Source: Standard Handbook for Civil Engineers 17 Thomas A Ostrom Steven L Mellon Chief Office of Structures-North California Department of Transportation Sacramento, California Senior Bridge Design Engineer Quincy Engineering, Inc Sacramento, California BRIDGE ENGINEERING B ridge engineering covers the planning, design, construction, operation, and maintenance of structures that carry facilities for movement of humans, animals, or materials over natural or created obstacles Most of the diagrams used in this section were taken from the “Manual of Bridge Design Practice,” State of California Department of Transportation and “Standard Specifications for Highway Bridges,” American Association of State Highway and Transportation Officials The authors express their appreciation for permission to use these illustrations from this comprehensive and authoritative publication General Design Considerations 17.1 Bridge Types Bridges are of two general types: fixed and movable They also can be grouped according to the following characteristics: Supported facilities: Highway or railway bridges and viaducts, canal bridges and aqueducts, pedestrian or cattle crossings, material-handling bridges, pipeline bridges Bridge-over facilities or natural features: Bridges over highways and over railways; river bridges; bay, lake, slough and valley crossings Basic geometry: In plan—straight or curved, square or skewed bridges; in elevation—low-level bridges, including causeways and trestles, or highlevel bridges Structural systems: Single-span or continuousbeam bridges, single- or multiple-arch bridges, suspension bridges, frame-type bridges Construction materials: Timber, masonry, concrete, and steel bridges 17.2 Design Specifications Designs of highway and railway bridges of concrete or steel often are based on the latest editions of the “Standard Specifications for Highway Bridges” or the “Load and Resistance Factor Design Specifications” (LRFD) of the American Association of State Highway and Transportation Officials (AASHTO) and the “Manual for Railway Engineering” of the American Railway Engineering and Maintenance-of-Way Association (AREMA) Also useful are standard plans issued by various highway administrations and railway companies Length, width, elevation, alignment, and angle of intersection of a bridge must satisfy the functional requirements of the supported facilities and the geometric or hydraulic requirements of the bridged-over facilities or natural features Figure 17.1 shows typical highway clearance diagrams Selection of the structural system and of the construction material and detail dimensions is governed by requirements of structural safety; economy of fabrication, erection, operation, and maintenance; and aesthetic considerations Highway bridge decks should offer comfortable, well-drained riding surfaces Longitudinal grades and cross sections are subject to standards similar to those for open highways (Sec 16) Provisions for roadway lighting and emergency services should be made on long bridges Barrier railings should keep vehicles within the roadways and, if necessary, separate vehicular Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.2 n Section Seventeen Fig 17.1 Minimum clearances for highway structures (a) Elevation of a highway bridge showing minimum vertical clearances below it (b) Typical bridge cross sections indicating minimum horizontal clearances Long-span bridges may have different details and requirements lanes from pedestrians and bicyclists Utilities carried on or under bridges should be adequately protected and equipped to accommodate expansion or contraction of the structures Most railroads require that the ballast bed be continuous across bridges to facilitate vertical track adjustments Long bridges should be equipped with service walkways 17.3 Design Loads for Bridges Bridges must support the following loads without exceeding permissible stresses and deflections: Dead load D, including permanent utilities Live load L and impact I Longitudinal forces due to acceleration or deceleration LF and friction F Centrifugal forces CF Wind pressure acting on the structure W and the moving load WL Earthquake forces EQ Earth E, water and ice pressure ICE, stream flow SF, and uplift B acting on the substructure Forces resulting from elastic deformations, including rib shortening R Forces resulting from thermal deformations T, including shrinkage S, and secondary prestressing effects 17.3.1 Highway Bridge Loads Vehicular live load of highway bridges is expressed in terms of design lanes and lane loadings The number of design lanes depends on the width of the roadway Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.3 In the standard specifications, each lane load is represented by a standard truck with trailer (Fig 17.3) or, alternatively, as a 10-ft-wide uniform load in combination with a concentrated load (Fig 17.2) As indicated in Fig 17.3, there are two classes of loading: HS20 and HS15, which represent a truck and trailer with three loaded axles These loading designations are followed by a 44, which indicates that the loading standard was adopted in 1944 The LRFD HL-93 vehicular live load consists of a combination of the HS20-44 design truck depicted in Fig 17.3, or the LRFD design tandem, and the LRFD live load The LRFD design tandem is defined as a pair of 25 kip axles spaced 4.0 ft apart The LRFD live load consists of 0.64 k/lf applied uniformly in the longitudinal and transverse direction When proportioning any member, all lane loads should be assumed to occupy, within their respective lanes, the positions that produce maximum stress in that member Table 17.1 gives maximum moments, shears, and reactions for one loaded lane Effects resulting from the simultaneous loading of more than two lanes may be reduced by a loading factor, which is 0.90 for three lanes and 0.75 for four lanes In design of steel grid and timber floors for HS20 loading, one axle load of 24 kips or two axle loads of 16 kips each, spaced ft apart, may be used, whichever produces the greater stress, instead of the 32-kip axle shown in Fig 17.3 For slab design, the centerline of the wheel should be assumed to be ft from the face of the curb Wind forces generally are considered as moving loads that may act horizontally in any direction They apply pressure to the exposed area of the superstructure, as seen in side elevation; to traffic on the bridge, with the center of gravity ft above the deck; and to the exposed areas of the substructure, as seen in lateral or front elevation Wind loads in Tables 17.2 and 17.3 were taken from “Standard Specifications for Highway Bridges,” American Association of State Highway and Transportation Officials They are based on 100mi/h wind velocity They should be multiplied by (V/100)2 for other design velocities except for Group III loading (Art 17.4) In investigation of overturning, add to horizontal wind forces acting normal to the longitudinal bridge axis an upward force of 20 lb/ft2 for the structure without live load or lb/ft2 when the structure carries live load This force should be applied to the deck and sidewalk area in plan at the windward quarter point of the transverse superstructure width Impact is expressed as a fraction of live-load stress and determined by the formula: I¼ Fig 17.2 HS loadings for simply supported spans For maximum negative moment in continuous spans, an additional concentrated load of equal weight should be placed in one other span for maximum effect For maximum positive moment, only one concentrated load should be used per lane, but combined with as many spans loaded uniformly as required for maximum effect 50 30% maximum 125 þ l (17:1) where l ¼ span, ft; or for truck loads on cantilevers, length from moment center to farthermost axle; or for shear due to truck load, length of loaded portion of span For negative moments in continuous spans, use the average of two adjacent loaded spans For cantilever shear, use I ¼ 30% Impact is not figured for abutments, retaining walls, piers, piles (except for steel and concrete piles above ground rigidly framed into the superstructure), foundation pressures and footings, and sidewalk loads Longitudinal forces on highway bridges should be assumed at 5% of the lane load plus concentrated load for moment headed in one Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.4 n Section Seventeen Fig 17.3 Standard truck loading HS trucks: W ¼ combined weight on the first two axles, which is the same weight as for H trucks V indicates a variable spacing from 14 to 30 ft that should be selected to produce maximum stress direction, plus forces resulting from friction in bridge expansion bearings Centrifugal forces should be computed as a percentage of design live load C¼ 6:68S2 R where S ¼ design speed, mi/h R ¼ radius of curvature, ft (17:2) These forces are assumed to act horizontally ft above deck level and perpendicular to the bridge centerline Restraint forces, generated by preventing rotations of deformations, must be considered in design Thermal forces, in particular, from restraint, may cause overstress, buckling, or cracking Provision should be made for expansion and contraction due to temperature variations, and Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.5 Table 17.1 Maximum Moments, Shears, and Reactions for Truck Loads on One Lane, Simple Spans* H15 H20 HS15 HS20 Span, ft Moment† End shear and end reaction‡ Moment† End shear and end reaction‡ Moment† End shear and end reaction‡ Moment† End shear and end reaction‡ 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 60.0§ 120.0§ 185.0§ 259.5§ 334.2§ 418.5 530.3 654.0 789.8 937.5 1097.3 1269.0 1452.8 1648.5 1856.3 2076.0 2307.8 2551.5 2807.3 3075.0 3646.5 4266.0 4933.5 5649.0 6412.5 24.0§ 25.8§ 27.2§ 29.1 31.5 33.9 36.3 38.7 41.1 43.5 45.9 48.3 50.7 53.1 55.5 57.9 60.3 62.7 65.1 67.5 72.3 77.1 81.9 86.7 91.5 80.0§ 160.0§ 246.6§ 346.0§ 445.6§ 558.0 707.0 872.0 1053.0 1250.0 1463.0 1692.0 1937.0 2198.0 2475.0 2768.0 3077.0 3402.0 3743.0 4100.0 4862.0 5688.0 6578.0 7532.0 8550.0 32.0§ 34.4§ 36.3§ 38.8 42.0 45.2 48.4 51.6 54.8 58.0 61.2 64.4 67.6 70.8 74.0 77.2 80.4 83.6 86.8 90.0 96.4 102.8 109.2 115.6 122.0 60.0§ 120.0§ 211.6§ 337.4§ 470.9§ 604.9§ 739.2§ 873.7§ 1008.3§ 1143.0§ 1277.7§ 1412.5§ 1547.3§ 1682.1§ 1856.3 2076.0 2307.8 2551.5 2807.3 3075.0 3646.5 4266.0 4933.5 5649.0 6412.5 24.0§ 32.2§ 37.2§ 41.4§ 43.9§ 45.6§ 46.8§ 47.7§ 48.4§ 49.0§ 49.4§ 49.8§ 50.7 53.1 55.5 57.9 60.3 62.7 65.1 67.5 72.3 77.1 81.9 86.7 91.5 80.0§ 160.0§ 282.1§ 449.8§ 627.9§ 806.5§ 985.6§ 1164.9§ 1344.4§ 1524.0§ 1703.6§ 1883.3§ 2063.1§ 2242.8§ 2475.1 2768.0 3077.0 3402.0 3743.0 4100.0 4862.0 5688.0 6578.0 7532.0 8550.0 32.0§ 41.6§ 49.6§ 55.2§ 58.5§ 60.8§ 62.4§ 63.6§ 64.5§ 65.3§ 65.9§ 66.4§ 67.6 70.8 74.0 77.2 80.4 83.6 86.8 90.0 96.4 102.8 109.2 115.6 122.0 * Based on “Standard Specifications for Highway Bridges,” American Association of State Highway and Transportation Officials Impact not included † Moments in thousands of ft-lb (ft-kips) ‡ Shear and reaction in kips Concentrated load is considered placed at the support Loads used are those stipulated for shear § Maximum value determined by standard truck loading Otherwise, standard lane loading governs Table 17.2 Wind Loads for Superstructure Design Trusses and arches Wind load 75 lb/ft2 Minimums: On loaded chord On unloaded chord On girders 300 lb/lin ft 150 lb/lin ft Beams and girders 50 lb/ft2 Live Load 100 lb/lin ft 300 lb/lin ft Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.6 n Section Seventeen Table 17.3 Wind Loads for Substructure Design a Loads transmitted by superstructure to substructure slab and girder bridges (up to 125-ft span) Wind on superstructure when not carrying live load, lb/ft Wind on superstructure when carrying live load, lb/ft2 Wind on live load, lb/lin ft* Transverse Longitudinal 50 15 100 12 40 Major and unusual structures No live load on bridge Wind on trusses, lb/ft2 Live load on bridge Wind on girders, lb/ft2 Wind on trusses, lb/ft2 Wind on girders, lb/ft2 Wind on live load, lb/lin ft* Skew angle, or wind, deg Lateral load Longitudinal load Lateral load Longitudinal load Lateral load Longitudinal load Lateral load Longitudinal load Lateral load Longitudinal load 15 30 45 60 75 70 65 47 25 12 28 41 50 50 44 41 33 17 12 16 19 22.5 21 19.5 14.1 7.5 3.6 8.4 12.3 15 15 13.2 12.3 9.9 5.1 1.8 3.6 4.8 5.7 100 88 82 66 34 12 24 32 38 b Loads from wind acting directly on the substructure† Horizontal wind—no live load on bridge, lb/ft2 Horizontal wind—live load on bridge, lb/ft2 40 12 * Acting ft above deck † Resolve wind forces acting at a skew into components perpendicular to side and front elevations of the substructure and apply at centers of gravity of exposed areas These loads act simultaneously with wind loads from superstructure on concrete structures, also for shrinkage For the continental United States, Table 17.4 covers temperature ranges of most locations and includes the effect of shrinkage on ordinary beam-type concrete structures The coefficient of thermal expansion for both concrete and steel per 8Fahrenheit is 0.0000065 (approximately 1⁄150,000 ) The shrinkage coefficient for concrete arches and rigid frames should be assumed as 0.002, equivalent to a temperature drop of 31 8F Stream-flow pressure on a pier should be computed from P ¼ KV (17:3) where P ¼ pressure, lb/ft2 V ¼ velocity of water, ft/s K ¼ 4⁄3 for square ends, 1⁄2 for angle ends when angle is 308 or less, and 2⁄3 for circular piers Ice pressure should be assumed as 400 psi The design thickness should be determined locally Earth pressure on piers and abutments should be computed by recognized soil-mechanics formulas, but the equivalent fluid pressure should be at least 36 lb/ft3 when it increases stresses and not more than 27 lb/ft3 when it decreases stresses Sidewalks and their direct supports should be designed for a uniform live load of 85 lb/ft2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.7 Table 17.4 Expansion and Contraction of Structures* Concrete† Steel Temp rise and fall, 8F Movement per unit length Temp rise and fall, 8F Movement per unit length Extreme: 120 8F, certain mountain and desert locations 60 0.00039 40 0.00024 Moderate: 100 8F, interior valleys and most mountain locations 50 0.00033 35 0.00021 40 0.00026 30 0.00018 Air temp range Mild: 80 8F, coastal areas, Los Angeles, and San Francisco Bay area * This table was developed for California For other parts of the United States, the temperature limits given by AASHTO “Standard Specifications for Highway Bridges” should be used † Includes shrinkage The effect of sidewalk live loading on main bridge members should be computed from 3000 55 À w P ¼ 30 þ l 50 60 lb=ft2 (17:4) where P ¼ sidewalk live load, lb/ft2 Impact loads, as a percentage of railroad live loads, may be computed from Table 17.5 Longitudinal forces should be computed for braking and traction and centrifugal forces should be computed corresponding to each axle See the AREMA ‘‘Manual for Railway Engineering’’ for more information (www.arema.org) l ¼ loaded length of sidewalk, ft w ¼ sidewalk width, ft Curbs should resist a force of 500 lb/lin ft acting 10 in above the floor For design loads for railings, see Fig 17.4 17.3.2 Railway Bridge Loads Live load is specified by axle-load diagrams or by the E number of a “Cooper’s train,” consisting of two locomotives and an indefinite number of freight cars Figure 17.5 shows the typical axle spacing and axle loads for E80 loading Members receiving load from more than one track should be assumed to be carrying the following proportions of live load: For two tracks, full live load; for three tracks, full live load from two tracks and half from the third track; for four tracks, full live load from two, half from one, and onefourth from the remaining one 17.3.3 Proportioning of Bridge Members and Sections The following groups represent various combinations of loads and forces to which a structure may be subjected Each component of the structure, or the foundation on which it rests, should be proportioned to withstand safely all group combinations of these forces that are applicable to the particular site or type Group loading combinations for service load design and load factor design are given by Group (N) ¼ g[bD D þ bL (L þ I) þ bC CF þ bE E þ bB B þ bS SF þ bW W (17:5) þ bWL WL þ bL LF þ bR (R þ S þ T) þ bEQ EQ þ bICE ICE] Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.8 n Section Seventeen Fig 17.4 Service loads for railings: P ¼ 10 kips, L ¼ post spacing, w ¼ 50 lb/ft Rail loads are shown on the left, post loads on the right (Rail shapes are for illustrative purposes only.) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.9 Fig 17.5 Axle Spacing and Axle Loads for E80 loading w ¼ resistance factor, a statistically based multiplier reflecting certainty in value for particular material property where N ¼ group number, or number assigned to a specific combination of loads g ¼ capacity reduction factor to provide for small adverse variations in materials, workmanship, and dimensions within acceptable tolerances b ¼ load factor (subscript indicates applicable type of load) See Table 17.6 for appropriate coefficients See also Art 17.3.1 and Secs and AASHTO LRFD associates load combinations with various limit states according to design objectives The sum of the factored loads must be less than the sum of the factored resistance: X hi gi Qi wRn (17:6) where hi ¼ load modifier relating to ductility, redundancy, and operational importance gi ¼ load factor, a statistically based multiplier reflecting certainty in the value for force effect Qi ¼ force effect i See Table 17.7 and 17.8 for design objectives, limit state load combinations and load factors Resistance factors vary according to material and characteristic such as bending, shear, bearing, torsion, etc., and are not shown In LRFD, both the g’s and w’s have been calibrated to achieve a uniform level of safety throughout the structure 17.4 Seismic Design Seismic forces are an important loading consideration that often controls the design of bridges in seismically active regions All bridges should be designed to insure life safety under the demands imparted by the Maximum Considered Earthquake (MCE) Higher levels of performance may be required by the bridge owner to provide post earthquake access to emergency facilities or when the time required to restore service after an earthquake would create a major economic impact Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.10 n Section Seventeen Table 17.5 Railroad Impact Factors Structure type Impact percent* Prestressed concrete: L2 500 L , 60 35 À 60 , L , 135 800 þ 14 LÀ2 L ! 135 20% 100LL LL þ DL Reinforced concrete: (80% max for steam engines) (60% max for diesel engines) Steel:** Non-hammerblow engine equipment L , 80 3L2 1600 600 RE þ 16 þ L À 30 L2 RE þ 60 À 500 1800 RE þ 10 þ L À 40 4000 RE þ 15 þ L þ 25 RE þ 40 À L ! 80 Steam engine equipment with hammerblow L , 100 L ! 100 Truss spans * For ballasted decks use 90% of calculated impact (steel bridges only) L ¼ span, ft; S ¼ longitudinal beam spacing, ft; DL ¼ applicable dead load; LL ¼ applicable live load RE ¼ the rocking effect consisting of the percentage of downward on one rail and upward on the other rail, increasing and decreasing, respectively, the loads otherwise specified RE shall be expressed as a percentage; either 10% of the axle load or 20% of the wheel load ** Impact is reduced for L 175 ft or when load is received from more than two tracks All bridges should have a clearly identifiable system to resist forces and deformations imposed by seismic events Experimental research and past performance has demonstrated that simple bridge features lead to more predictable seismic response Irregular features lead to complex and less predictable seismic response and should be avoided in high seismic region whenever possible (See Table 17.9) Every effort should be made to balance the effective lateral stiffness between adjacent bents within a frame, adjacent columns within a bent, and adjacent frames If irregular features or significant variations in lateral stiffness are unavoidable, they should be assessed with more rigorous analysis and designed for a higher level of seismic performance Seismic effects for box culverts and buried structures need not be considered, except when they cross active faults 17.4.1 Seismic Design Approach Ordinarily bridges are not designed to remain elastic during the MCE because of economic constraints and the uncertainties in predicting seismic demands Design codes permit the designer to take advantage of ductility and post elastic strength as long as the expected deformations not exceed the bridge’s lateral displacement capacity Ductile Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.55 bridge in Fig 17.37, S ¼ 30 ft and E ¼ þ 0:06 Â 30 ¼ 5:8 ft The distributed load for a 4-kip front wheel then is 4/5.8, or 0.69 kips, and for a 16-kip rear or trailer wheel load, 16/5.8, or 2.76 kips, per foot of slab width For an alternative 12-kip wheel load, the distributed load is 12/5.8, or 2.07 kips per foot of slab width (see Fig 17.38) Step Assume a slab depth Step Determine dead-load moments for the assumed slab depth Step Determine live-load moment at point of maximum moment (This is done at this stage to get a check on the assumed slab depth.) Step Combine dead-load, live-load, and impact moments at point of maximum moment Compare the required slab depth with the assumed depth Step Adjust the slab depth, if necessary If the required depth differs from the assumed depth of step 2, the dead-load moments should be revised and step repeated Usually, the second assumption is sufficient to yield the proper slab depth Steps through follow conventional structural theory Step Place live loads for maximum moments at other points on the structure to obtain intermediate values for drawing envelope curves of maximum moment Step Draw the envelope curves Determine the sizes and points of cutoff for reinforcing bars Step Determine distribution steel Step 10 Determine the number of piles required at each bent Figures 17.39 and 17.40 illustrate typical steel reinforcement patterns for a single-span and a twospan concrete-slab bridge, respectively, similar to Fig 17.37, suitable for spans ranging from 16 to 44 ft and carrying HS20 or alternate loading Reinforcement parallel to traffic in the single-span bridge is mainly in the bottom of the slab (Fig 17.39b), rather than in the top (Fig 17.39a) The twospan bridge has main steel reinforcement in the top of the slab (Fig 17.40b) over the center bent, to resist negative moments and main steel reinforcement in the bottom of the slab (Fig 17.40a) in positive-moment regions Reinforcement in multispan bridges is arranged similarly Transverse distribution steel is spaced typically at 11 to 12 in The thickness of the concrete slab and reinforcement sizes depend on the specified 28-day concrete compressive strength fc0 and yield point of the reinforcement steel For skews up to 208, transverse reinforcement should be placed parallel to the bent For larger skews, transverse reinforcement should be placed perpendicular to the center line of the bridge Skews exceeding 508 require special design (“Bridge Design Aids,” Division of Structures, California Department of Transportation, Sacramento, Calif (www.dot.ca.gov).) 17.20 Concrete T-Beam Bridges Widely used in highway construction, this type of bridge consists of a concrete slab supported on, and integral with, girders (Fig 17.41) It is especially economical in the 50- to 80-ft range Where falsework is prohibited, because of traffic conditions or clearance limitations, precast construction of reinforced or prestressed concrete may be used 17.20.1 Fig 17.38 Wheel load per foot width of slab for bridge of Fig 17.37 Design of Transverse Slabs Since the girders are parallel to traffic, main reinforcing in the slab is perpendicular to traffic For simply supported slabs, the span should be the distance center to center of supports but need not exceed the clear distance plus thickness of slabs Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.56 n Section Seventeen Fig 17.39 Arrangement of slab reinforcement for a single-span bridge carrying HS20-44 or alternative loading Fig 17.40 Arrangement of slab reinforcement for a two-span bridge carrying HS20-44 or alternative loading Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.57 Fig 17.41 Four-span bridge with concrete T beams For slabs continuous over more than two girders, the span may be taken as the clear distance between girders The live-load moment, ft-kips, for HS20 loading on simply supported slab spans is given by M ¼ 0:5(S þ 2) (17:28) where S ¼ span, ft For slabs continuous over three or more supports, multiply M in Eq (17.28) by 0.8 for both positive and negative moment For HS15 loading, multiply M by 3⁄4 Reinforcement also should be placed in the slab parallel to traffic to distribute concentrated live loads The amount should be the following percentage of the main reinforcing steel required for pffiffiffi positive moment: 220= S, but need not exceed 67% Where a slab cantilevers over a girder, the wheel load should be distributed over a distance, ft, parallel to the girder of E ¼ 0:8X þ 3:75 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website (17:29) BRIDGE ENGINEERING 17.58 n Section Seventeen where X ¼ distance, ft, from load to point of support The moment, ft-kips per foot of slab parallel to girder, is M¼ P X E (17:30) where P ¼ 16 kips for HS20 loading and 12 kips for HS15 Equations (17.28) to (17.30) apply also to concrete slabs supported on steel girders, including composite construction In design of the slabs, a l-ft-wide strip is selected and its thickness and reinforcing determined The dead-load moments, ft-kips, positive and negative, can be assumed to be wS2/10, where w is the dead load, kips/ft2 Live-load moments are given by Eq (17.28) with a 20% reduction for continuity Impact is a maximum of 30% With these values, standard charts can be developed for design of slabs on steel and concrete girders Figure 17.42 shows a typical slab-reinforcement layout 17.20.2 T-Beam Design The structure shown in Fig 17.41 is a typical fourspan grade-separation structure The structural frame assumed for analysis is shown in Fig 17.43 Columns with a pinned base are less stiff than fixed columns which minimizes shrinkage and temperature moments In addition, foundation pressures in Fig 17.42 Fig 17.43 Assumed support conditions for the bridge in Fig 17.41 pinned columns are considered fairly uniform, resulting in an economical footing size and design For concrete girder design, curves of maximum moments for dead load plus live load plus impact may be developed to determine reinforcement For live-load moments, truck loadings are moved across the bridge As they move, they generate changing moments, shears, and reactions It is necessary to accumulate maximum combinations of moments to provide an adequate design For heavy moving loads, extensive investigation is necessary to find the maximum stresses in continuous structures Figure 17.44 shows curves of maximum moments consisting of dead load plus live load plus impact combinations that are maximum along the span From these curves, reinforcing steel amounts and lengths may be determined by plotting the moments developed Figure 17.45 shows curves of maximum shears Figure 17.46 shows the girder steel Typical layout of reinforcement in the deck of a concrete T-beam bridge Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.59 Fig 17.44 Reinforcing for T beams of Fig 17.41 is determined from curves of maximum bending moment Numbers at the ends of the bars are distances, ft, from the center line of the span or bent reinforcement layout Maximum-shear requirements are derived theoretically by a point-to-point study of variations Usually, a straight line between center line and end maximums is adequate Girder spacing ranges from about to ft Usually, a deck slab overhang of about ft in is economical When the slab is made integral with the girder, its effective width of compression flange in design may not exceed the distance center to center of girders, one-fourth the girder span, or girder webwidth plus 12 times the least thickness of slab For exterior girders, however, effective overhang width may not exceed half the clear distance to the next Fig 17.45 Curves of maximum shear for T beams of Fig 17.41 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.60 n Section Seventeen Fig 17.46 Reinforcement layout for T beams of Fig 17.41 Reinforcement is symmetrical about the center lines of the bridge and bent Numbers at the ends of the bars indicate distances, ft, from the center line of bent or span girder, one-twelfth the girder span, or six times the slab thickness Ratios of beam depths to spans used in continuous T-beam bridges generally range from 0.065 to 0.075 An economical depth usually results when a small amount of compressive reinforcement is required at the interior supports Design of intermediate supports or bents varies widely, according to the designer’s preference A simple two-column bent is shown in Fig 17.41 But considerable shape variations in column cross section and elevation are possible Abutments are usually seat type or a monolithic end diaphragm supported on piles (“Bridge Design Aids,” Division of Structures, California Department of Transportation, Sacramento, Calif (www.dot.ca.gov).) 17.21 Concrete Box-Girder Bridges Box or hollow concrete girders (Fig 17.47) are favored by many designers because of the smooth plane of the bottom surface, uncluttered by lines of individual girders Provision of space in the open cells for utilities is both a structural and an aesthetic advantage Utilities are supported by the bottom Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.61 Fig 17.47 Three-span, reinforced concrete box-girder bridge For more details, see Fig 17.51 slab, and access can be made available for inspection and repair of utilities For sites where structure depth is not severely limited, box girders and T beams have been about equal in price in the 80-ft span range For shorter spans, T beams usually are cheaper, and for longer spans, box girders These cost relations hold in general, but box girders have, in some instances, been economical for spans as short as 50 ft when structure depth was restricted 17.21.1 entire cross section as a unit because of its inherent transverse stiffness Requirements in “Standard Specifications for Highway Bridges,” American Association of State Highway and Transportation Officials, however, are based on live-load distributions for individual girders, and so design usu- Girder Design Structural analysis is usually based on two typical segments, interior and exterior girders (Fig 17.48) An argument could be made for analyzing the Fig 17.48 Typical design sections hatched) for a box-girder bridge Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website (cross- BRIDGE ENGINEERING 17.62 n Section Seventeen ally is based on the assumption that a box-girder bridge is composed of separate girders Effective width of slab as compression flange of an interior girder may be taken as the smallest of the distance center to center of girders, one-fourth the girder span, and girder-web width plus 12 times the least thickness of slab Effective overhang width for an exterior girder may be taken as the smallest of half the clear distance to the next girder, one-twelfth the girder span, and six times the least thickness of the slab Usual depth-to-span ratio for continuous spans is 0.055 This may be reduced to about 0.048 with balanced spans, at some sacrifice in economy and increase in deflections Simple spans usually require a minimum depth-to-span ratio of 0.06 A typical concrete box-girder highway bridge is illustrated in Fig 17.47 Girder spacing is approximately 11⁄2 times the structure depth Minimum girder web thickness is determined by shear but generally is at least in Changes should be gradual, spread over a distance at least 12 times the difference in web thickness Top-slab design follows the procedure described for T-beam bridges in Art 17.20 Bottomslab thickness and secondary reinforcement are usually controlled by specification minimums AASHTO Specifications require that slab thickness be at least one-sixteenth the clear distance between girders but not less than in for the top slab and 51⁄2 in for the bottom slab Fillets should be provided at the intersections of all surfaces within the cells Minimum flange reinforcement parallel to the girder should be 0.6% of the flange area This steel may be distributed at top and bottom or placed in a single layer at the center of the slab Spacing should not exceed 18 in Minimum flange reinforcing normal to the girder should be 0.5% and similarly distributed Bottom-flange bars should be bent up into the exterior-girder webs and anchored using a standard 908 hook or equivalent At least one-third of the top flange tension reinforcement should extend to the exterior face of the outside girder and should be anchored with 908 bends or, where the flange projects beyond the girder sufficiently, extended far enough to develop bar strength in bond When the top slab is placed after the web walls have set, at least 10% of the negative-moment reinforcing should be placed in the web The bars should extend a distance of at least one-fourth the span on each side of the intermediate supports of continuous spans, one-fifth the span from the restrained ends of continuous spans, and the entire length of cantilevers In any event, the web should have reinforcing placed horizontally in both faces, to prevent temperature and shrinkage cracks The bars should be spaced not more than 12 inches c to c Total area of this steel should be at least 10% of the area of flexural tension reinforcement Analysis of the structure in Fig 17.47 for dead loads follows conventional moment-distribution procedure Assumed end conditions are shown in Fig 17.49a Fig 17.49 Loading patterns stresses in a box-girder bridge for maximum Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.63 Live loads, positioned to produce maximum negative moments in the girders over Pier 2, are shown in Fig 17.49b to d Similar loadings should be applied to find maximum positive and negative moments at other critical points Moments should be distributed and points plotted on a maximummoment diagram (for dead load plus live load plus impact), as shown in Fig 17.50 Layout of main girder reinforcement follows directly from this diagram Figure 17.51 shows a typical layout (“Bridge Design Details,” Division of Structures, California Department of Transportation, Sacramento, Calif (www.dot.ca.gov).) 17.22 Prestressed-Concrete Bridges In prestressed-concrete construction, concrete is subjected to permanent compressive stresses of such magnitude that little or no tension develops when design loading is applied (Art 8.42) Prestressing allows considerably better utilization of concrete than conventional reinforcement It results in an overall dead-load reduction, which makes long spans possible with concrete, sometimes competitive in cost with those of steel Prestressed concrete, however, requires greater sophistication in design, higher quality of materials (both concrete and steel), and greater refinement and controls in fabrication than does reinforced concrete Depending on the methods and sequence of fabrication, prestressed concrete may be precast, pretensioned; precast, posttensioned; cast-in-place posttentioned; composite; or partly prestressed In precast-beam bridges, the primary structure consists of precast-concrete units, usually I beams, channels, T beams, or box girders They may be either pretensioned or posttensioned Precast slabs may be solid or hollow Precast I beams (Fig 17.52) may be combined with fully or partly cast-in-place decks This construction has the advantage that the deck can be shaped closely to the desired specifications Precast slabs, incorporated into the deck, may be used in lieu of removable deck forms where accessibility is poor, for example, on overwater trestles or causeways Precast T beams (Fig 17.53) offer no advantage over the easier to fabricate, more compact I sections Alignment of Fig 17.50 Curves of maximum moment determine reinforcing for a box girder Numbers at the ends of the bars indicate distances, ft, from the center line of piers or span Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.64 n Section Seventeen Fig 17.51 Reinforcing layout for the box-girder bridge Fig 17.47 of and moment curves of Fig 17.50 Design stresses for HS20 loading: fc0 ¼ 3500 psi, fy ¼ 60 ksi the flanges of T sections often is difficult And as with I beams, the flanges must be connected with cast-in-place concrete Precast box sections may be placed side by side to form a bridge span If desired, they may be posttensioned transversely Precast beams mainly are used for spans up to about 90 ft where erection of conventional falsework is not feasible or desirable Such beams are particularly economical if conditions are favorable for mass fabrication, for example, in multispan viaducts or causeways or in the vicinity of centralized fabrication plants Longer spans are possible but require increasingly heavy handling equipment Standard designs for precast, prestressed girders have been developed by the Federal Highway Administration and state highway departments Cast-in-place prestressed concrete often is used for low-level bridges, where ground conditions favor erection of conventional falsework Typical cross sections are essentially similar to those used for conventionally reinforced sections, except that, in general, prestressing permits structures with thinner depths Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.65 Fig 17.52 Typical precast, prestressed I beam used in highway bridges Fig 17.53 Typical precast, prestressed T beam used in highway bridges For fully cast-in-place single-span bridges, posttensioning differs only quantitatively from that for precast elements In design of multispan continuous bridges, the following must be considered: Frictional prestress losses depend on the draping pattern of the ducts To reduce potential losses and increase the reliability of effective prestress, avoid continuously waving tendon patterns Instead, use discontinuous simple patterns Another method is to place tendons, usually bundles of cables, in the hollows of box girders and to bend the tendons at lubricated, accessible bearings Prestressed concrete is competitive with other materials for spans of 150 to 250 ft or more Construction techniques and improvements in prestressing hardware, such as smooth, lightweight conduits, which reduce friction losses, have brought prestressed concrete bridges into direct competition with structural steel, once preeminent in medium and long spans Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.66 n Section Seventeen Segmental construction, both precast and castin-place, has eliminated the need for expensive falsework, which previously made concrete bridges uneconomical in locations requiring long spans over navigation channels or deep canyons The two types of segmental construction used most in the United States are the cast-in-place and precast balanced cantilever types For cast-in-place construction, the movable formwork is supported by a structural framework, or traveler, which cantilevers from an adjacent completed section of the superstructure As each section is cast, cured, and posttensioned, the framework is moved out and the process repeated Figure 17.54 illustrates this type of construction For precast construction the procedure is similar, except that the sections are prefabricated Other methods, such as full-span and incremental launching procedures, can be used to fit site conditions In all segmental construction, special attention should be given in the erection plan to limitation of temporary stresses and to maintenance of balance during erection and prior to span closing Also important are an accurate prediction of creep and accurate calculation of deflections to ensure attainment of the desired structure profile and deck grades in the completed structure Posttensioning makes possible widening or strengthening or other remodeling of existing concrete structures For example, Fig 17.55 shows a cross section through a double-deck viaduct The row of columns under the upper deck had to be removed, and capacity had to be increased from H15 to HS20 loading No interference with upperdeck traffic and a minimum of interference with lower-deck traffic were permitted This objective was accomplished by reinforcing each floor beam with precast units incorporating preformed ducts for tendons Then the entire upper deck was prestressed transversely This permitted the beams to span the full width of the bridge and carry the heavier loading Similar remodeling has been done with cast-in-place concrete Determination of stresses in prestressed bridges is similar to that for other structures In analysis of statically indeterminate systems, however, the deformations caused by prestressing must be taken into account (see also Arts 8.42 to 8.45) [C A Ballinger and W Podolny, Jr., “Segmental Bridge Construction in Western Europe,” Transportation Research Board, Record 665, 1978; A Grand, “Incremental Launching of Concrete Structures,” Journal of the American Concrete Institute, August 1975; W Baur, “Bridge Erection Fig 17.54 Segmental cast-in-place concrete construction in progress for the Pine Valley Bridge, California (California Department of Transportation.) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.67 Fig 17.55 Double-deck viaduct strengthened by prestressing to permit removal of column and passage of heavier trucks by Launching Is Fast, Safe, and Efficient,” Civil Engineering, March 1977; F Leonhardt, “New Trends in Design and Construction of LongSpan Bridges and Viaducts (Skew, Flat Slabs, Torsion Box),” Eighth Congress, International Association for Bridge and Structural Engineering, New York, Sept to 14, 1968.] 17.23 Concrete Bridge Piers and Abutments Bridge piers are the intermediate supports of the superstructure of bridges with two or more openings Abutments are the end supports and usually have the additional function of retaining earth fill for the bridge approaches The minimum height of piers and abutments is governed by requirements of accessibility for maintenance of the superstructure, including bearings; of protection against spray for bridges over water; and of vertical clearance requirements for bridges over traveled ways There is no upper limit for pier heights, except that imposed by economic considerations One of the piers of the Europa Bridge, which carries an international freeway in Austria, for instance, soars to 492 ft above the ground surface of the valley The top surface of piers must have adequate length and width to accommodate the bridge Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING 17.68 n Section Seventeen bearings of the superstructure On abutments, added width is required for the back wall (curtain wall or bulkhead), which retains approach fill and protects the end section of the superstructure In designing the aboveground sections of piers, restrictions resulting from lateral-clearance requirements of adjacent traveled ways and visibility needs may have to be taken into account Length and width at the base level are controlled by stability, stress limitations in the pier shaft, and foundation design For stress and stability analyses, the reactions from loadings (dead and live, but not impact) acting on the superstructure should be combined with those acting directly on the substructure Longitudinal reactions depend on the type of bearing, whether fixed or expansion 17.23.1 Piers A number of basic pier shapes have been developed to meet the widely varying requirements Enumerated below are some of the more common types and their preferred uses Trestle-type piers are preferred on low-level “causeways” carried over shallow waters or seasonally flooded land on concrete slab or beam-andslab superstructures Each pier or bent consists of two or more bearing piles, usually all driven in the same plane, and a thick concrete deck or a prismatic cap into which the piles are framed (Fig 17.37) Both cap and piles may be of timber or, for more permanent construction, of precast conventionally reinforced or prestressed concrete Wall-type concrete piers on spread footings are generally used as supports for two-lane overcrossings over divided highways Given adequate longitudinal support of the superstructure, these piers may be designed as pendulum walls, with joints at top and bottom; otherwise, as cantilever walls T-shaped piers on spread footings, with or without bearing piles, may be used to advantage as supports of twin girders The girders are seated on bearings at both tips of the cross beam atop the pier stem T-shaped piers have been built either entirely of reinforced concrete or of reinforced concrete in various combinations with structural steel Single-column piers of rectangular or circular cross section on spread footings may be used to support box girders, with built-in diaphragms acting as cross beams (Fig 17.47) Portal frames may be used as piers under heavy steel girders, with bearings located directly over the portal legs (columns) When more than two girders are to be supported, the designer may choose to strengthen the portal cap beam or to add more columns Preferably, all legs of each portal frame should rest on a common base plate If, instead, separate footings are used, as, for instance, on separate pile clusters, adequate tie bars must be used to prevent unintended spreading Massive masonry piers have been built since antiquity for multiple-arch river bridges, high-level aqueducts, and more recently, viaducts In the twentieth century, their place has been taken by massive concrete construction, with or without natural stone facing Where reduction of dead load is of the essence, hollow piers, often of heavily reinforced concrete, may be used Steel towers on concrete pedestals may be used for high bridge piers They may be designed either as thin-membered, special trellis or as closed box portals, or combinations of these (Figs 17.20 and 17.26) Very tall piers, when used, are usually constructed of reinforced or prestressed concrete, either solid or cellular in design (Fig 17.33) Bridge abutments basically are piers with flanking (wing) walls Abutments for short-span concrete bridges, such as T-beam or slab-type highway overcrossings, are frequently simple concrete trestles built monolithically with the superstructure (see Figs 17.37 and 17.47) Abutments for steel bridges and for long-span concrete bridges that are subject to substantial end rotation and longitudinal movements should be designed as separate structures that provide a level area for the bridge bearings (bridge seat) and a back wall (curtain wall or bulkhead) The wall (stem) below the bridge seat of such abutments may be of solid concrete or thin-walled reinforced-concrete construction, with or without counterfort walls; but on rare occasions, masonry is used Sidewalls, which retain approach fill, should have adequate length to prevent erosion and undesired spill of the backfill They may be built either monolithically with the abutment stem and backwall in which case they are designed as cantilevers subject to two-way bending, or as selfsupporting retaining walls on independent footings Sidewalls may be arranged in a straight line with the abutment face, parallel to the bridge axis, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.69 or at any intermediate angle to the abutment face that may suit local conditions Given adequate foundation conditions, the parallel-to-bridge-axis arrangement (U-shaped abutment) is often preferred because of its inherent stability Abutments must be safe against overturning about the toe of the footing, against sliding on the footing, and against crushing of the underlying soil or overloading of piles In earth-pressure computations, the vehicular load on highways may be taken into account in the form of an equivalent layer of soil ft thick Live loads from railroads may be assumed to be 0.5 kip/ft2 over a 14-ft-wide strip for each track In computations of internal stresses and stability, the weight of the fill material over an inclined or stepped rear face and over reinforced concrete spread footings should be considered as fully effective No earth pressures however, should be assumed from the earth prism in front of the wall Buoyancy should be taken into account if it may occur Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website [...]... one of these at a time – – – – 1.00 – – – – – – CV BRIDGE ENGINEERING 17.12 n Section Seventeen Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.13 Table 17.8 Load Factors for Permanent... IV 2.0 Soft clays or silts greater than 40 ft of depth Description Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.15 Fig 17.6 Equivalent static earthquake loads longitudinal axis defined... concrete at 28 days (ksi) fy ¼ yield strength of reinforcing bars (ksi) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.17 For rectangular sections the total gross sectional area of rectangular... for the three types of I-Girder sections are shown in Table 17.14 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.19 Fig 17.9 Two-lane deck-girder highway bridge Design Limitations on Depth... obtained, but with greater labor costs, by adding cover plates in Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.23 Table 17.16 Design Strength of Connectors Strength (fF) Type of fastener... possible limitations in effectiveness of the composite section as such Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.25 Fig 17.10 Welded plate girder (a) Flow chart gives steps in load-factor... composite plate girder: (a) steel section alone; (b) composite section Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.27 17.11 Steel Section for Slab and Girder Loads (Fig 17.11a) y Ay2 Ay Material... that are hung from towers, or pylons The cables are curved if the Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.29 Table 17.18 Fatigue Stress Categories for Bridge Members (a) Stress Categories... difficulties in defining the weld between closed ribs and deck plate Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.31 Table 17.20 Allowable Stress Cycles for Bridge Members Main (longitudinal)... flange, supported on girders; (d) girder with deck plate as top flange Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.33 including the stresses the deck plate receives as their top flange System ... a time – – – – 1.00 – – – – – – CV BRIDGE ENGINEERING 17.12 n Section Seventeen Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The... rights reserved Any use is subject to the Terms of Use as given at the website BRIDGE ENGINEERING Bridge Engineering n 17.3 In the standard specifications, each lane load is represented by a standard... plus concentrated load for moment headed in one Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights