.V.G, RFS.CFL.G, RFS.TFL.G, RFS.Web.G, ( ) 23.44=:=

H10 RFH10.G min RFH10.M.G RFH10.V.G, RFH10.CFL.G, RFH10.TFL.G, RFH10.Web.G, ( ) 2.21=:=

Snow

Groomer RFGroomer.G min RFGroomer.M.G RFGroomer.V.G, RFGroomer.CFL.G, RFGroomer.TFL.G, RFGroomer.Web.G, ( ) 1.56=:=

Snow &

Snowmobile

RFSS.G min RFSS.M.G RFSS.V.G, RFSS.CFL.G, RFSS.TFL.G, RFSS.Web.G, ( ) 1.20=:=

Snow &

Snow

Groomer

RFSG.G min RFSG.M.G RFSG.V.G, RFSG.CFL.G, RFSG.TFL.G, RFSG.Web.G, ( ) 1.05=:=

W30x108_70' Span.xmcd 30 of 32 Designed: ASG

BRIDGE DESIGN SUMMARY:

A summary of the design parameters is shown below.

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.52 0.09 560 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.73 0.13 311 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.27 0.05 5879 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.52 0.10 1231 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.63 0.12 947 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.75 0.14 394 OK OK OK OK OK OK

M V Deflection Lat Flexa Flexb Flexc Flexd Flexe

0.82 0.15 312 OK OK OK OK OK OK

Lata Latb Flexa Flexb Flexc Flexd Flexe

OK OK OK OK OK OK OK

C. Flange T. Flange Web

OK OK OK

SERVICE II

Steel Girder

STRENGTH I: Pedestrian

STRENGTH III

STRENGTH I: Snow

STRENGTH I: Snowmobile

STRENGTH I: H10

STRENGTH I: Snow Groomer

STRENGTH I: Snow & Snowmobile

STRENGTH I: Snow & Snow Groomer

W30x108_70' Span.xmcd 31 of 32 Designed: ASG

BRIDGE RATING FACTOR SUMMARY:

A summary of the rating factors for each superstructure element evaluated is shown below. The safe load capacity is given in tons. If the vehicle rating factor is greater than 1.0, then the vehicle weight rating is

GVW*RF. If that condition is not satisfied, safe posting loads are calculated using equation {6A.8.3-1} from the Manual for Bridge Evaluation.{6A.8.3}

M V C. Flange T. Flange Web

Pedestrian 2.23 19.38 2.60 2.60 3.47

Snow 1.24 10.77 1.44 1.44 1.93

Snowmoblie 23.44 203.44 27.28 27.28 36.41

H10 2.21 16.95 2.57 2.57 3.43

Snow Groomer 1.56 13.32 1.82 1.82 2.42

Snow & Snowmobile 1.20 10.45 1.37 1.37 1.83

Snow & Snow Groomer 1.05 9.04 1.23 1.23 1.64

Summary

Pedestrian 2.23 - -

Snow 1.24 - -

Snowmoblie 23.44 - -

H10 2.21 20 44.2

Snow Groomer 1.56 13 20.3

Snow & Snowmobile 1.20 - -

Snow & Snow Groomer 1.05 - -

Safe Load

Capacity

Vehicle

Vehicle

STRENGTH I & II SERVICE II

Steel Girder

RF

GVW

(tons)

Safe Load Capacity: {6A.8.3-1}

RF GVW RF 1.0if

GVW

0.7 RF 0.3-( ) RF 1.0<if

W30x108_70' Span.xmcd 32 of 32 Designed: ASG

DJ & A, P.C.

Ammon Groesbeck

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ELASTOMERIC BEARING DESIGN Steel Reinforced Elastomeric Bearing Pad

Calculations are in accordance with AASHTO LRFD Bridge Design Specifications, 8th Ed. & AASHTO Manual for Bridge Evaluation, 3rd Ed.

References to the Design Specifications are shown in [ ] brackets, references to the

Bridge Evaluation Manual are shown in { } brackets.

GENERAL COMMENTS AND ASSUMPTIONS

LRFD Bridge Design methodology is used.

Bearing pad design Method A used.

MATERIAL PROPERTIES

Steel Reinforced Elastomeric Pad:

L 8 in:= Pad Length

W 11 in:= Pad Width hc 0.25 in:= Cover Pad Thickness - Per Layer hri 0.5 in:= Internal Pad Thickness - Per Layer n 1:= Number of Internal Pad Layers hs 0.0625 in:= Steel Thickness - 16 gauge

Fy 36 ksi:= Yield Stress of Steel

Covercheck "OK" hc 0.7 hriif

"FAIL" otherwise

:= Covercheck "OK"= [14.7.6.1]

Temp Zone = D [Table 14.7.5.2-1]

Hardness 60:= Elastomer Hardness (Duro - Shore A) [Table 14.7.6.2-1] aCR 0.35:= Creep Deflection @ 25 Years Divided by Initial Deflection [Table 14.7.6.2-1]

G 0.150 ksi:= Elastomer Shear Modulus [Table 14.7.6.2-1]

Sc

L W

2 hc L W+( ) 9.26=:= Si

L W

2 hri L W+( ) 4.63=:= Shape Factors [14.7.5.1-1]

ShapeInt "OK" Si n 22<if

"FAIL" otherwise

:= ShapeInt "OK"=Si n 21.45= [14.7.6.1]

Bridge Properties:

L∆ 70 ft:= Thermal Expansion Length

TempMax 120:= deg F Steel Structure, Cold Climate [Table 3.12.2.1-1]

TempMin 45:= deg F Assumed Set Temperature = 45o F αs 0.0000065:= Coefficient of Thermal Expansion - Steel

Bearing Pad Design - Reinforced_Steel Girder_70' Span.xmcd

1 of 4 Designed: ASG

DESIGN LOADS

All reactions are maximum service loads applied to the bearing pad. Loads are SERVICE I

(Load Factors = 1.0).

DL 7.45 6.95+( ) kip 14.40 kip=:= Dead Load Reaction (From Girder Design)

Snow 22.67 kip:= Uniform Snow Load (From Girder Design)

GroomerandSnow 24.18 8.66+( ) kip 32.84 kip=:= Snow Groomer + Snow Depth (From Girder Design)

IM 1.33:= Dynamic Load Allowance - Impact [Table 3.6.2.1-1]

LL max Snow GroomerandSnow, ( ) 32.84 kip=:= Live Load Reaction with Impact

BEARING PAD DESIGN

Plain Elastomeric Bearing Pads are designed using Method A outlined in 14.7.6. The sections below are the required design checks.

14.7.6.3.2 - Compressive Stress

14.7.6.3.3 - Compressive Deflection

14.7.6.3.4 - Shear

14.7.6.3.5 - Rotation

14.7.6.3.6 - Stability

14.7.6.3.7 - Reinforcement

14.7.6.3.8 - Seismic & Other Extreme Event Provisions

COMPRESSIVE STRESS - 14.7.6.3.2

Compressive Stresses:

σDL

DL

L W

0.16 ksi=:= Compressive Stress Due to Dead Load σLL

LL

L W

0.37 ksi=:= Compressive Stress Due to Live Load with Impact σLL.2

LL

IM L W

0.28 ksi=:= Compressive Stress Due to Live Load without Impact

For Steel Reinforced Elastomeric Pads:

σs.MAX.c min 1.25 G Sc 1.25 ksi, ( ) 1.25 ksi=:= [14.7.6.3.2-7 & 8] σs.MAX.i min 1.25 G Si 1.25 ksi, ( ) 0.87 ksi=:= σs σDL σLL+ 0.54 ksi=:=

PadComp.c "OK" σs σs.MAX.cif

"FAIL" otherwise

:= PadComp.c "OK"= σs σs.MAX.c

0.43=

PadComp.i "OK" σs σs.MAX.iif

"FAIL" otherwise

:= PadComp.i "OK"= σs σs.MAX.i

0.62=

Bearing Pad Design - Reinforced_Steel Girder_70' Span.xmcd

2 of 4 Designed: ASG

COMPRESSIVE DEFLECTION - 14.7.6.3.3

Compressive Strains:

εDL.c σDL

4.8 G Sc

0.00265=:= εDL.i σDL

4.8 G Si

0.01059=:= [C14.7.5.3.6-1] εLL.c σLL

0.00604=:= εLL.i σLL

0.02416=:= [C14.7.5.3.6-1] εLL.2.c σLL.2

0.00454=:= εLL.2.i σLL.2

0.01817=:= [C14.7.5.3.6-1]

Instantaneous Deflections:

δLL 2 εLL.c hc n εLL.i hri+ 0.0151 in=:= [14.7.5.3.6-1] δDL 2 εDL.c hc n εDL.i hri+ 0.00662 in=:= [14.7.5.3.6-2] δinitial 2 εLL.2.c εDL.c+( ) hc n εLL.2.i εDL.i+( ) hri+ 0.01798 in=:= [14.7.6.3.3]

Long-Term DL Deflection:

Long-Term DL Deflection

(Including Creep) δLT δDL aCR δDL+ 0.00894 in=:= [14.7.5.3.6-3]

Limit Live Load Deflection to 1/8" max. (Suggested)

Padδ1 "OK" δLL 0.125 inif

"FAIL" otherwise

:= Padδ1 "OK"= [C14.7.5.3.6]

Padδ2 "OK" δinitial 0.09 hriif

"FAIL" otherwise

:= Padδ2 "OK"= [14.7.6.3.3]

SHEAR DEFORMATION - 14.7.6.3.4

Bridge Thermal Movement:

γTU 1.2:= Max Thermal Expansion Factor [C3.4.1]

∆T TempMax TempMin- 75.00=:= deg F [3.12.2.3-1]

∆s γTU L∆ ∆T αs 0.49 in=:= Maximum Total Shear Deformation

Assumes Infinitely Stiff Abutment

(Conservative for Bearing Design) hrt 2 hc hri n+ 1.000 in=:= hrt.min 2 ∆s 0.98 in=:= Minimum Elastomer Thickness [14.7.6.3.4-1]

Pad∆ "OK" hrt hrt.minif

"FAIL" otherwise

:= Pad∆ "OK"=

Bearing Pad Design - Reinforced_Steel Girder_70' Span.xmcd

3 of 4 Designed: ASG

ROTATION - 14.7.6.3.5

Uplift is accounted for in the geometric and stress limits given for Method A for elastomeric bearing pads.

[C14.7.6.3.5a]

STABILITY - 14.7.6.3.6

Pad is considered stable if the total pad thickness is less than L/3 and W/3. [14.7.6.3.6] hpad 2 hc hri n+ n 1+( ) hs+ 1.125 in=:=

PadStability "OK" hpad min L W, ( ) if

"FAIL" otherwise

PadStability "OK"=

REINFORCEMENT - 14.7.6.3.7

hs 0.0625 in= Steel Thickness hmax max hc hri, ( ) 0.500 in=:=

∆FTH 24 ksi:= Fatigue Threshold - Category A [Table 6.6.1.2.3-1]

MinThickness "OK" 0.0625 in hsif

"FAIL" otherwise

:= MinThickness "OK"= [14.7.5.3.5]

ServiceThickness "OK" hs

3 hmax σs

Fy if

"FAIL" otherwise

:= ServiceThickness "OK"= [14.7.5.3.5-1]

FatigueThickness "OK" hs

2 hmax σLL

∆FTH

if

"FAIL" otherwise

:= FatigueThickness "OK"= [14.7.5.3.5-2]

SEISMIC & OTHER EXTREME EVENT PROVISIONS - 14.7.6.3.8

Anchorage is designed to resist all applicable seismic and extreme event forces.

BEARING PAD DESIGN SUMMARY:

A summary of the design parameters is shown below.

Cover Internal

0.43 0.62 OK OK OK N/A OK

Min t Service t Fatigue t

OK OK OK N/A

Seismic Reinforcement

Steel Reinforced Elastomeric Pad

Compression δ1 δ2 Shear Rotation Stability

Bearing Pad Design - Reinforced_Steel Girder_70' Span.xmcd

4 of 4 Designed: ASG

Substructure Design

SUBJECT Yale Kilgore - Trail Bridge

JOB NO. 6839.002 SHEET

BY A. Groesbeck DATE 6/9/2021

BRIDGE ABUTMENT DESIGN Backwall

Design in Accordance with AASHTO LRFD, 8th Ed.

Assumed Soil Properties

Backfill F= 30 deg. Ka= 0.333 (1-sinF)/(1+sinF)

Ko= 0.500 1-sinF

Kp= 3.000 1/Ka

Fill Soil Weight= 120 pcf

Passive Soil Weight= 120 pcf

Load and Resistance Factors [Tables 3.4.1-1 and 3.4.1-2]

MAX MIN

Load Factors: hi= 1.00 1.00 Typical structure gp: DC= 1.25 0.90 DL Components

LL= 1.75 1.75 Live Load

LS= 1.75 1.75 Live Load Surcharge

EV= 1.35 1.00 Vertical Earth

EHa= 1.50 0.90 Horizontal Earth, active pressure

EHo= 1.35 0.90 Horizontal Earth, at-rest pressure

ES= 1.50 0.75 Earth Surcharge

Concrete Resist. Factors: Fb= 0.90 Flexure

Fv= 0.90 Shear

Wall Data Concrete Density= 150 pcf

Wall Height= 3.333 ft

Wall Thickness= 0.833 ft

Depth & Top of Wall = 0.00 ft From FG

Depth & Bottom of Wall = 3.33 ft From FG

Unsupported Span = 4.33 ft

Unsupported Cantilever = 1.50 ft

HORIZ Forces…