2017 MT ST HELENS HAUL ROAD BRIDGE DESIGN LOAD RATING.PDF

DESIGN LOAD RATING

of

Mt St Helens Haul Rd Bridge

Cowlitz County, Washington

Bridge No. CENNWPWA000BD14 for the

US Army Corps of Engineers

Portland District

June 2017

Prepared by:

US Army Corps of Engineers Kansas City District Sacramento District

TABLE OF CONTENTS

Executive Summary 1

Load Rating Results for Girders 1

Explanation of Assumptions 2

Interior Girder Load Rating at Mid-Span 3

Exterior Girder Load Rating at Mid-Span 13

Design Load STAAD Pro Report 24

Load Rating ATR Checklist & Certification 30

EXECUTIVE SUMMARY

The Design Load Rating for the Mt St Helens Haul Rd Bridge is included in this report. The rating is based on the July 2012 inspection results. The load rating was performed using the Load and Resistance Factor Rating (LRFR) method in accordance with the Engineering and Design USACE Bridge Safety Program (ER 1110-2-111 publication date 1 Aug 07), and the AASHTO Manual for Bridge Evaluation, Second Edition/2011 with Interim Revisions. Based on this load rating, the bridge evaluated herein meets the criteria for the Design Load Rating. No posting is required.

Rating Factors for NBI Data:

The appropriate values for reporting in the National Bridge Inventory (NBI) based on the controlling HL-93 rating factors for the interior span are as follows:

• NBI Item #63- 8

• NBI Item #64 – Operating Rating: 382

• NBI Item #65- 8

• NBI Item #66 – Inventory Rating: 294

Load Rating Results for Girders for Strength I Limit State:

Exterior Beam

General Load Rating Equation

RF f.inv RF v.inv RF f.op RF v.op Design Load HL-93 2.94 3.52 3.82 4.57

Interior Beam

RF f.inv RF v.inv RF f.op RF v.op Design Load HL-93 3.09 4.19 4.01 5.44

Load Rating Results for Girders for Service III Limit State:

Exterior Beam-Midspan General Load Rating Equation

RF

Design Load HL-93 3.5

Interior Beam-Midspan

RF

Design Load HL-93 3.73

EXPLANATION OF ASSUMPTIONS

The material properties and prestressed strand configuration were taken directly from the as-built design drawings.

Live load effects on the girders resulting from the HL-93 design truck and design tandem were analyzed using STAAD Pro V8i. The girders were analyzed as being simply supported and the span length was taken as the centerline to centerline distance between bearings.

The procedure in the current MBE (Article 6A.5.6) for reducing the flexural resistance of concrete members which do not satisfy the minimum flexural reinforcement provisions of LRFD 5.7.3.3.2 does not appear to be consistent with the most current edition of the LRFD Design Specification. The 2010 LRFD requires that the flexural resistance, Mr, be greater that the members cracking moment, Mcr, with a factor of 1.2 applied to it. The current method for determining that cracking moment per the 2014 LRFD includes gamma factors that replace the

1.2 factor; however, the current MBE still includes a factor of 1.2 in determining the reduction ratio, K.

Additionally. Article 5.4.2.6 of the 2010 LRFD requires that the modulus of rupture, fr, be calculated as 0.37√f’c when evaluating minimum reinforcement, whereas the 2014 LRFD reduces this value to 0.24√f’c. This revision appears to be independent of the revisions to Article 5.7.3.3.2. It is considered appropriate to continue to use requirements from the 2010 LRFD for determining Mr until MBE has been revised to be consistent with it;

however, it is not necessary to apply this approach to the determination of fr.

REFERENCES

1. ER 1110-2-111 (dated 1 August 2007) Engineering and Design USACE Bridge Safety Program

2. AASHTO Manual for Bridge Evaluation, Second Edition 2011 with 2016 Interim Revisions

3. July 2012 Routine Bridge Inspection Report for CENNWPWA000BD14

4. As-Built Plans: Haul Road Bridge, Mt St Helens Sediment Control, Cowlitz and Toutle Rivers (1986).

5. AASHTO LRFD Bridge Design Specifications, 2014 with 2015 Interim Revisions

Design Load Rated by: Brad Ninnis, P.E. Date: November 2016 Design Load Checked by: Brett Meyring P.E. Date: March 2017

ATR by: Jose A. Albarran-Garcia, P.E. Date: April 2017

References: 1. AASHTO LRFD Bridge Design Specifications, 7th Ed with 2015 Interim Rev

2. AASHTO Manual for Bridge Evaluation (MBE), 2nd Ed w/ 2016 Interim Rev

3. "Haul Road Bridge for Granite Construction" As-Build Drawings, 1986

4. 2012 USACE Bridge Inspection Report for CENNWPWA000BD14

Bridge Data:

Span Length: L = 90 ft Box Beam Elevation Year Built: 1986 P/S Beam Conc: f'ci = 3.5 ksi General Notes P/S Beam Conc: f'c = 5 ksi General Notes Prestressing Steel: fpu = 270 ksi 1/2" dia, 7 wire, ASTM 416, Gr 270 low relax strands fpy = 243 ksi Table 6A.5.4.2.2b-1 MBE Reinforcing Steel: fy = 60 ksi General Notes ADTT: 0 Inspection report Skew: 0 deg Superstructure Condition Rating = 7 Inspection report

Bridge is in GOOD Condition

48 in x 60 in Deep Non-Composite Adjacent Box Beam Section Properties:

b = 48 in o/o width of beam d = 60 in o/o depth of beam SW = 5 in stem thickness TH1 = 6.5 in top flange thickness BH1 = 5.5 in bottom flange thickness SS = 3 in fillet

A1 = b x d = 2880 in^2 A2 = (b - 2SW) x (d - TH1 - BH1) = 1824 in^2 void A3 = 18 in^2 total area for 4 fillets

A = A1 - A2 + A3 = 1074 in^2 (note: Area verified by LEAP CONSPAN Program)

Determine C.G.

Top flange area, Atop = 312 in^2 y(top) = 56.75 in Bott flange area, Ab = 264 in^2 Yb = 2.75 in total stem area, Astem = 498 in^2 (incl fillets) y(stem) = 29.5 in y(top fillet) = 52.5 Y(bott fillet) = 6.5

CG = 30.9 in (from bottom side of box-verified by CONSPAN)

Determine Ixx

Top flange 209583.9 in^4 Bott flange 209865 in^4 Stems 93100.8 in^4 Top fillets 4212.54 in^4 Bott fillets 5371.74 in^4

Ʃ = 522135 in^4 (note: Ixx verified by LEAP CONSPAN Program)

Determine Section Modulus yb = 30.9 in Sb = Ixx/yb = 16898 in^3 ytop = 29.1 in Stop = 17943 in^3

Dead Load Analysis- Interior Girder

Components and Attachments, DC:

ϒconc = 150 pcf

Beam Self Wt = A* ϒconc = 1.12 kpf 9-inch Thick Conc Diaphragms spaced 22.5' = 0.1 kpf

Tot DC = 1.22 kpf

Maximum Mid-Span Moment, Mdc:

Mdc = 1/8* (Tot DC) L^2 = 1236 ft-k

Maximum Shear at Critical Section (x), Vdc: x = 3.6 ft from bearing CL ( = dv ) Vdc = Tot DC * (L/2 - x ) = 50.6 k

Live Load Analysis- Interior Girder

Live Load Distribution Factors for an Interior Beam per LRFD Design Table 4.6.2.2.2b-1 (ref: cross section Type "g")

Nb = 7 k = 2.5(Nb)^-0.2 = 1.695 > 1.5, OK Table 4.6.2.2.2b-1

LRFD

I = 522135 in^4 b = 48 in d = 60 in

Per Table 4.6.2.2.1-3, I/J = 0.54(d/b) + 0.16 = 0.835

For One Design Lane Loaded:

gm1 = k (b/33.3L)^.5(I/J)^.25 = 0.206 Table 4.6.2.2.2b-1 LRFD gv1 = (b/130L)^0.15(I/J)^.05 = 0.435 Table 4.6.2.2.3a-1 LRFD

For Two Design Lanes Loaded:

gm2 = k (b/305)^0.6 (b/12L)^0.2 (I/J)^.06 = 0.297 Table 4.6.2.2.2b-1 LRFD

(Controls) gv2 = (b/156)^0.4(b/12L)^0.1 (I/J)^.05 (b/48) = 0.454 ( Controls)

Maximum Live Load (HL-93) Effects on Interior Beam

Reference STAAD Output:

Design Lane Load, M(DLL) = 648 ft-k (at mid-span) V(DLL) = 26.5 k (at critical section)

HL-93 Design Truck, M(Dtruck) = 1340 ft-k (controls at mid-span) V(Dtruck) = 61.3 k (controls)

HL-93 Tandem Truck, M(tand) = 1075 ft-k (mid-span) V(tand) = 48.9 k

IM = 33 %

M(LL + IM) = M(DLL) + M(Dtruck) x IM = 2430.2 ft-k

V(LL + IM) = V(DLL) + V(Dtruck) x IM = 108.1 k (at critical section) gm x M(LL + IM) = 722 ft-k gv x V(LL + IM) = 49.1 k

Compute Nominal Flexural Resistance

LRFD Design Eq 5.7.3.1.1-1 k = 0.28 LRFD Design Table C5.7.3.1.1-1 fpu = 270 ksi

Calculate CG of (30) 1/2" 7-wire, 270k Strands as shown on precast shop drawings section (above):

Row # of Strands, n y n * y

(IN)

1 18 1.75 31.5 2 4 3.25 13 3 8 3.25 26

Ʃ n = 30 Ʃ(n* y) = 70.5

CGstrand = Ʃ(n* y) /Ʃn = 2.4 in (from bottom of beam) dp = d - CG = 57.6 in

As = 0.153 in^2 1/2" A416 strand area n = 30 total number of strands

Aps = As * n = 4.59 in^2

LRFD Design Eq 5.7.3.1.1-4 β1 = 0.8 5.7.2.2 c = 7.33 in a = β1 c = 5.864 in LRFD 5.7.2.2 a < TH1, OK fps = 260.4 ksi LRFD 5.7.3.1.1-1

Mn = Aps*fps ( dp - a/2 ) = 5445.1 ft-k LRFD Eq 5.7.3.2.2-1 Neglects nonprestressed reinforcement.

Check Maximum Reinforcement (C6A.5.5) ϵc = 0.003 c = 7.33 in d = 57.6 in

LRFD Design C5.7.2.1

Ref LRFD Design 5.7.2.1 and 5.5.4.2 :

ϵt = 0.0206 > 0.005, so section is tensioned controlled φ = 1

Check Minimum Reinforcement per LRFD Design 5.7.3.3.2

Amount of reinforcement must be sufficient to develop Mr equal to the lesser of:

1.33Mu and 1.2Mcr

Mr = φMn = 5445.1 ft-k

Mu = 1.75*gm x M(LL + IM) + 1.25* Mdc 2808.5 ft-k

1.33Mu = 3735.4 ft-k 1.33Mu < Mr, OK

Minimum reinforcement check is satisfied

Determine Modulus of Rupture, fr for determining Mcre, fr = 0.2√f'c = 0.448 ksi LRFD 5.4.2.6 for checking cracking moment, fr = 0.24√f'c = 0.537 ksi LRFD 5.4.2.6

Determine Effective Prestress Force, Ppe: Ppe = Aps fpe

Total Prestress Losses:

ΔfpT = ΔfpES + ΔfpLT immediately before transfer LRFD Design Eq 5.9.5.1-1

Effective Prestress:

fpe = Initial Prestress - Total Prestress Losses

Initial Prestress , pi = 31 k /strand (general notes) n = 30 total number of strands

As = 0.153 in^2 1/2" strand area

Pi = n * pi = 930 k e = yb - CGstrand = 28.5 in

Loss Due to Elastic Shortening, ΔfpES (LRFD Design 5.9.5.2.3a)

Ep = 28500 ksi LRFD 5.4.4.2 f'ci = 3.5 ksi (at release)

Ect = 3404 ksi LRFD Design Eq C 5.4.2.4-1

Beam wt = 1.22 kpf

Md = 1/8(Beam wt)L^2 = 14832 in-k

I = 522135 in^4 A = 1074 in^2 fcgp = Pi/A + Pi * e^2/I - Md * e/I = 1.504 ksi

ΔfpES = (Ep/Ect) fcgp = 12.6 ksi LRFD Eq 5.9.5.2.3a-1

Approximate Lump Sum Estimate of Time-Dependent Losses, ΔfpLT (LRFD 5.9.5.3)

LRFD Eq 5.9.5.3-1

ϒh = 1.7 - 0.01 H 5.9.5.3-2 H = 70 % Fig 5.4.2.3.3-1 LRFD

ϒh = 1 f'ci = 3.5 ksi

ϒst = 5/(1 + f'ci) = 1.12 5.9.5.3-3

Aps = 4.59 in^2 Ag = 1074 in^2 ΔfpR = 2.4 ksi Page 5-107 LRFD fpi = pi/As = 202.7 ksi

ΔfpLT = 25.6 ksi LRFD Eq 5.9.5.3-1

ΔfpT = ΔfpES + ΔfpLT 38.2 ksi LRFD Eq 5.9.5.1-1 fpe = fpi - ΔfpT = 164.5 ksi

Ppe = fpe * Aps = 755.1 k e = 28.5 in fcpe = Ppe/A + Ppe*e/Sb = 1.98 ksi

LRFD Eq 5.7.3.3.2-1

Mcr = 42532.27 in-kip Sc*fr = 9074.226 in-k < Mcr, OK 1.2Mcr = 4253.3 ft-k 1.2Mcr < Mr, OK

Compute Nominal Shear Resistance at Critical Section at distance "x" from bearing centerline (Reference 5.8.3.3 LRFD) x = 3.6 ft ( = dv)

Determine Vi: V(LL + IM)*gv = 49.1 k Vd = Vdc = 50.6 k Vu = 1.75V(LL + IM) + 1.25Vd = 149.2 k (for Strength I limit state) Vi = Vu - Vd = 98.6 k

Determine Mmax: M(DLL) = 99.5 ft-k Design lane load moment at critical section M(Dtruck) = 221 ft-k at critcial section M(LL + IM) = M(DLL) + M(Dtruck) x IM = 393.43 ft-k Md = (Tot DC * x /2) * ( L - x ) = 189.8 ft-k at critical section Mu = gm * 1.75 M(LL + IM) + 1.25 Md = 5300.9 in-k Mmax = Mu - Md = 3023.3 in-k

Determine Mcre: Sc = Snc = 16898 in^3 fr = 0.448 ksi fcpe = 1.98 ksi Mdnc = Md = 2277.6 in-k at critical section

Mcre = Sc ( fr + fcpe - Mdnc/Snc ) = 38750.74 in-k Eq 5.8.3.4.3-2

Determine bv :

bv = 2*SW = 10 in effective web width

Determine dv:

de = dp = 57.6 in h = 60 in dv1 = 0.9de = 51.84 in 5.8.2.9 LRFD dv2 = 0.72h = 43.2 in (use dv2 to be conservative) dv = 43.2 in f'c = 5 ksi

Check Minimum Transv Reinf per 5.8.2.5 AASHTO Bridge Design Specs Av > 0.0316 √f'c bv * s/fy 5.8.2.5-1 s = 12 in Stirrup spacing at critical section shown on box beam elevation bv = 10 in f'c = 5 ksi Av,prov = 0.4 in^2 Av= 0.15 in^2 Av < Av,prov OK

Vci = 0.02√f'c bv dv + Vd + Vi Mcre/Mmax = 1333.8 k Eq 5.8.3.4.3-1

Compare Vcw with Vci : assume Vp = 0 fpc = 1.98 ksi

Vcw = (0.06√f'c + 0.30fpc)bv dv + Vp = 314.6 k Eq 5.8.3.4.3-3

Vc is lesser of Vci and Vcw, Vc = 314.6 k 5.8.3.4.3 cotθ = 3.66 Eq 5.8.3.4.3-4 α = 90 deg

(cotθ)max = 1.8 Use cotθ = 1.8

Av' = 0.2 in^2 ( #4 stirrup) n = 2 (number of stirrup legs)

Av = nAv' = 0.4 in^2

Vs = Av fy dv cotθ/s = 155.52 k C5.8.3.3-1

Vp = 0

Vn = Vc + Vs + Vp = 470.2 k (controls) Eq 5.8.3.3-1

Vn,max = 0.25f'c bv dv + Vp = 540 k > Vn, so Vn controls Eq 5.8.3.3-2

Evaluation Factors for Strength I Limit States φf = 1 5.5.4.2 LRFD for tension controlled flexural section φv = 0.9 shear per 5.5.4.2 LRFD φc = 1 Table 6A.4.2.3-1 MBE φs = 1 Table 6A.4.2.4-1 MBE (for shear and flexure)

Check Lower Limit requirement of φcφs > 0.85 6A.4.2.1-3 MBE φcφs = 1 > 0.85, OK

Design Load Rating for Flexure at Midspan (6A.4.3 MBE):

Load Inventory Operating Mn = 5445.1 ft-k DC 1.25 1.25 M(LL + IM)= 722 ft-k DW 1.5 1.5 Mdc = 1236 ft-k

LL + IM 1.75 1.35

Inventory:

RF = 3.09

Operating:

RF = 4.01

Design Load Rating for Shear at Critical Section (6A.4.3 MBE):

Load Inventory Operating Vn = 470.2 k DC 1.25 1.25 V(LL + IM)= 49.1 k

Vdc = 50.6 k

LL + IM 1.75 1.35

Inventory:

RF = 4.19

Operating:

RF = 5.44

Service III Limit State for Inventory Level (6A.5.4.1 MBE)

RF = -0.96

fpb = 1.98 ksi compressive stress due to effective prestress

Allowable Tensile Stress, ft = 0.19√f'c = 0.425 ksi Table 5.9.4.2.2-1 LRFD fr = fpb + ft = 2.405 ksi

Dead Load Stress : Sb = 16898 in^3 fdc = Mdc/Sb = 0.878 ksi

Live Load Stress: Sb= 16898 in^3 f(LL + IM) = M(LL + IM)/Sb = 0.513 ksi

ϒL = 0.8

ϒD = 1

RF = 3.73

References: 1. AASHTO LRFD Bridge Design Specifications, 7th Ed with 2015 Interim Rev

2. AASHTO Manual for Bridge Evaluation (MBE), 2nd Ed w/ 2016 Interim Rev

3. "Haul Road Bridge for Granite Construction" As-Build Drawings, 1986

4. 2012 USACE Bridge Inspection Report for CENNWPWA000BD14

Bridge Data:

Span Length: L = 90 ft Box Beam Elevation Year Built: 1986 P/S Beam Conc: f'ci = 3.5 ksi General Notes P/S Beam Conc: f'c = 5 ksi General Notes Prestressing Steel: fpu = 270 ksi 1/2" dia, 7 wire, ASTM 416, Gr 270 low relax strands fpy = 243 ksi Table 6A.5.4.2.2b-1 MBE Reinforcing Steel: fy = 60 ksi General Notes ADTT: 0 Inspection report Skew: 0 deg Superstructure Condition Rating = 7 Inspection report

Bridge is in GOOD Condition

48 in x 60 in Deep Non-Composite Adjacent Box Beam Section Properties:

b = 48 in o/o width of beam d = 60 in o/o depth of beam SW = 5 in stem thickness TH1 = 6.5 in top flange thickness BH1 = 5.5 in bottom flange thickness SS = 3 in fillet

A1 = b x d = 2880 in^2 A2 = (b - 2SW) x (d - TH1 - BH1) = 1824 in^2 void A3 = 18 in^2 total area for 4 fillets

A = A1 - A2 + A3 = 1074 in^2 (note: Area verified by LEAP CONSPAN Program)

Determine C.G.

Top flange area, Atop = 312 in^2 y(top) = 56.75 in Bott flange area, Ab = 264 in^2 Yb = 2.75 in total stem area, Astem = 498 in^2 (incl fillets) y(stem) = 29.5 in y(top fillet) = 52.5 Y(bott fillet) = 6.5

CG = 30.9 in (from bottom side of box-verified by CONSPAN)

Determine Ixx

Top flange 209583.9 in^4 Bott flange 209865 in^4 Stems 93100.8 in^4 Top fillets 4212.54 in^4 Bott fillets 5371.74 in^4

Ʃ = 522135 in^4 (note: Ixx verified by LEAP CONSPAN Program)

Determine Section Modulus yb = 30.9 in Sb = Ixx/yb = 16898 in^3 ytop = 29.1 in Stop = 17943 in^3

Dead Load Analysis- Exterior Girder

Components and Attachments, DC:

ϒconc = 150 pcf

Beam Self Wt = A* ϒconc = 1.12 kpf 12" x 24" timber curb 0.1 kpf (inspection report photos) 2"x 9 ga x 8' ht chain link fence mesh (assume 0.71 psf) 0.01 kpf (inspection report photos) 2-1/2" dia x 8' std pipe fence posts at 6' (assumed) 0.01 kpf 9-inch Thick Conc Diaphragms spaced 22.5' = 0.1 kpf

Tot DC = 1.34 kpf

Maximum Mid-Span Moment, Mdc:

Mdc = 1/8* (Tot DC) L^2 = 1357 ft-k

Maximum Shear at Critical Section (x), Vdc: x = 3.6 ft from bearing CL ( = dv ) Vdc = Tot DC * (L/2 - x ) = 55.5 k

Live Load Analysis- Exterior Girder

Live Load Distribution Factors for an Exterior Beam per LRFD Design Table 4.6.2.2.2d-1 (ref: cross section Type "g") de = horiz distance from centerline of the exterior web of the exterior beam to the interior edge of curb de = -0.79 ft CL of exterior web is outboard of the int face of curb (4.6.2.2.2d LRFD)

For Moment with One Design Lane Loaded:

e = 1.125 + de/30 = 1.099 > 1 OK Table 4.6.2.2.2d-1 LRFD ginterior 0.206 (see calculations for LL distrib for moment for interior girder) gm1 = e ginterior = 0.227 Table 4.6.2.2.2d-1 LRFD

For Shear with One Design Lane Loaded:

e = 1.25 + de/20 = 1.2105 > 1.0 OK Table 4.6.2.2.3b-1 LRFD ginterior = 0.435 (see calculations for LL distrib for shear for interior girder) gv1 = e ginterior = 0.527

For Moment with Two Design Lanes Loaded:

e = 1.04 + de/25 = 1.009 > 1 OK Table 4.6.2.2.2d-1 LRFD ginterior = 0.297 (see calculations for LL distrib for moment for interior girder) gm2 = e ginterior = 0.3 (controls) Table 4.6.2.2.2d-1 LRFD

For Shear with Two Design Lanes Loaded:

e = 1 + ((de + b/12 -2 )/40)^0.5 = 1.174 Table 4.6.2.2.3b-1 LRFD

48/b = 1 <= 1 OK ginterior = 0.454 (see calculations for LL distrib for shear for interior girder) gv2 = e ginterior (48/b) = 0.533 (controls)

Maximum Live Load (HL-93) Effects on Exterior Beam

Reference STAAD Output:

Design Lane Load, M(DLL) = 648 ft-k (at mid-span) V(DLL) = 26.5 k (at critical section)

HL-93 Design Truck, M(Dtruck) = 1340 ft-k (controls at mid-span) V(Dtruck) = 61.3 k (controls)

HL-93 Tandem Truck, M(tand) = 1075 ft-k (mid-span) V(tand) = 48.9 k

IM = 33 %

M(LL + IM) = M(DLL) + M(Dtruck) x IM = 2430.2 ft-k

V(LL + IM) = V(DLL) + V(Dtruck) x IM = 108.1 k (at critical section) gm x M(LL + IM) = 730 ft-k gv x V(LL + IM) = 57.7 k

Compute Nominal Flexural Resistance

LRFD Design Eq 5.7.3.1.1-1 k = 0.28 LRFD Design Table C5.7.3.1.1-1 fpu = 270 ksi

Calculate CG of (30) 1/2" 7-wire, 270k Strands as shown on precast shop drawings section (above):

Row # of Strands, n y n * y

(IN)

1 18 1.75 31.5 2 4 3.25 13 3 8 3.25 26

Ʃ n = 30 Ʃ(n* y) = 70.5

CGstrand = Ʃ(n* y) /Ʃn = 2.4 in (from bottom of beam) dp = d - CG = 57.6 in

As = 0.153 in^2 1/2" A416 strand area n = 30 total number of strands

Aps = As * n = 4.59 in^2

LRFD Design Eq 5.7.3.1.1-4 β1 = 0.8 5.7.2.2 c = 7.33 in a = β1 c = 5.864 in LRFD 5.7.2.2 a < TH1, OK fps = 260.4 ksi LRFD 5.7.3.1.1-1

Mn = Aps*fps ( dp - a/2 ) = 5445.1 ft-k LRFD Eq 5.7.3.2.2-1 Neglects nonprestressed reinforcement.

Check Maximum Reinforcement (C6A.5.5) ϵc = 0.003 c = 7.33 in d = 57.6 in

LRFD Design C5.7.2.1

Ref LRFD Design 5.7.2.1 and 5.5.4.2 :

ϵt = 0.0206 > 0.005, so section is tensioned controlled φ = 1

Check Minimum Reinforcement per LRFD Design 5.7.3.3.2

Amount of reinforcement must be sufficient to develop Mr equal to the lesser of:

1.33Mu and 1.2Mcr

Mr = φMn = 5445.1 ft-k

Mu = 1.75*gm x M(LL + IM) + 1.25* Mdc 2973.75 ft-k

1.33Mu = 3955.1 ft-k 1.33Mu < Mr, OK

Minimum reinforcement check is satisfied

Determine Modulus of Rupture, fr for determining Mcre, fr = 0.2√f'c = 0.448 ksi LRFD 5.4.2.6 for checking cracking moment, fr = 0.24√f'c = 0.537 ksi LRFD 5.4.2.6

Determine Effective Prestress Force, Ppe: Ppe = Aps fpe

Total Prestress Losses:

ΔfpT = ΔfpES + ΔfpLT immediately before transfer LRFD Design Eq 5.9.5.1-1

Effective Prestress:

fpe = Initial Prestress - Total Prestress Losses

Initial Prestress , pi = 31 k /strand (general notes) n = 30 total number of strands

As = 0.153 in^2 1/2" strand area

Pi = n * pi = 930 k e = yb - CGstrand = 28.5 in

Loss Due to Elastic Shortening, ΔfpES (LRFD Design 5.9.5.2.3a)

Ep = 28500 ksi LRFD 5.4.4.2 f'ci = 3.5 ksi (at release)

Ect = 3404 ksi LRFD Design Eq C 5.4.2.4-1

Beam wt = 1.34 kpf

Md = 1/8(Beam wt)L^2 = 16284 in-k

I = 522135 in^4 A = 1074 in^2 fcgp = Pi/A + Pi * e^2/I - Md * e/I = 1.424 ksi

ΔfpES = (Ep/Ect) fcgp = 11.93 ksi LRFD Eq 5.9.5.2.3a-1

Approximate Lump Sum Estimate of Time-Dependent Losses, ΔfpLT (LRFD 5.9.5.3)

LRFD Eq 5.9.5.3-1

ϒh = 1.7 - 0.01 H 5.9.5.3-2 H = 70 % Fig 5.4.2.3.3-1 LRFD

ϒh = 1 f'ci = 3.5 ksi

ϒst = 5/(1 + f'ci) = 1.12 5.9.5.3-3

Aps = 4.59 in^2 Ag = 1074 in^2 ΔfpR = 2.4 ksi Page 5-107 LRFD fpi = pi/As = 202.7 ksi

ΔfpLT = 25.6 ksi LRFD Eq 5.9.5.3-1

ΔfpT = ΔfpES + ΔfpLT = 37.53 ksi LRFD Eq 5.9.5.1-1 fpe = fpi - ΔfpT = 165.2 ksi

Ppe = fpe * Aps = 758.3 k e = 28.5 in fcpe = Ppe/A + Ppe*e/Sb = 1.99 ksi

LRFD Eq 5.7.3.3.2-1

Mcr = 42701.25 in-kip Sc*fr = 9074.226 in-k < Mcr, OK 1.2Mcr = 4270.2 ft-k 1.2Mcr < Mr, OK

Compute Nominal Shear Resistance at Critical Section at distance "x" from bearing centerline (Reference 5.8.3.3 LRFD) x = 3.6 ft ( = dv)

Determine Vi: V(LL + IM)*gv = 57.7 k Vd = Vdc = 55.5 k Vu = 1.75V(LL + IM) + 1.25Vd = 170.4 k (for Strength I limit state) Vi = Vu - Vd = 114.9 k

Determine Mmax: M(DLL) = 99.5 ft-k Design lane load moment at critical section M(Dtruck) = 221 ft-k at critcial section M(LL + IM) = M(DLL) + M(Dtruck) x IM = 393.43 ft-k Md = (Tot DC * x /2) * ( L - x ) = 208.4 ft-k at critical section Mu = gm * 1.75 M(LL + IM) + 1.25 Md = 5604.7 in-k Mmax = Mu - Md = 3103.9 in-k

Determine Mcre: Sc = Snc = 16898 in^3 fr = 0.448 ksi fcpe = 1.99 ksi Mdnc = Md = 2500.8 in-k at critical section

Mcre = Sc ( fr + fcpe - Mdnc/Snc ) = 38696.52 in-k Eq 5.8.3.4.3-2

Determine bv :

bv = 2*SW = 10 in effective web width

Determine dv:

de = dp = 57.6 in h = 60 in dv1 = 0.9de = 51.84 in 5.8.2.9 LRFD dv2 = 0.72h = 43.2 in (use dv2 to be conservative) dv = 43.2 in f'c = 5 ksi

Check Minimum Transv Reinf per 5.8.2.5 AASHTO Bridge Design Specs Av > 0.0316 √f'c bv * s/fy 5.8.2.5-1 s = 12 in Stirrup spacing at critical section shown on box beam elevation bv = 10 in f'c = 5 ksi Av,prov = 0.4 in^2 Av= 0.15 in^2 Av < Av,prov OK

Vci = 0.02√f'c bv dv + Vd + Vi Mcre/Mmax = 1507.3 k Eq 5.8.3.4.3-1

Compare Vcw with Vci : assume Vp = 0 fpc = 1.99 ksi

Vcw = (0.06√f'c + 0.30fpc)bv dv + Vp = 315.9 k Eq 5.8.3.4.3-3

Vc is lesser of Vci and Vcw, Vc = 315.9 k 5.8.3.4.3 cotθ = 3.67 Eq 5.8.3.4.3-4 α = 90 deg

(cotθ)max = 1.8 Use cotθ = 1.8

Av' = 0.2 in^2 ( #4 stirrup) n = 2 (number of stirrup legs)

Av = nAv' = 0.4 in^2 s = 12 in Stirrup spacing at critical section shown on box beam elevation

Vs = Av fy dv cotθ/s = 155.52 k C5.8.3.3-1

Vp = 0

Vn = Vc + Vs + Vp = 471.5 k (controls) Eq 5.8.3.3-1

Vn,max = 0.25f'c bv dv + Vp = 540 k > Vn, so Vn controls Eq 5.8.3.3-2

Evaluation Factors for Strength I Limit States φf = 1 5.5.4.2 LRFD for tension controlled flexural section φv = 0.9 shear per 5.5.4.2 LRFD φc = 1 Table 6A.4.2.3-1 MBE φs = 1 Table 6A.4.2.4-1 MBE (for shear and flexure)

Check Lower Limit requirement of φcφs > 0.85 6A.4.2.1-3 MBE φcφs = 1 > 0.85, OK

Design Load Rating for Flexure at Midspan (6A.4.3 MBE):

Load Inventory Operating Mn = 5445.1 ft-k DC 1.25 1.25 M(LL + IM)= 730 ft-k DW 1.5 1.5 Mdc = 1357 ft-k

LL + IM 1.75 1.35

Inventory:

RF = 2.94

Operating:

RF = 3.82

Design Load Rating for Shear at Critical Section (6A.4.3 MBE):

Load Inventory Operating Vn = 471.5 k DC 1.25 1.25 V(LL + IM)= 57.7 k

Vdc = 55.5 k

LL + IM 1.75 1.35

Inventory:

RF = 3.52

Operating:

RF = 4.57

Service III Limit State for Inventory Level (6A.5.4.1 MBE)

RF = -0.9

fpb = 1.99 ksi compressive stress due to effective prestress

Allowable Tensile Stress, ft = 0.19√f'c = 0.425 ksi Table 5.9.4.2.2-1 LRFD fr = fpb + ft = 2.415 ksi

Dead Load Stress : Sb = 16898 in^3 fdc = Mdc/Sb = 0.964 ksi

Live Load Stress: Sb= 16898 in^3 f(LL + IM) = M(LL + IM)/Sb = 0.519 ksi

ϒL = 0.8

ϒD = 1

RF = 3.5

BD14 with HL-93.ANL

� PAGE NO. 1

* STAAD.Pro V8i SELECTseries4 *

* Version 20.07.09.31 *

* Proprietary Program of *

* Bentley Systems, Inc. *

* Date= NOV 21, 2016 *

* Time= 17:16: 8 *

* USER ID: US Army Corps of Engineers *

1. STAAD PLANE

INPUT FILE: BD14 with HL-93.STD

2. START JOB INFORMATION

3. ENGINEER DATE 6/8/16

4. JOB NAME BRIDGE BD14 DESIGN LOAD RATING

5. ENGINEER NAME BN

6. ENGINEER NAME BN

7. JOB NO BRIDGE BD14 DESIGN LOAD RATING

8. JOB COMMENT HL-93

9. END JOB INFORMATION

10. INPUT WIDTH 79

11. UNIT FEET KIP

12. JOINT COORDINATES

13. 1 0 0 0; 2 90 0 0; 3 3.6 0 0; 4 86.4 0 0

14. MEMBER INCIDENCES

15. 1 1 3; 2 3 4; 3 4 2

16. DEFINE MATERIAL START

17. ISOTROPIC CONCRETE

18. E 453600

19. POISSON 0.17

20. DENSITY 0.150336

21. ALPHA 5E-006

22. DAMP 0.05

23. TYPE CONCRETE

24. STRENGTH FCU 576

25. END DEFINE MATERIAL

26. MEMBER PROPERTY AMERICAN

27. 1 TO 3 PRIS YD 1.33 ZD 3.375

28. CONSTANTS

29. MATERIAL CONCRETE ALL

30. SUPPORTS

31. 1 2 PINNED

32. DEFINE MOVING LOAD

33. *HL93 DESIGN TRUCK

34. TYPE 1 LOAD 8 32 32

35. DIST 14 14

36. LOAD 1

37. MEMBER LOAD

38. 1 TO 3 UNI GY -0.64

� STAAD PLANE -- PAGE NO. 2

39. LOAD GENERATION 220

40. TYPE 1 -15 0 0 XINC 0.5

41. PERFORM ANALYSIS PRINT LOAD DATA

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 2 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 2 WHEEL 2 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 3 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 3 WHEEL 2 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 4 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 5 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 6 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 7 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 8 WHEEL 1 OF 3

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 9 WHEEL 1 OF 3

*ADDITIONAL MOVING LOAD MESSAGES SUPPRESSED

*ADDITIONAL MOVING LOAD MESSAGES SUPPRESSED

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

NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3

NUMBER OF PLATES 0 NUMBER OF SOLIDS 0

NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2

SOLVER USED IS THE IN-CORE ADVANCED SOLVER

TOTAL PRIMARY LOAD CASES = 221, TOTAL DEGREES OF FREEDOM = 8

� STAAD PLANE -- PAGE NO. 3

LOADING 1

MEMBER LOAD - UNIT KIP FEET

MEMBER UDL L1 L2 CON L LIN1 LIN2

1 -0.6400 GY 0.00 3.60

2 -0.6400 GY 0.00 82.80

3 -0.6400 GY 0.00 3.60

LOADING 2

MEMBER LOAD - UNIT KIP FEET

MEMBER UDL L1 L2 CON L LIN1 LIN2

2 -32.0000 GY 9.40

2 MAX 56.18 0.00 12 0.00 0.00 213

0.00 0.00 1 0.00 0.00 1 0.00 0.00 1

MIN -61.33 82.80 148 -1340.00 41.40 94

0.00 82.80 221 0.00 82.80 221 0.00 82.80 221

3 MAX 0.31 0.00 205 0.00 0.00 213

0.00 0.00 1 0.00 0.00 1 0.00 0.00 1

MIN -64.53 3.60 156 -220.80 0.00 148

0.00 3.60 221 0.00 3.60 221 0.00 3.60 221

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

43. FINISH

*********** END OF THE STAAD.Pro RUN ***********

**** DATE= NOV 21,2016 TIME= 17:16:30 ****

� STAAD PLANE -- PAGE NO. 56

* For questions on STAAD.Pro, please contact *

* Bentley Systems or Partner offices *

* Telephone Web / Email *

* USA +1 (714) 974-2500 *

* UK +44 (0) 808 101 9246 *

* SINGAPORE +65 6225-6158 *

* FRANCE +33 (0) 1 55238400 *

* GERMANY +49 0931 40468 *

* INDIA +91 (033) 4006-2021 *

* JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp *

* CHINA +86 21 6288 4040 *

* THAILAND +66 (0)2645-1018/19 partha.p@reisoftwareth.com*

* Worldwide http://selectservices.bentley.com/en-US/ *

BD14 with Tandem.ANL

� PAGE NO. 1

* STAAD.Pro V8i SELECTseries4 *

* Version 20.07.09.31 *

* Proprietary Program of *

* Bentley Systems, Inc. *

* Date= NOV 21, 2016 *

* Time= 12:45:34 *

* USER ID: US Army Corps of Engineers *

1. STAAD PLANE

INPUT FILE: BD14 with Tandem.STD

2. START JOB INFORMATION

3. ENGINEER DATE 03-MAY-16

4. JOB NAME BD14 BRIDGE LOAD RATING

5. JOB COMMENT ASSUME SPAN = 90'

6. JOB COMMENT (CENTERLINE TO CENTERLINE OF BEARINGS)

7. JOB COMMENT TANDEM LOADING

8. ENGINEER NAME BN

9. ENGINEER NAME BN

10. CHECKER NAME KM

11. END JOB INFORMATION

12. INPUT WIDTH 79

13. UNIT FEET KIP

14. JOINT COORDINATES

15. 1 0 0 0; 2 90 0 0

16. MEMBER INCIDENCES

17. 1 1 2

18. DEFINE MATERIAL START

19. ISOTROPIC CONCRETE

20. E 453600

21. POISSON 0.17

22. DENSITY 0.150336

23. ALPHA 5E-006

24. DAMP 0.05

25. TYPE CONCRETE

26. STRENGTH FCU 576

27. END DEFINE MATERIAL

28. MEMBER PROPERTY AMERICAN

29. 1 PRIS YD 1.33 ZD 3.375

30. CONSTANTS

31. MATERIAL CONCRETE ALL

32. SUPPORTS

33. 1 2 PINNED

34. DEFINE MOVING LOAD

35. *HL93 TANDEM

36. TYPE 1 LOAD 25 25

37. DIST 4

38. LOAD GENERATION 180

� STAAD PLANE -- PAGE NO. 2

39. TYPE 1 0 0 0 XINC 0.5

40. PERFORM ANALYSIS PRINT LOAD DATA

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 174 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 175 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 176 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 177 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 178 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 179 WHEEL 2 OF 2

**WARNING-A MOVING LOAD THAT WOULD HAVE BEEN APPLIED BEYOND THE X AND Z RANGES

OF THE STRUCTURE HAS BEEN IGNORED. CASE= 180 WHEEL 2 OF 2

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

NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1

NUMBER OF PLATES 0 NUMBER OF SOLIDS 0

NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2

SOLVER USED IS THE IN-CORE ADVANCED SOLVER

TOTAL PRIMARY LOAD CASES = 180, TOTAL DEGREES OF FREEDOM = 2

� STAAD PLANE -- PAGE NO. 3

LOADING 1

MEMBER LOAD - UNIT KIP FEET

MEMBER UDL L1 L2 CON L LIN1 LIN2

1 -25.0000 GY 0.01

1 -25.0000 GY 4.00

LOADING 2

MEMBER LOAD - UNIT KIP FEET

MEMBER UDL L1 L2 CON L LIN1 LIN2

1 -25.0000 GY 0.50

1 -25.0000 GY 4.50

LOADING 3

MEMBER LOAD - UNIT KIP FEET

MEMBER UDL L1 L2 CON L LIN1 LIN2

� � MAXFORCE ENVELOPE ALL

� STAAD PLANE -- PAGE NO. 43

MEMBER FORCE ENVELOPE

ALL UNITS ARE KIP FEET

MAX AND MIN FORCE VALUES AMONGST ALL SECTION LOCATIONS

MEMB FY/ DIST LD MZ/ DIST LD

FZ DIST LD MY DIST LD FX DIST LD

1 MAX 48.89 0.00 1 0.00 0.00 1

0.00 0.00 1 0.00 0.00 1 0.00 0.00 1

MIN -48.89 90.00 173 -1075.00 45.00 91

0.00 90.00 180 0.00 90.00 180 0.00 90.00 180

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

42. FINISH

*********** END OF THE STAAD.Pro RUN ***********

**** DATE= NOV 21,2016 TIME= 12:45:51 ****

� STAAD PLANE -- PAGE NO. 44

* For questions on STAAD.Pro, please contact *

* Bentley Systems or Partner offices *

* Telephone Web / Email *

* USA +1 (714) 974-2500 *

* UK +44 (0) 808 101 9246 *

* SINGAPORE +65 6225-6158 *

* FRANCE +33 (0) 1 55238400 *

* GERMANY +49 0931 40468 *

* INDIA +91 (033) 4006-2021 *

* JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp *

* CHINA +86 21 6288 4040 *

* THAILAND +66 (0)2645-1018/19 partha.p@reisoftwareth.com*

* Worldwide http://selectservices.bentley.com/en-US/ *

ATR CHECK LIST

Load Rating ATR Checklist & Certification

Date: July 13, 2017 Bridge No. Mt St Helens Haul Rd Bridge; CENNWPWA000BD14

ATR Name & Signature: José A. Albarran-Garcia

1. Has the load rating analysis considered information available in the available plans, previous load ratings, bridge-specific correspondence, maintenance/repair costs, Plans of Action, photographs, field notes and reports, and any other pertinent information?

Yes

2. Are the Engineer qualifications aligned with the requirements and properly documented in the PMP?

3. Is the inspection current for a valid load rating?

4. Are the repair/maintenance recommendations consistent with deterioration?

N/A

5. Have all noted deficiencies or deterioration been addressed in the analysis?

6. Are there any critical deficiencies and have they been properly handled?

7. Do the analysis and computations reflect on-site conditions?

8. Have any changes in condition occurred that need to be reflected in the load rating?

9. Are the posting recommendations in place (This should include photos)?

10. Have all condition ratings of 4 or less for Items 58, 59, 60, and 62, or a rating of 3 or less for Item 113A, been documented properly with photos and notes?

11. Are the correct forms used?

12. Have all references used in the load rating been correctly documented?

ALBARRAN-

GARCIA.JOSE.A.1188229596

Digitally signed by ALBARRAN-

GARCIA.JOSE.A.1188229596

DN: c=US, o=U.S. Government, ou=DoD, ou=PKI, ou=USA, cn=ALBARRAN-GARCIA.JOSE.A.1188229596 Date: 2017.07.13 09:36:45 -05'00'

13. Have all necessary bridge cross sections, deck thickness, overlay thickness, concrete/steel properties, utility and deck layout and geometric information been provided to identify all dead loads?

14. Is there a clear indication on where the critical load path is?

15. Are the assumptions for support conditions, joint behavior identified?

16. Is the controlling load combination clearly documented?

17. Is there a free body diagram sketch to illustrate the bridge layout, loading and behavior?

18. Is there a narrative and summary of results (include all controlling vehicle rating results for moment, shear, etc.)?

19. Are all calculations checked, initialed and dated by Responsible Engineer and DQC individual(s)?

20. Has the load rating method used been identified? (Allowable Stress Design [ASD], Load Factor Design [LFD], Load and Resistance Factor Rating [LRFR]).

21. Has the correct type of load rating been performed? (Design, Legal, Permit).

22. Are the correct live load, dead load, impact, etc. load factors used?

23. Have the correct number of lanes and type of live load vehicles been evaluated?

24. Are the MBE limit states analyzed listed in the calculations?

25. Is the bridge accurately modeled? (simple span, continuous span, fixed/pinned connections)

26. Are all assumptions listed?

27. Has the load rating program(s) used been identified?

28. Is the load rating program(s) an approved program?

29. Have all data sources used, i.e., design plans, as-built plans, measurements, inspection report, etc., been identified?

Comments:

None.