AASHTO- Load and Resistance Factor Design (LRFD) Railings V 1.2 Rev. 1.17.08
Credits The content for this class has been provided by the following PB employees: Paul Pilarski, P.E., S.E. Emily Elwood, E.I.T. Ali Askari, E.I.T. If you have any questions about the content of this course please contact Paul Pilarski. If you have any technical difficulties, please contact your IT Help Desk.
Download Information As with all of our LRFD courses, you may download a PDF version of this course for your future reference. Click on the ATTACHMENTS link located in the upper right corner of this course window to access the document and save the file to your desktop.
Successful Completion After completing the content within the class you will be asked to take a final test to ensure that you mastered the key training objectives. You will need to make a minimum score of 80% to receive credit for passing the class. Successful completion of the class will earn 0.1 IACET CEU. Please refer to your state s specific continuing education requirements regarding applicability.
Curriculum This class is the final class in the Structures TRC curriculum for LRFD Design, developed internally at PB. The LRFD Specifications introduce a new section that specifically addresses railings. Introduction to LRFD Loads and Load Factors Concrete Structures Steel Structures Buried Structures Foundations Deck & Deck Systems Joints and Bearings Abutments, Piers, and Walls Railings
Objectives At the end of this course you should be able to identify: 1. The variety of railing types that exist 2. Common design issues with railings 3. The LRFD Test Level railing categories and applications 4. Applications of yield line theory to concrete railing design 5. Examples of LRFD loading applications to common pedestrian and traffic railing designs This course will take you approximately one hour to complete.
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Topic 1 Topic 1 Railing Types and Considerations
Topic 1- Railing Types and Considerations Railing Selection Applicable railing design/retrofit: All new bridges Bridge Widening Projects Deck Replacements Railing reconstruction with design speeds in excess of 45 mph General factors/considerations: Variations in traffic volume, speed, vehicle mix, roadway alignment, activities and conditions beneath the structure (C13.7.1.1) Traffic on structure, vehicular (highway), pedestrian Ultimate strength, durability, ductility, maintenance, ease of replacement, and long term behavior (C13.5) Average Daily Traffic (ADT), Average Daily Truck Traffic (ADTT), Design Hourly Volume (DHV)
Topic 1- Railing Types and Considerations LRFD Railing Types (Chapter 13) Traffic Railing (Art. 13.7) Pedestrian Railing (Art. 13.8) Bicycle Railings (Art. 13.9) Combination Railings (Art 13.10)
Topic 1- Railing Types and Considerations Rail Application Guidelines C13.4 Highway traffic only Traffic Railing Highway traffic and pedestrians: low-speed highways ( 45mph) Combination Railing, Barrier Curb Application Highway traffic and pedestrians: high-speed highways (> 45mph) Combination Railing, Outboard & Inboard Application Pedestrians only Pedestrian/Bicycle Rail
Topic 1- Railing Types and Considerations Common Materials Steel Aluminum Concrete Timber See Commentary Section C13.5
Topic 1- Railing Types and Considerations Railing Selection Standard Availability Cost Non-Standard Increased Fabrication Increased Design Review Possible crash testing required Funding TH Projects SA Projects
Topic 1- Railing Types and Considerations Maintenance Issues Snow plow Galvanizing and painting Galvanize for protection Paint for aesthetics Rub Rail
Topic 1 Railing Types and Considerations LRFD Limit States and Resistance Factors Applicable load combinations: Table 3.4.1-1 Resistance factors specified in Articles 5.5.4, 6.5.4, 7.5.4, and 8.5.2 Strength Limit State Pedestrian and Bicycle Railings Loads (LL) given in Section 13 Extreme Event Limit State Traffic Railings Impact forces (CT), as described in 3.6.5 Section 3.6.5 outlines need for impact protection Loads given in Section 13 Appendix A
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Topic 2 Topic 2 Traffic Railings
Topic 2 - Traffic Railings Traffic Railing (Art. 13.7.1.1) Consideration should be given to: Protection of the occupants of a vehicle in collision with the railing Protection of other vehicles near the collision Protection of persons and property on roadways and other areas underneath the structure Possible future rail upgrading Railing cost-effectiveness Appearance and freedom of view from passing vehicles
Topic 2 Traffic Railings Traffic Railing (13.7.2) Test Level Index Test Level Application Test Speed Vehicle Characteristics TL-1 Work zones, low posted speeds, low volume 30 mph 30 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) Low speed local streets TL-2 Work zones Local and collector roads, small number of heavy vehicles, reduced posted speeds 45 mph 45 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) TL-3 Wide range of high-speed arterial highways, low mixtures of heavy vehicles 60 mph 60 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) Favorable site conditions
Topic 2 Traffic Railings Traffic Railing (13.7.2) Test Level Index (Cont.) Test Level Application Test Speed Vehicle Characteristics TL-4 High speed highways, freeways, expressways and Interstate highways Mixture of trucks and heavy vehicles 60 mph 60 mph 50 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) Single-Unit Truck (18,000 lbs) TL-5 Same applications as TL-4, large average daily truck traffic, unfavorable site conditions 60 mph 60 mph 50 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) Tractor Trailer (80,000 lbs) TL-6 Tanker-type trucks or similar high center of gravity vehicles Unfavorable site conditions 60 mph 60 mph 50 mph Small Auto (1550 lbs, 1800 lbs) Pickup Truck (4500 lbs) Tractor-Tanker Trailer (80,000 lbs)
Topic 2 Traffic Railings Common Traffic Railings: W-Beam Bridge Rail Thrie-Beam Bridge Rail Metal Tube Bridge Rail Vertical Concrete Parapet F-Shape Concrete Barrier/Single Slope Timber Bridge Rail
W-Beam Bridge Rail Texas T101 Transition Rail Height: 32 Test Level: TL-2 Utilized in: Federal Lands Box Beam Rail (W-Beam Backed with Steel Beam) Height: 27 Test Level: TL-2 Utilized in: Ohio
Thrie-Beam Bridge Rail Oregon Thrie-Beam Side Mount Height: 29 Test Level: TL-2 Utilized in: Oregon Michigan Bridge Railing, Thrie-Beam Retrofit (R4 Type) Height: 34 Test Level: TL-4 Utilized in: Michigan
Metal Tube Bridge Rail Illinois 2399 Type Side Mount (Steel Tube Bridge Rail Attached to Side of Deck) Height: 32 Test Level: TL-4 Utilized in: Illinois Oregon 2 Tube Curb Mount (Steel Tube Bridge Rail Attached to Curb) Height: 32 Test Level: TL-2 Utilized in: Oregon Minnesota Combination Bridge Rail, Design #3 (Steel Tube Bridge Rail Attached to Parapet) Height: 36 Test Level: TL-4 Utilized in: Minnesota
Metal Tube Bridge Rail Foothills Parkway Aluminum Bridge Rail (Aluminum Tube Bridge Rail) Height: 33 Test Level: TL-2 Utilized in: Federal Lands California Type 18 (Steel Tube Bridge Rail Attached to Side of Deck) Height: 36 Test Level: TL-2 Utilized in: California
Vertical Concrete Parapet New Jersey Barrier Height: 32 Test Level: TL-4 Utilized in: Georgia 32 /42 F-Shape Height: 32 /42 Test Level: TL-4 Utilized in: Florida Type 732 Concrete Barrier Height: 32 Test Level: TL-4 Utilized in: California
F-Shape concrete Barrier/Single Slope & Timber Bridge Rail Timber Rail 3 Bridge Rail Height: 27 Test Level: TL-2
Topic 2 Traffic Railings Custom or New Traffic Railings: Testing required for new systems per LRFD 13.7.3.1.2 Previously tested railings may be used provided no changes made to the features tested (LRFD 13.7.3.1.1) Geometry must meet geometric constraints previously mentioned Design according to LRFD 13.7.3 and Appendix A
Topic 2 Traffic Railings Minimum Height of Traffic Parapet or Railing (Art 13.7.3.2) Ref. Table A13.2-1 Test Level TL-1 TL-2 TL-3 TL-4 TL-5 TL-6 Minimum Railing Height, H 27.0 in 27.0 in 27.0 in 32.0 in 42.0 in 90.0 in
Topic 2 - Traffic Railings Traffic Railing Geometry (A13.1.1) Figure 1: Typical Traffic Railings Distance below bottom rail, c b Setback distance, S Maximum opening, c Minimum Height, H Rail Height, A ΣA i > 25% of H
Topic 2 - Traffic Railings Traffic Railing Geometry (A13.1.1) Figure 2: Potential for Wheel, Bumper, or Hood Impact with Post Vertical clear opening, c Post setback, S
Topic 2 - Traffic Railings Traffic Railing Geometry Figure 3: Post setback and rail configuration limits
Topic 2 Traffic Railings Traffic Rail Traffic Railing Design Forces (Ref. Article A13.2) The effective height of the vehicle rollover force, H e is: H e = G 12WB 2F t Eqn. A13.2 1 where: G = height of vehicle center of gravity above bridge deck, as specified in Table 13.7.2-1 (in) W = weight of vehicle corresponding to the required test level, as specified in Table 13.7.2-1 (kips) B = out-to-out wheel spacing on an axle, as specified in Table 13.7.2-1 (ft) F t = transverse force corresponding to the required test level as specified in Table A13.2-1 H e
Topic 2 Traffic Railings Traffic Rail Traffic Railing Design Forces (Ref. Article A13.2) The effective height of the vehicle rollover force, H e is: H e = G 12WB 2F t Eqn. A13.2 1 LRFD Table 13.7.2-1
Topic 2 Traffic Railings Traffic Railing Design Forces
Topic 2 Traffic Railings Traffic Railing Design Forces R = R i F t Y = (R Y ) i R i He 12
Topic 2 Traffic Railings Traffic Railing Impact Resistance R = R R + R W (A13.3.3 1) Y = R R H R + R R W H W (A13.3.3 2) where : R R H H R W W R = ultimate capacity of rail over one span (kips) = ultimate capacity of wall as specified in Article A13.3.1(kips) = height of wall (ft.) = height of rail (ft.)
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Topic 3 Railing Design Example
Topic 3 Railing Design Example Design Example: Type F Barrier, TL-4 Barrier Type F Barrier Design Outline: Barrier Flexural Resistance Interior Region Exterior Region Shear Capacity Check
Topic 3 Railing Design Example LRFD Design Example Type F Barrier Design Method described in LRFD Article A13.3.1 Yield Line Theory Under loading cracks develop Increase loads reinforcement begins to yield in area of crack (yield line develops) Load resistance shifts to non-yielded sections Cracks migrate and divides element into rigid regions Regions rotate about yield lines and pivot about their axis of rotation Work dissipated by hinges in lines = work expended by loads causing displacements Before Impact First yield and hinge formation Additional hinge formation/yield lines
Topic 3 Railing Design Example
Topic 3 Railing Design Example Typical reinforcement and geometry: Horizontal reinforcement: eight #4 bars Vertical reinforcement: two #5 bars anchored in the deck and projects 10 into the rail closed stirrup that laps the other #5 bar TL-4 minimum height, 32
Topic 3 Railing Design Example Moment resistance components: M b = the flexural capacity of the cap beam (if present) M w = the flexural capacity of the railing about its vertical axis M c = the flexural capacity of the railing about a horizontal axis
Topic 3 Railing Design Example L ce = length of the end regions L ci = length of interior yield line mechanisms
Topic 3 Railing Design Example Determine M b : Type F barrier has no additional beam section at its top. M b = 0 Determine M w : 1,3,5, and 7: yield lines that produce tension on the inside face of the rail 2, 4, 6, and 8: yield line has tension on the outside face of the rail
Topic 3 Railing Design Example M w Interior Region: ϕm n ϕ = 1.0 = ϕa s f y d a 2 Eqn.5.7.3.2.2 1 (for Extreme Event Limit State), Ref. Art. A f y s = 0.20in = 60ksi 2 (for #4 bar) b = height of rail = 34 in. where, a = cβ a 2 = 1 0.42 2 Astotal fy = 0.85f' b c = 0.21in 4 0.20 0.60 = 0.85 4.0 34 = 0.42in
Topic 3 Railing Design Example M w Interior Region (cont.): Bar d (in) Lever Arm d-a/2 (in) φm ni for Inside Face Tension (k-in) φm no for Outside Face Tension (k-in) 1 7.72 7.51 90.1 2 7.94 7.73 92.8 3 8.88 8.67 104.0 4 9.07 8.86 106.3 5 10.04 9.83 118.0 6 11.93 11.72 140.6 7 10.77 10.56 126.7 8 14.87 14.66 175.9 Totals 438.8 515.6
Topic 3 Railing Design Example M w Interior Region (cont.): M M wi wo ϕm = H ni ϕm = H no = = 438.8 /12 2.83 515.6 /12 2.83 = 12.92kip ft / ft = 15.18kip ft / ft For interior rail regions there is one outside tension yield line and two inside tension yield lines. Compute the average Mw: M w int 2 Mwi + 1 Mwo = 3 2 12.92 + 1 15.18 = 3 = 13.7kip ft / ft
Topic 3 Railing Design Example M w End Region: BAR Embedded Length (in) Bar Fraction Developed Developed Bar Area A s (in 2 ) 1 36 1.00 0.20 3 24.9 1.00 0.20 5 10.9 0.91 0.18 7 2.1 0.18 0.04 Total 0.62
Topic 3 Railing Design Example M w End Region: ϕm n ϕ = 1.0 = ϕa s f y d a 2 BAR Embedded Length (in) Bar Fraction Developed Developed Bar Area A s (in 2 ) A f y a = cβ a 2 s = 0.20in = 60ksi = 1 = 0.32 2 A 2 stotal 0.85f' f c y b = 0.16in = 0.62 0.60 0.85 4.0 34 = 0.32in 1 36 1.00 0.20 3 24.9 1.00 0.20 5 10.9 0.91 0.18 7 2.1 0.18 0.04 Total 0.62
Topic 3 Railing Design Example Capacities φm n for End Region: BAR Embedded Length (in) Bar Fraction Developed Developed Bar Area A s (in 2 ) d (in) Lever Arm d-a/2 (in) φm n for Inside Face Tension (k-in) 1 36 1.00 0.20 7.72 7.56 90.7 3 24.9 1.00 0.20 8.88 8.72 104.6 5 10.9 0.91 0.18 10.04 9.88 106.7 7 2.1 0.18 0.04 10.77 10.61 25.5 Total 0.62 Total 327.5 M w is found by averaging the capacity of the rail over the height of the rail: M wend ϕm = H n = 327.5 /12 2.83 = 9.6kip ft / ft
Topic 3 Railing Design Example Section for M c (flexural capacity about horizontal axis) and shear: Location d (in) Average d (in) Top 7.97 Mid Top 10.50 Mid Bottom 11.02 Bottom 14.25 9.24 12.64
Topic 3 Railing Design Example M c Interior Region Bottom Portion : #5 bar basic hook development length l 38.0 d f' c ( ) 38.0 0.625 b hb = = = Modification factors 4 11.88in ( )( 11.88) 9.98in l db = 1.2 0.7 = Avg. d = 12.64 % developed 5.2in + 4.5in = 9.98in = 97% 4.5 5.2 MnDOT chose to assume 75%
Topic 3 Railing Design Example Determine M c (Bottom Portion): Bottom Portion A stop = 0.31in 2 /ft x 75% = 0.23 in 2 /ft Compression block depth and moment per foot: Location d (in) Average d (in) Top 7.97 Mid Top 10.50 Mid Bottom 11.02 Bottom 14.25 9.24 12.64 a M bot cbot = cβ 1 = ϕm A sbot fy = 0.85 f' b n = ϕa 0.34 1 2 12 ( )( 60) 12.64 = 14.3kip ft / ft = 1.0 0.23 sbot c f y d 0.23 60 = 0.85 4 12 bot a 2 bot = 0.34in
Topic 3 Railing Design Example Determine M c (Top Portion): Top Portion A stop = 0.31in 2 /ft Compression block depth and moment per foot: Location d (in) Average d (in) Top 7.97 Mid Top 10.50 Mid Bottom 11.02 Bottom 14.25 9.24 12.64 a M top ctop = cβ 1 = = ϕm n A stop 0.85f' = ϕa f c y stop b d a = 1.0( 0.31)( 60) 9.24 = 14.0kip ft / ft f y = 0.31 0.60 0.85 4.0 12 top top 2 = 0.46 2 0.46in 1 12
Topic 3 Railing Design Example Determine M c (Average): M c int 14.0kip ft / ft = 2.83 ft = 14.1 kip ft / ft ( 1.83 ft) + 14.3kip ft / ft( 1.00 ft)
Topic 3 Railing Design Example M c End Region: For the top portion, A stop = 0.62in 2 /ft a M top ctop = cβ 1 = ϕm A stop fy = 0.85 f' b n = ϕa stop c f y d 0.62 60 = = 0.91in 0.85 4 12 a 2 0.91 1 = 1.0 0.62 2 12 For the bottom portion, A sbot = 0.75(0.62) = 0.47 in 2 /ft M cend a M bot cbot = cβ = ϕm = 1.0 top top ( )( 60) 9.24 = 27.2kip ft / ft 1 A sbot fy = = 0.85 f' b n = ϕa sbot ( ) + 28.9( 1.00) 27.2 1.83 = 2.83 c fy d bot 0.47 60 = 0.69in 0.85 4 12 a 2 bot 0.69 1 2 12 ( 0.47)( 60) 12.64 = 28.9kip ft / ft = 27.8kip ft / ft
Topic 3 Railing Design Example Summary of Flexural Capacities Axis Interior Region End Region Mw (Bending about vertical axis) 13.7 9.6 (Average k-ft/ft) Mc (Bending about horizontal axis) (Average k-ft/ft) 14.1 27.8
Topic 3 Railing Design Example Flexural Capacity Check Interior Region (Article A13.3.1): M bint = 0 M wint = 13.7 kip-ft/ft M cint = 14.1 kip-ft/ft L t = 3.5 ft per Table A13.2-1 L R ci wi Lt = 2 + Lt 2 2 = 2L ci Lt 2 8M ( M H) 8H Mbint + + M bint + 8M c int w int w int M + L H c int = 9.8 ft 2 ci = 98.0kips Eqn.A13.3.1 2 Eqn.A13.3.1 1 H = height of wall (ft) L c = critical length of yield line failure pattern (ft) L t = longitudinal length of distribution of impact force F t (ft) R w = total transverse resistance of the railing
Topic 3 Railing Design Example Type F Barrier, TL-4 Barrier F t Transverse (kip) = 54 F L Longitudinal (kip) = 18 F V Vertical/Down (kip) = 18 L t and L L (ft) = 3.5 H e Minimum Height of Horizontal Loads (in) = 32 H Minimum Height of Rail (in) =32
Topic 3 Railing Design Example Flexural Capacity Check Exterior Region (Article A13.3.1): M bend = 0 M wend = 9.6 kip-ft/ft M cend = 27.8 kip-ft/ft L t = 3.5 ft per Table A13.2-1 L R ce we Lt = 2 + = 2L ce Lt 2 2 L t 2 M ( M * H) H Mbend + + M bend + M wend cend wend M H + L H cend = 4.2ft 2 ce = 81.8kips Eqn.A13.3.1 4 Eqn.A13.3.1 3
Topic 3 Railing Design Example Shear Capacity Check Exterior Region (Article A13.3.1): F t = 54 kips F L = 18 kips Ref. Table A13.2-1 Ref. Table A13.2-1 2 2 2 2 Vres = Ft + FL = 54 + 18 = 56.9kips Re f. 5.8.4 Shear friction formula: n [ ca µ ( A f P )] ϕv = ϕ + cv vf y c Use µ = 0.60 and substitute V res for φv n : A vfreq A A vfreq b vres = ϕvµ f y = 1.76 = 5.7 legs 0.31 56.9kips 0.90 0.60 60ksi = 1.76in 2
Topic 3 Railing Design Example Shear Capacity Check (continued): 5.7 legs of #5 reinforcement required Interior Region: L ci = 9.9 ft 10 provided Exterior Region: L ci = 4.2 ft 9 provided
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Topic 4 Topic 4 Pedestrian/Bicycle Railing
Topic 4 Pedestrian/Bicycle Railing Pedestrian Railing (Art. 13.8) Design: Minimum height 42.0 in. measured from the top of the walkway Max openings horizontal rails only: 6 sphere cannot pass through Max openings horizontal and vertical elements (grid): 6 sphere cannot pass through lower 27 8 sphere cannot pass through openings above 27 Max openings Rails with fencing Fence openings < 2.0 Suggested that rails should project beyond posts and that a curb should be provided
Topic 4 Pedestrian/Bicycle Railing Pedestrian Railing (Art. 13.8) Design 13.8.2 Railings P LL = 0.05 kips/ft Horizontally and vertically Posts P LL = 0.20 + 0.050L Chain link fence where L = post spacing (feet) P LL = 0.015 ksf on fence area assuming enclosed
Topic 4 Pedestrian/Bicycle Railing Bicycle Railing (Art. 13.9) Same as pedestrian bridge except: Geometry Railing at 27 spacing or less Railing outside of posts to prevent catch hazard Rubrails are optional Design Design of rails 54 above surface are left up to the owner/designer Railing design load identical to pedestrian railing
Topic 4 Pedestrian/Bicycle Railing Pedestrian Railing (Art. 13.8) Pedestrian railing examples:
Topic 4 Pedestrian/Bicycle Railing Bicycle Railing (Art. 13.9) Bicycle railing examples:
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Topic 5 Combination Railings
Topic 5 Combination Railings Combination Railings (Art. 13.10) High Speed Combination Railing Low Speed Combination Railing
Topic 5 Combination Railings Combination Railings (Art. 13.10) High-Speed Highways: Applicable for design speeds in excess of 45 mph Shall conform to pedestrian or bicycle railing requirements (whichever is applicable) Arts. 13.8 and 13.9 Traffic railing portion: Art. 13.7 Design loads for pedestrians/bicycles shall not be applied simultaneously with the vehicular impact loads (Ref. Art. 13.10.3)
Topic 5 Combination Railings Combination Railings (Art. 13.10) Low-Speed Highways Applicable for design speeds less than 45 mph Minimum curb height adjacent to sidewalk is 6 in. Shall conform to pedestrian or bicycle railing requirements (whichever is applicable) Arts. 13.8 and 13.9 Traffic railing portion: Art. 13.7 Design loads for pedestrians/bicycles shall not be applied simultaneously with the vehicular impact loads (Ref. Art. 13.10.3)
Course Outline LRFD Railings Course Outline 1. Railing Types and Considerations 2. Traffic Railings 3. Railing Design Example 4. Pedestrian/Bicycle Railings 5. Combination Railings
Objective Review You should now be able to identify: 1. The variety of railing types that exist 2. Common design issues with railings 3. The LRFD Test Level railing categories and applications 4. Applications of yield line theory to concrete railing design 5. Examples of LRFD loading applications to common pedestrian and traffic railing designs
References American Association of State and Highway Transportation Officials, "AASHTO LRFD Bridge Design Specifications" 4th Edition 2007, Section 13 Railings, Appendix A13 Railings. Federal Highway Administration, FHWA California Division, "Bridge Rail Guide 2005". http://www.fhwa.dot.gov/bridge/bridgerail/bridgerail.pdf Goodchild, Charles and Kennedy, Gerald, "Practical Yield Line Design". Reinforced Concrete Council, British Cement Association 2003. http://www.concretecentre.com/pdf/pyld240603a.pdf Kettleson, Paul, Railings, Presented at LRFD Bridge Design Workshop, June 12, 2007. Minnesota Department of Transportation Bridge Office. http://dot.state.mn.us/bridge/manuals/lrfd/june2007workshop/11a%20railings.pdf Minnesota Department of Transportation, "Mn/DOT Bridge Office LRFD Bridge Design Manual". Minnesota Department of Transportation Manual 5-392, Oakdale, MN, July 2007. Section 13 Railings. http://ihub.dot.state.mn.us/bridge/manuals/lrfd/lrfd-manual.pdf Western, Kevin, LRFD Railing Design, Presented at LRFD Bridge Design Workshop, 2004. Minnesota Department of Transportation Bridge Office.
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