Bridge Ratings By Howard Swanson PE SE Engineer

Bridge Ratings By Howard Swanson PE SE Engineer Structures Norfolk Southern

Calvin and Hobbes By Bill Watterson

Controlling Everyday Loads

Every Day Loads 286, 000

Basic Freight Car Configurations • 263 k • 286 k

Basic Freight Car Configurations • 286 k • 315 k

Dimensional Load

Design vs. Rating Design Process • Live Load • Trial Section Properties • Other Loads • Dead Load • Impact • Total Loads • Allowable Stress • Final Section Properties Rating Process • • Section Properties Allowable Stresses Total Allowable Load Constant Loads • Dead Load • Wind • Loads that vary with speed • Impact • Centrifugal Force • Live Load

Steel Beam Span

Section Properties

Section Properties Top Flange Web Bottom Flange

300, 000 3, 000 250, 000 2, 500, 000 2, 000 150, 000 1, 500, 000 1, 000 Moment (Ft-Lbs) Shear (Lbs) Shear and Moment 50, 000 500, 000 0 5 10 15 20 25 30 35 40 45 Distance along Span (Ft) Shear Bending 50 55 60

Section Properties

Corrosion

Damage

Allowable Tensile Stress

Allowable Compression Stress

Total Allowable Capacity • Shear = Allowable Shear Stress x Web Area • Moment = Allowable Bending Stress x Section Modulus Total Capacity of Span

Dead Load • Rail • Ties • Ballast Deck • Ballast • Deck • Span

Wind Load • Wind force on the train shall be taken as 300 lbs per linear foot on one track applied 8 feet above the top of rail. • On the bridge, lateral wind pressure shall be taken at 30 PSF normal to 1. 5 times the vertical projection

Constant Loads • Dead Load • • Rail Ballast Deck Span • Wind Load Total Capacity of Span Rail Ballast Deck Span Wind Variable Loads

Impact Factor Impact as Percentage of Live Load • Impact converts dynamic loads to static loads • Full Impact is based on span length and girder centers • AREMA has provisions to reduce impact with reductions in speed 40% 35% 30% 25% 20% 15% 10% 5% 0% 0 20 40 Speed in MPH 60

Steam vs. Rolling Loads Impact as a Percentage of Live Load • The Impact Factor for Steam Locomotives was higher than the current factors for Rolling Loads • Diesel and Electric Locomotives and Freight and Passenger Cars are considered Rolling Loads Impact Factor 80% 70% 60% 50% 40% 30% 20% 10% 0% 0 20 40 60 Span Length in Ft Diesel Impact Steam Impact 80

Centrifugal Force • On Curves, a centrifugal force shall be applied horizontally through a point 8 feet above the top of the rail measured along a line perpendicular to the plane at the top of rails and equidistance from them. • The resulting centrifugal force shall correspond to the percentage of axle load without impact, determined by the following formula: C=0. 0017 S 2 D • S = Speed • D = Degree of Curvature

Centrifugal Force

Variable Loads • Impact and Centrifugal force are expressed as a percentage of Live Load • Live Load can be solved for by the following: Total Capacity of Span Allowable Variable Load = Live Load (100% + %Impact + %Centrifugal Force) Constant Loads Impact Centrifugal Force Live Load

• The percentage of Live Load for Impact and Centrifugal force decreases with lower speeds • By slowing down a load we can increase the amount of live load available to carry the load Total Capacity of Span Increasing Available Live Load 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 60 35 25 10 MPH MPH Dead Load Impact Centrifigual Live Load

Cooper Loading • Developed by Theodore Cooper around 1900. • Cooper Ratings are expressed as an E-”value”. The value is the weight on the drivers in 1, 000 lbs. • All of the axles are proportional to the drivers

Cooper Loading • The loading was based on two Erie Railroad consolidation steam locomotives operating coupled together

Cooper Loading Moment Envelope Moment per Rail (Ft-Kips) 1, 400 1, 200 1, 000 800 600 400 200 0 0 5 10 E-80 load 15 20 25 Location along Span (Ft) 286 k load 30 315 k load 35 40

Conversion of Load to Cooper Loading •

Clearing a Load • • • 40’ Bridge Span Rated at E 59. 8 at 60 MPH in Bending Rated at E 67. 1 at 35 MPH in Bending A 286 k car required E 61. 3 Capacity The maximum speed that 286 k cars can be handled over this span is 35 MPH. • Norfolk Southern’s rating database contains design stress ratings at 60 MPH, 35 MPH, 25 MPH and 10 MPH. The database also includes rating stress ratings at 10 MPH.

Questions