A002 bridge structures structural engineering handbook

Toma, S.; Duan, L and Chen, W.F “Bridge Structures” Structural Engineering Handbook Ed Chen Wai-Fah Boca Raton: CRC Press LLC, 1999 tailieuxdcd@gmail.com Bridge Structures 10.1 General 10.2 Steel Bridges 10.3 Concrete Bridges 10.4 Concrete Substructures 10.5 Floor System 10.6 Bearings, Expansion Joints, and Railings Shouji Toma 10.7 Girder Bridges Department of Civil Engineering, Hokkai-Gakuen University, Sapporo, Japan 10.8 Truss Bridges 10.9 Rigid Frame Bridges (Rahmen Bridges) 10.10Arch Bridges Lian Duan Division of Structures, California 10.11Cable-Stayed Bridges Department of Transportation, Sacramento, 10.12Suspension Bridges CA 10.13Defining Terms Acknowledgment Wai-Fah Chen References School of Civil Engineering, Further Reading Purdue University, West Lafayette, IN Appendix: Design Examples 10.1 General 10.1.1 Introduction A bridge is a structure that crosses over a river, bay, or other obstruction, permitting the smooth and safe passage of vehicles, trains, and pedestrians An elevation view of a typical bridge is shown in Figure 10.1 A bridge structure is divided into an upper part (the superstructure), which consists of the slab, the floor system, and the main truss or girders, and a lower part (the substructure), which are columns, piers, towers, footings, piles, and abutments The superstructure provides horizontal spans such as deck and girders and carries traffic loads directly The substructure supports the horizontal spans, elevating above the ground surface In this chapter, main structural features of common types of steel and concrete bridges are discussed Two design examples, a two-span continuous, cast-in-place, prestressed concrete box girder bridge and a three-span continuous, composite plate girder bridge, are given in the Appendix c 1999 by CRC Press LLC tailieuxdcd@gmail.com c 1999 by CRC Press LLC FIGURE 10.1: Elevation view of a typical bridge tailieuxdcd@gmail.com 10.1.2 Classification Classification by Materials Steel bridges: A steel bridge may use a wide variety of structural steel components and systems: girders, frames, trusses, arches, and suspension cables Concrete bridges: There are two primary types of concrete bridges: reinforced and prestressed Timber bridges: Wooden bridges are used when the span is relatively short Metal alloy bridges: Metal alloys such as aluminum alloy and stainless steel are also used in bridge construction Classification by Objectives Highway bridges: bridges on highways Railway bridges: bridges on railroads Combined bridges: bridges carrying vehicles and trains Pedestrian bridges: bridges carrying pedestrian traffic Aqueduct bridges: bridges supporting pipes with channeled waterflow Bridges can alternatively be classified into movable (for ships to pass the river) or fixed and permanent or temporary categories Classification by Structural System (Superstructures) Plate girder bridges: The main girders consist of a plate assemblage of upper and lower flanges and a web H- or I-cross-sections effectively resist bending and shear Box girder bridges: The single (or multiple) main girder consists of a box beam fabricated from steel plates or formed from concrete, which resists not only bending and shear but also torsion effectively T-beam bridges: A number of reinforced concrete T-beams are placed side by side to support the live load Composite girder bridges:The concrete deck slab works in conjunction with the steel girders to support loads as a united beam The steel girder takes mainly tension, while the concrete slab takes the compression component of the bending moment Grillage girder bridges: The main girders are connected transversely by floor beams to form a grid pattern which shares the loads with the main girders Truss bridges: Truss bar members are theoretically considered to be connected with pins at their ends to form triangles Each member resists an axial force, either in compression or tension Figure 10.1 shows a Warren truss bridge with vertical members, which is a “trough bridge”, i.e., the deck slab passes through the lower part of the bridge Figure 10.2 shows a comparison of the four design alternatives evaluated for Minato Oh-Hasshi in Osaka, Japan The truss frame design was selected Arch bridges: The arch is a structure that resists load mainly in axial compression In ancient times stone was the most common material used to construct magnificent arch bridges There is a wide variety of arch bridges as will be discussed in Section 10.10 c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.2: Design comparison for Minato Oh-Hashi, Japan (From Hanshin Expressway Public Corporation, Construction Records of Minato Oh-Hashi, Japan Society of Civil Engineers, Tokyo [in Japanese], 1975 With permission.) Cable-stayed bridges:The girders are supported by highly strengthened cables (often composed of tightly bound steel strands) which stem directly from the tower These are most suited to bridge long distances Suspension bridges: The girders are suspended by hangers tied to the main cables which hang from the towers The load is transmitted mainly by tension in cable c 1999 by CRC Press LLC tailieuxdcd@gmail.com This design is suitable for very long span bridges Table 10.1 shows the span lengths appropriate to each type of bridge Classification by Support Condition Figure 10.3 shows three different support conditions for girder bridges Simply supported bridges: The main girders or trusses are supported by a movable hinge at one end and a fixed hinge at the other (simple support); thus they can be analyzed using only the conditions of equilibrium Continuously supported bridges: Girders or trusses are supported continuously by more than three supports, resulting in a structurally indeterminate system These tend to be more economical since fewer expansion joints, which have a common cause of service and maintenance problems, are needed Sinkage at the supports must be avoided Gerber bridges (cantilever bridge): A continuous bridge is rendered determinate by placing intermediate hinges between the supports Minato Oh-Hashi’s bridge, shown in Figure 10.2a, is an example of a Gerber truss bridge 10.1.3 Plan Before the structural design of a bridge is considered, a bridge project will start with planning the fundamental design conditions A bridge plan must consider the following factors: Passing Line and Location A bridge, being a continuation of a road, does best to follow the line of the road A right angle bridge is easy to design and construct but often forces the line to be bent A skewed bridge or a curved bridge is commonly required for expressways or railroads where the road line must be kept straight or curved, even at the cost of a more difficult design (see Figure 10.4) Width The width of a highway bridge is usually defined as the width of the roadway plus that of the sidewalk, and often the same dimension as that of the approaching road Type of Structure and Span Length The types of substructures and superstructures are determined by factors such as the surrounding geographical features, the soil foundation, the passing line and its width, the length and span of the bridge, aesthetics, the requirement for clearance below the bridge, transportation of the construction materials and erection procedures, construction cost, period, and so forth Aesthetics A bridge is required not only to fulfill its function as a thoroughfare, but also to use its structure and form to blend, harmonize, and enhance its surroundings 10.1.4 Design The bridge design includes selection of a bridge type, structural analysis and member design, and preparation of detailed plans and drawings The size of members that satisfy the requirements of design codes are chosen [1, 17] They must sustain prescribed loads Structural analyses are performed on a model of the bridge to ensure safety as well as to judge the economy of the design The final design is committed to drawings and given to contractors c 1999 by CRC Press LLC tailieuxdcd@gmail.com c 1999 by CRC Press LLC TABLE10.1 Types of Bridges and Applicable Span Lengths From JASBC, Manual Design Data Book, Japan Association of Steel Bridge Construction, Tokyo (in Japanese), 1981 With permission tailieuxdcd@gmail.com FIGURE 10.3: Supporting conditions FIGURE 10.4: Bridge lines 10.1.5 Loads Designers should consider the following loads in bridge design: Primary loads exert constantly or continuously on the bridge Dead load: weight of the bridge Live load: vehicles, trains, or pedestrians, including the effect of impact A vehicular load is classified into three parts by AASHTO [1]: the truck axle load, a tandem load, and a uniformly distributed lane load Other primary loads may be generated by prestressing forces, the creep of concrete, the shrinkage of concrete, soil pressure, water pressure, buoyancy, snow, and centrifugal actions or waves c 1999 by CRC Press LLC tailieuxdcd@gmail.com Secondary loads occur at infrequent intervals Wind load: a typhoon or hurricane Earthquake load: especially critical in its effect on the substructure Other secondary loads come about with changes in temperature, acceleration, or temporary loads during erection, collision forces, and so forth 10.1.6 Influence Lines Since the live loads by definition move, the worst case scenario along the bridge must be determined The maximum live load bending moment and shear envelopes are calculated conveniently using influence lines The influence line graphically illustrates the maximum forces (bending moment and shear), reactions, and deflections over a section of girder as a load travels along its length Influence lines for the bending moment and shear force of a simply supported beam are shown in Figure 10.5 For a concentrated load, the bending moment or shear at section A can be calculated by multiplying the load and the influence line scalar For a uniformly distributed load, it is the product of the load intensity and the net area of the corresponding influence line diagram 10.2 Steel Bridges 10.2.1 Introduction The main part of a steel bridge is made up of steel plates which compose main girders or frames to support a concrete deck Gas flame cutting is generally used to cut steel plates to designated dimensions Fabrication by welding is conducted in the shop where the bridge components are prepared before being assembled (usually bolted) on the construction site Several members for two typical steel bridges, plate girder and truss bridges, are given in Figure 10.6 The composite plate girder bridge in Figure 10.6a is a deck type while the truss bridge in Figure 10.6b is a through-deck type Steel has higher strength, ductility, and toughness than many other structural materials such as concrete or wood, and thus makes an economical design However, steel must be painted to prevent rusting and also stiffened to prevent a local buckling of thin members and plates 10.2.2 Welding Welding is the most effective means of connecting steel plates The properties of steel change when heated and this change is usually for the worse Molten steel must be shielded from the air to prevent oxidization Welding can be categorized by the method of heating and the shielding procedure Shielded metal arc welding (SMAW), submerged arc welding (SAW), CO2 gas metal arc welding (GMAW), tungsten arc inert gas welding (TIG), metal arc inert gas welding (MIG), electric beam welding, laser beam welding, and friction welding are common methods The first two welding procedures mentioned above, SMAW and SAW, are used extensively in bridge construction due to their high efficiency Both use an electric arc, which is generally considered the most efficient method of applying heat SMAW is done by hand and is suitable for welding complicated joints but is less efficient than SAW SAW is generally automated and can be very effective for welding simple parts such as the connection between the flange and web of plate girders A typical placement of these welding methods is shown in Figure 10.7 TIG and MIG use an electric arc for heat source and inert gas for shielding An electric beam weld must not be exposed to air, and therefore must be laid in a vacuum chamber A laser beam weld can be placed in air but is less versatile than other types of welding It cannot be c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.5: Influence lines used on thick plates but is ideal for minute or artistic work Since the welding equipment necessary for heating and shielding is not easy to handle on a construction site, all welds are usually laid in the fabrication shop The heating and cooling processes during welding induce residual stresses to the connected parts The steel surfaces or parts of the cross section at some distance from the hot weld, cool first When the area close to the weld then cools, it tries to shrink but is restrained by the more solidified and c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.76: Plastic moment capacity state Fy = MAD = MD2 MAD MD1 + + Ss S3n Sn MD2 MD1 − Sn Fy − Ss S3n (10.52) (10.53) (10.54) where Ss , Sn , and S3n (see Tables 10.24 to 10.26) are section moduli for the noncomposite steel, the short-term and the long-term composite section, respectively From Table 10.21, maximum factored positive moments MD1 and MD2 in span are obtained at the location of 0.4L1 MD1 MD2 = (0.95)(1.25)(MDC1 ) = (0.95)(1.25)(4260) = 5,059 kips-ft = (0.95) (1.25MDC2 + 1.5MDW ) = (.095) [1.25(435) + 1.5(788)] = 1,640 kips-ft For the top flange: MAD 5,059(12) 1,640(12) − 2,898 9,355 = 715,552 kips-in = 59,629 kips-ft (80,842 kN-m) = (26,553) 50 − For the bottom flange: c 1999 by CRC Press LLC tailieuxdcd@gmail.com MAD My 5,059(12) 1,640(12) − 3,656 4,774 = 153,623 kips-in = 12,802 kips-ft (17,356 kN-m) (controls) = (5,248) 50 − = 5,059 + 1,640 + 12,802 = 19,501 kips-ft (26,438 kN-m) Flexural Strength Design, Strength Limit State I 6.1) Compactness of Steel Girder Section The steel section is first checked to meet the requirements of a compact section (AASHTO Article 6.10.5.2.2) (a) Ductility requirement: Dp ≤ d + ts + th 7.5 where Dp is the depth from the top of the concrete deck to the PNA, d is the depth of the steel girder, and th is the thickness of the concrete haunch above the top flange of the steel girder The purpose of this requirement is to prevent permanent crashing of the concrete slab when the composite section approaches its plastic moment capacity For this example, referring to Figure 10.75 and 10.76, we obtain: Dp Dp 10.875 + 4.375 − + 0.705 = 14.955 in (381 mm) 98.75 + 10.875 + 3.375 d + ts + th = 14.955 in < = 7.5 7.5 = 15.067 in O.K = (b) Web slenderness requirement, 2Dcp tw ≤ 3.76 E Fyc where Dcp is the depth of the web in compression at the plastic moment state Since the PNA is within the top flange, Dcp is equal to zero The web slenderness requirement is satisfied (c) Compression flange slenderness and compression flange bracing requirement It is usually assumed that the top flange is adequately braced by the hardened concrete deck; there are, therefore, no requirements for the compression flange slenderness and bracing for compact composite sections at the strength limit state the section is a compact composite section 6.2) Moment of Inertia Ratio Limit (AASHTO Article 6.10.1.1) The flexural members shall meet the following requirement: 0.1 ≤ Iyc ≤ 0.9 Iy where Iyc and Iy are the moments of inertia of the compression flange and steel girder about the vertical axis in the plane of web, respectively This limit ensures that the lateral torsional bucking formulas are valid c 1999 by CRC Press LLC tailieuxdcd@gmail.com (1)(18)3 = 486 in.4 12 (1.75)(18)3 (96)(0.625)3 + + 1338 in.4 Iy = 486 + 12 12 Iyc 486 = 0.36 < 0.9 O.K 0.1 < = Iy 1338 Iyc = 6.3) Nominal Flexure Resistance, Mn (AASHTO Article 10.5.2.2a) It is assumed that the adjacent interior-pier section is noncompact For continuous spans with the noncompact interior support section, the nominal flexure resistance of a compact composite section is taken as: Mn = 1.3Rh My ≤ Mp (10.55) where Rh is a flange stress reduction factor taken as 1.0 for this homogeneous girder Mn = 1.3(1.0)(19,501) = 25,351 kips-ft < Mp = 28,185 kips-ft 6.4) Strength Limit State I AASHTO-LRFD [1] requires that for strength limit state I Mu ≤ φf Mn (10.56) where φf is the flexural resistance factor = 1.0 For the composite section in the positive flexure region in span 1, the maximum moment occurs at 0.4L1 (see Table 10.21) Mu = 13,684 kips-ft < φf Mn = (1.0)(25,351) = 25,351 kips-ft O.K Shear Strength Design, Strength Limit State I 7.1) Nominal Shear Resistance, Vn (a) Vn for an unstiffened web (AASHTO Article 6.10.7.2)   Vp = 0.58Fyw Dtw    1.48tw2 EFyw Vn =     4.55tw E D For D tw For 2.46 For D tw ≤ 2.46 E Fyw < > 3.07 E Fyw D tw ≤ E Fyw 3.07 E Fyw (10.57) where D is depth of web and tw is thickness of web D tw = E 29,000 96 = 153.6 > 3.07 = 73.9 3.07 0.625 Fyw 50 Vn = 4.55(0.625)3 (29,000) 4.55tw3 E = = 335.6 kips (1,493 kN) D 96 (b) Vn for an end-stiffened web panel (AASHTO Article 6.10.7.3.3c) c 1999 by CRC Press LLC tailieuxdcd@gmail.com Vn C = CVp   1.0    1.10 = (D/tw )     1.52 (D/tw )2 k = 5+ (10.58) For Ek Fyw Ek Fyw D tw For 1.10 For D tw < 1.10 Ek Fyw ≤ > 1.38 Ek Fyw D tw ≤ Ek Fyw 1.38 Ek Fyw (10.59) (do /D)2 (10.60) in which is the spacing of transverse stiffeners (Figure 10.77) FIGURE 10.77: Typical steel girder dimensions For = 240 in and k = + D tw C Vp Vn c = 153.6 > 1.38 (240/96)2 = 5.80 Ek 29,000(5.8) = 1.38 = 80 Fyw 50 152 29,000(5.80) = 0.374 = 50 (153.6) = 0.58Fyw Dtw = 0.58(50)(96)(0.625) = 1,740 kips (7,740 kN) = CVp = 0.374(1740) = 650.8 kips (2,895 kN) = 1999 by CRC Press LLC tailieuxdcd@gmail.com (c) Vn for interior-stiffened web panel (AASHTO Article 6.10.7.3a) Vn =   0.87(1−C)   Vp C + √ For Mu ≤ 0.5φf Mp 1+(do /D)  0.87(1−C)   RVp C + √ 1+(do /D) where R = 0.6 + 0.4 (10.61) For Mu > 0.5φf Mp ≥ CVp φf Mn − Mu φf Mn − 0.75φf My ≤ 1.0 (10.62) 7.2) Strength Limit State I AASHTO-LRFD [1] requires that for strength limit state I Vu ≤ φν Vn (10.63) where φν is the shear resistance factor = 1.0 (a) Left end of span 1: Vu = 445.4 kips > φν Vn (for unstiffened web) = 335.6 kips Stiffeners are needed to increase shear capacity In order to facilitate handling of web panel sections, the spacing of transverse stiffeners shall meet (AASHTO Article 6.10.7.3.2) the following requirement: ≤ D 260 (D/tw ) (10.64) Try = 240 in for end-stiffened web panel = 240 in < D 260 (D/tw ) = 96 260 96/0.625 = 275 in O.K and then φν Vn = (1.0)650.8 = 650.8 kips > Vu = 445.4 kips O.K (b) Location of the first intermediate stiffeners, 20 ft (6.1m) from the left end in span 1: Factored shear for this location can be obtained using linear interpolation from Table 10.22 Since Vu = 328.0 kips (1459 kN) is less than the shear capacity of the unstiffened web, φν Vn = 335.5 kips (1492 kN), the intermediate transverse stiffeners may be omitted after the first intermediate stiffeners Similar calculations can be used to determine the remaining stiffeners along the girder Fatigue Design, Fatigue and Fracture Limit State The base metal at the connection plate welds to flanges, and webs located at 96 ft (29.26 m) (0.6L1) from the left end of span will be checked for the fatigue load combination c 1999 by CRC Press LLC tailieuxdcd@gmail.com 8.1) Load-Induced Fatigue (AASHTO Article 6.6.1.2) The design requirements for load-induced fatigue apply only to (1) details subjected to a net applied tensile stress and (2) regions where the unfactored permanent loads produce compression, and only if the compressive stress is less than twice the maximum tensile stress resulting from the fatigue load combination In the fatigue limit state, all stresses are calculated using the elastic section properties (Tables 10.24 to 10.26) (a) Top-flange weld The compressive stress at the top-flange weld due to unfactored permanent loads is obtained: fDC MDC1 (yst − tf c ) (MDC2 + MDW )(yst − tf c ) + Igirder Icom−3n 2462(12)(55.087 − 1.0) (251 + 455)(12)(33.367 − 1.0) = + 159,619 312,155 = 10.89 ksi (75.09 MPa) = Assume that the negative fatigue moments are carried by the steel section only in the positive flexure region The maximum tensile stress at the top-flange weld at this location due to factored fatigue moment is fLL+I M − (MLL+I M )u yst − tf c 798(12)(54.087) = Igirder 159,619 = 3.25 ksi (22.41 MPa) fDC = 10.89 ksi > 2fLL+I M = 6.49 ksi = no need to check fatigue for the top-flange weld (b) Bottom-flange weld • Factored fatigue stress range, ( f )u For the positive flexure region, we assume that positive fatigue moments are applied to the short-term composite section and negative fatigue moments are applied to the noncomposite steel section only ( f )u − (MLL+I M )u ysb − tf t (MLL+I M )u ysb−n − tf t + Icom−n Igirder 1465(12)(82.454 − 1.75) 798(12)(43.663 − 1.75) + = 432,707 159,619 = 5.79 ksi (39.92 MPa) = • Nominal fatigue resistance range, ( F )n For filet-welded connections with weld lines normal to the direction of stress, the base metal at transverse stiffeners to flange welds is fatigue detail category C ′ (AASHTO Table 6.6.1.2.3.-1) c 1999 by CRC Press LLC tailieuxdcd@gmail.com ( F )n = 1/3 A N ≥ ( F )T H (10.65) where A is a constant dependent on detail category = 44(10)8 for category C ′ and N = (365)(75)n(ADT T )ST ADT TST = p(ADT T ) (10.66) (10.67) where p is a fraction of a truck in a single lane (AASHTO Table 3.6.1.4.2-1) = 0.8 for three-lane traffic, and n is the number of stress-range cycles per truck passage (AASHTO Table 6.6.1.2.5-2) = 1.0 for the positive flexure region N = (365)(75)(1.0)(0.8)(3600) = 7.844(10)7 For category C ′ detail, ( F )T H = 12 ksi (AASHTO Table 6.6.1.2.5-3) A N 1/3 ( F )n 44(10)8 7.844(10)7 = 1/3 = 3.83 ksi < ( F )T H = ksi ( F )T H = ksi (41.37 MPa) = • Fatigue limit state AASHTO requires that each detail shall satisfy: ( f )u ≤ ( F )n (10.68) For top-flange weld ( f )u = 5.79 ksi < ( F )n = ksi O.K 8.2) Fatigue Requirements for Web (AASHTO Article 6.10.4) The purpose of these requirements is to control out-of-plane flexing of the web due to flexure and shear under repeated live loadings The repeated live load is taken as twice the factored fatigue load (a) Flexure requirement    Rh Fyc      c Rh Fyc 3.58 − 0448 2D fcf ≤ tw      tw   28.9Rh E 2D c For Fyc E 2Dc tw ≤ 5.76 E Fyc E c For 5.76 FE ≤ 2D tw ≤ 6.43 Fyc yc For 2Dc tw > 6.43 (10.69) E Fyc where fcf is the maximum elastic flexural stress in the compression flange due to the unfactored permanent loads and repeated live loadings; Fyc is the yield strength of the compression flange; and Dc is the depth of the web in compression • Depth of web in compression, Dc Considering the algebraic sum of stresses acting on different sections based on elastic section properties, Dc can be obtained by the following formula: c 1999 by CRC Press LLC tailieuxdcd@gmail.com Dc = fDC1 + fDC2 + fDW + fLL+I M − tf c f fDC1 f +fDW M + DC2 + LL+I y y y st = st−n st−3n 2(MLL+I M )u MDC1 MDC2 +MDW + Sst + Sst−3n Sst−n − tf c 2(MLL+I M )u MDC1 MDC2 +MDW + Igirder + Icom−3n Icom−n (10.70) Substituting moments (Tables 10.21 and 10.23) and section properties (Tables 10.24 and 10.26) into Equation 10.70, we obtain: Dc 2Dc tw (435+788)(12) 9,355 (435+788)(12) 312,155 2(1607)(12) 26,553 2(1607)(12) 432,707 = 4260(12) 2,898 4260(12) 159,629 = 17.640 + 1.569 + 1.452 − = 44.29 in (1,125 mm) 0.320 + 0.047 + 0.089 + + + + −1 E 2(44.29) = 141.7 < 5.76 = 183.7 0.625 Fyc = • Maximum compressive stress in flange, fcf (at location 0.4L1 ) fcf fDC1 + fDC2 + fDW + fLL+I M MDC1 MDC2 + MDW 2(MLL+I M )u + + Sst Sst−3n Sst−n 17.64 + 1.57 + 1.45 = 20.66 < Rh Fyc = 50 ksi = = = (b) Shear (AASHTO Article 10.6.10.4.4) The left end of span is checked as follows: • Fatigue load Vu = VDC1 + VDC2 + VDW + 2(VLL+I M )u = 148.4 + 15.1 + 27.4 + 2(51.1) = 293.1 kips (1304 kN) • Fatigue shear stress νcf = 293.1 Vu = = 4.89 ksi (33.72 MPa) Dtw 96(0.625) • Fatigue shear resistance C νn c = 0.374 (see Step 7) = 0.58CFyw = 0.58(0.374)(50) = 10.85 ksi > νcf = 4.89 ksi O.K 1999 by CRC Press LLC tailieuxdcd@gmail.com 8.3) Distortion-Induced Fatigue (AASHTO Article 6.6.1.3) All transverse connection plates will be welded to both the tension and compression flanges to provide rigid load paths so distortion-induced fatigue (the development of significant secondary stresses) can be prevented 8.4) Fracture Limit State (AASHTO Article 6.6.2) Materials for main load-carrying components subjected to tensile stresses will meet the Charpy V-notch fracture toughness requirement (AASHTO Table 6.6.2-2) for temperature zone (AASHTO Table 6.6.2-1) Intermediate Transverse Stiffener Design The intermediate transverse stiffener consists of two plates welded to both sides of the web The design of the first intermediate transverse stiffener is discussed in the following 9.1) Projecting Width, bt , Requirements (AASHTO Article 6.10.8.1.2) To prevent local buckling of the transverse stiffeners, the width of each projecting stiffener shall satisfy these requirements: d 2.0 + 30 0.25bf 0.48tp ≤ bt ≤ E Fys (10.71) 16tp where bf is the full width of the steel flange and Fys is the specified minimum yield strength of the stiffener To allow adequate space for cross-frame connections, try stiffener width bt = in (152 mm): d 2.0 + 30 = 2.0 + 98.75 30 = 5.3 in 0.25bf = 0.25(18) = 4.5 in O.K bt = in > Try = 0.5 in (13 mm) and obtain: 0.48tp bt = in < E Fys = 0.48(0.5) 16tp = 16(0.5) = in 29,000 36 O.K = 6.8 in Use two in x 0.5 in (152 mm x 13 mm) transverse stiffener plates 9.2) Moment of Inertia Requirement (AASHTO Article 6.10.8.1.3) The purpose of this requirement is to ensure sufficient rigidity of transverse stiffeners to adequately develop a tension field in the web It J ≥ tw2 J = 2.5 Dp (10.72) − 2.0 ≥ 0.5 (10.73) where It is the moment of inertia for the transverse stiffener taken about the edge in contact with the web for single stiffeners and about the mid-thickness of the web for stiffener pairs (Figure 10.78); Dp is the web depth for webs without longitudinal stiffeners c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.78: Cross-section of web and transverse stiffener 96 240 − 2.0 = −1.6 < 0.5 Use J = 0.5 J = 2.5 It = > tw2 J = (240)(0.625)2 (0.5) = 46.88 in.4 O.K 63 (0.5) + (6)(0.5)(3.313)2 12 = 83.86 in.4 9.3) Area Requirement (AASHTO Article 6.10.8.1.4) This requirement ensures that transverse stiffeners have sufficient area to resist the vertical component of the tension field, and is only applied to transverse stiffeners required to carry the forces imposed by tension-field action As ≥ As = 0.15BDtw (1 − C) Vu − 18tw2 φν Vn Fyw Fys (10.74) where B = 1.0 for stiffener pairs From the previous calculation: C = 0.374, Fyw = 50 ksi, Vu = 328.0 kips, φf Vn = 335.5 kips, tw = 0.625 in As = 2(6)(0.5) = in.2 > As = = c 0.15(1.0)(96)(0.625)(1 − 0374) Fys = 36 ksi 328.0 − 18(0.625)2 335.5 50 36 − 0.635 in.2 1999 by CRC Press LLC tailieuxdcd@gmail.com The negative value of As indicates that the web has sufficient area to resist the vertical component of the tension field 10 Shear Connector Design In a composite girder, stud or channel shear connectors must be provided at the interface between the concrete deck slab and the steel section to resist the interface shear For a composite bridge girder, the shear connectors should be normally provided throughout the length of the bridge (AASHTO Article 6.10.7.4.1) Stud shear connectors are chosen in this example and will be designed for the fatigue limit state and then checked against the strength limit state The detailed calculations of the shear stud connectors for the positive flexure region of span are given in the following A similar procedure can be used to design the shear studs for other portions of the bridge 10.1) Stud Size (AASHTO Article 6.10.7.4.1a) To meet the limits for cover and penetration for shear connectors specified in AASHTO Article 6.10.7.4.1d, try: Stud height, Hstud = in > th + = 3.375 + = 5.375 in O.K O.K Stud diameter, dstud = 0.875 in < Hstud /4 = 1.75 in 10.2) Pitch of Shear Stud, p, for Fatigue Limit State (a) Basic requirements (AASHTO Article 6.10.7.4.1b) 6dstud ≤ p = nstud Zr Icom−n ≤ 24 in Vsr Q (10.75) where nstud is the number of shear connectors in a cross-section; Q is the first moment of transformed section (concrete deck) about the neutral axis of the shortterm composite section; Vsr is the shear force range in the fatigue limit state; and Zr is the shear fatigue resistance of an individual shear connector (b) Fatigue resistance, Zr (AASHTO Article 6.10.7.4.2) Zr α 2 ≥ 5.5dstud = αdstud = 34.5 − 4.28 log N (10.76) (10.77) where N is the number of cycles specified in AASHTO Article 6.6.1.2.5, N = 7.844(10)7 cycle (see Step 8) α Zr = 34.5 − 4.28 log(7.844 × 107 ) = 0.711 < 5.5 = 5.5dstud = 5.5(0.875)2 = 4.211 ksi (c) First moment, Q, and moment of initial, Icom−n (see Table 10.25) c 1999 by CRC Press LLC tailieuxdcd@gmail.com Q = = Icom−n = beff ts ts yst−n − th + 10.875 140(10.875) 16.296 + 3.375 + = 4247.52 in.3 432,707 in.4 (d) Required pitch for the fatigue limit state Assume that shear studs are spaced at in transversely across the top flange of a steel section (Figure 10.75) and, using nstud = for this example, obtain Prequired = 1,286.96 3(4.211)(432,707) = Vsr (4,247.52) Vsr The detailed calculations for the positive flexure region of span are shown in Table 10.27 TABLE10.27 Shear Connector Design for the Positive Flexure Region in Span Location (x/L) Vsr (kips) Prequired (in.) Pfinal (in.) ntotal-stud 0.0 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 60.1 51.6 47.8 46.2 45.7 45.7 46.2 47.8 50.3 21.4 24.9 26.9 27.9 28.2 28.2 27.9 26.9 25.6 12 12 18 18 18 12 12 12 51 99 132 165 162 114 66 Note: Vsr Prequired = = + VLL+I M u + − VLL+I M u nstud Zr Icom−n = 1286.96 Vsr Q Vsr ntotal-stud is the summation of number of shear studs between the locations of the zero moment and that location 10.3) Strength Limit State Check (a) Basic requirement (AASHTO Article 6.10.7.4.4a) The resulting number of shear connectors provided between the section of maximum positive moment and each adjacent point of zero moment shall satisfy the following requirement: ntotal-stud ≥ Vh φsc Qn (10.78) where φsc is the resistance factor for shear connectors, 0.85; Vh is the nominal horizontal shear force; and Qn is the nominal shear resistance of one stud shear connector (b) Nominal horizontal shear force (AASHTO Article 6.10.7.4.4b) c 1999 by CRC Press LLC tailieuxdcd@gmail.com Vh = the lesser of Vh−concrete Vh−steel Vh 0.85fc′ beff ts Fyw Dtw + fyt bf t tf t + Fyc bf c tf c (10.79) = 0.5fc′ beff ts = 0.85(3.25)(140)(10.875) = 4,206 kips = Fyw Dtw + Fyt bf t tf t + Fyc bf c tf c = 50 [(18)(1.0) + (96)(0.625) + (18)(1.75)] = 5,475 kips = 4,206 kips (18,708 kN) (c) Nominal shear resistance (AASHTO Article 6.10.7.4.4c) Qn = 0.5Asc fc′ Ec ≤ Asc Fu (10.80) where Asc is a cross-sectional area of a stud shear connector and Fu is the specified minimum tensile strength of a stud shear connector = 60 ksi (420 MPa) 0.5 fc′ Ec = 0.5 3.25(3,250) = 51.4 kips < Qn = 0.5Asc fc′ Ec = 51.4 π(0.875)2 Fu = 60 kips = 30.9 kips (d) Check resulting number of shear stud connectors (see Table 10.27) ntotal-stud = > 165 from left end 0.4L1 162 from 0.4L1 to 0.7L1 4206 Vh = = 160 O.K φsc Qn 0.85(30.9) 11 Constructability Check For unshored construction, AASHTO requires that all I-section bending members be investigated for strength and stability during construction stages using appropriate load combinations given in AASHTO Table 3.4.1-1 The following checks are made for the steel girder section only under factored dead load, DC1 It is assumed that the final total dead load, DC1, produces the controlling maximum moments 11.1) Web Slenderness Requirement (AASHTO 6.10.10.2.2) E 2Dc ≤ 6.77 tw fc (10.81) where fc is the stress in compression flange due to the factored dead load, DC1, and Dc is the depth of the web in compression in the elastic range c 1999 by CRC Press LLC tailieuxdcd@gmail.com Dc fc 2Dc tw = yst − tf c = 55.087 − = 54.087 in (1,374 mm) 0.95(1.25)(4260)(12) (0.95)(1.25)MDC1 = = 20.95 ksi (145 MPa) = Sst 2,898 = 2(54.087) E 29,000 = 6.77 = 173.1 ≤ 6.77 = 251.9 0.625 fc 20.95 O.K no longitudinal stiffener is required 11.2) Compression Flange Slenderness Requirement (AASHTO Article 6.10.10.2.3) This requirement prevents the local buckling of the top flange before the concrete deck hardens bf ≤ 1.38 2tf bf 18 = = ≤ 1.38 2tf 2(1.0) E fc 2Dc tw E fc (10.82) 2Dc tw = 1.38 29,000 = 14.2 O.K √ 20.95 173.1 11.3) Compression Flange Bracing Requirement (AASHTO Article 6.10.10.2.4) (a) Flexure (AASHTO Article 6.10.6.4.1) To ensure that a noncomposite steel girder has sufficient flexural resistance during construction, the moment capacity should be calculated considering lateral torsional buckling with an unbraced length, Lb (Figure 10.77) For a steel girder without longitudinal stiffeners and (2Dc /tw ) > λb E/Fyc , the nominal flexural resistance is  1.3Rh My ≤ Mp    L −L Cb Rb Rh My − 0.5 Lb −Lp ≤ Rb Rh My Mn = p r   M y Lr  ≤ Rb Rh My Cb Rb Rh L b Lp ≤ Lr = 1.76rt E Fyc 19.71Iyc d E Sxc Fyc For Lb ≤ Lp For Lp < Lb ≤ Lr (10.83) For Lb > Lr (10.84) (10.85) where λb equals 4.64 for a member with a compression flange area less than the tension flange area and 5.76 for members with a compression flange area equal to or greater than the tension flange area; rt is the minimum radius of gyration of the compression flange of the steel section about the vertical axis; Sxc is the section modulus about the horizontal axis of the section to the compression flange (equal to Sst in Table 10.24); Cb is the moment gradient correction factor; and Rb is a flange stress reduction factor considering local buckling of a slender web (AASHTO Article 6.10.5.4.2) c 1999 by CRC Press LLC tailieuxdcd@gmail.com Cb = 1.75 − 1.95 Pl Ph + 0.3 Pl Ph ≤ 2.3 (10.86) where Pl is the force in the compression flange at the braced point with the lower force due to the factored loading, and Ph is the force in the compression flange at the braced point with higher force due to the factored loading Cb is conservatively taken as 1.0 in this example rt = Iyf = Af Lp = 1.76rt Lr = 2Dc tw (18)3 (1.0)/12 = 5.20 in (132 mm) (18)(1.0) E 29,000 = 220 in < Lb = 240 in = 1.76(5.2) Fyc 50 19.71(486)(98.75) 29,000 = 435 in (11,049 mm) 2,898 50 = 173.1 < λb E 29,000 = 4.64 = 172.6 fc 20.95 Since these two values are very close, take Rb = 1.0 (AASHTO Article 6.10.5.4.2) My Lp Mn Mu = Sst Fy = 2,898(50) = 144,900 kips-in = 12,075 kips-ft = 220 in < Lb = 240 in < Lr = 435 in 240 − 220 = (1.0)(1.0)(1.0)(12,075) − 0.5 435 − 220 = 11,513 kips-ft < Rn Rh My = 12,075 kips-ft = 0.95(1.25)(4,260) = 5,059 kips-ft (6,859 kN-m) < φf Mn + (1.0)(11,513) = 11,513 kips-ft (15,609 kN-m) O.K (b) Shear (AASHTO Article 6.10.10.3) Check the section at the first intermediate transverse stiffener, 20 ft (6.10 m) from the left end of span Vu is taken conservatively from the location of 0.1L1 Vu = 0.95(125)VDC1 = 0.95(1.25)(107.5) = 120.9 kips (538 kN) For an unstiffened web, Vn = 335.5 kips (1,492 kN); therefore, we obtain: φν Vn = (1.0)(335.5) = 335.5 kips > Vu = 120.9 kips c O.K 1999 by CRC Press LLC tailieuxdcd@gmail.com [...]... Concrete bridge substructures will be discussed in Section 10.4 A design example of a two-span continuous, cast-in-place, prestressed concrete box girder bridge is given in the Appendix For a more detailed look at design procedures for concrete bridges, reference should be made to the recent books of Gerwick [7], Troitsky [24], Xanthakos [26, 27], and Tonias [23] 10.3.2 Reinforced Concrete Bridges Figure... skewed bridges Structural c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.11: Erections methods (From Japan Construction Mechanization Association, Cost Estimation of Bridge Erection, Tokyo, Japan [in Japanese], 1991 With permission.) depth-to-span ratios are 0.07 for simple spans and 0.065 for continuous spans The spacing of girders in a T-beam bridge depends on the overall width of the bridge, ... a structure A bridge structure is usually designed for the strength limit states and is then checked against the appropriate service and extreme event limit states c 1999 by CRC Press LLC tailieuxdcd@gmail.com 10.3.3 Prestressed Concrete Bridges Prestressed concrete, using high-strength materials, makes an attractive alternative for long-span bridges It has been widely used in bridge structures since... Administration, Standard PlansforHighway Bridges, Vol 1, ConcreteSuperstructures, U.S Department of Transportation, Washington, D.C., 1990 With permission.) 4 Segmental Bridge The segmentally constructed bridges have been successfully developed by combining the concepts of prestressing, box girder, and the cantilever construction [2, 20] The first prestressed segmental box girder bridge was built in Western Europe... Prestressed Components Stress type Compressive Tensile Nonsegmental bridge at service state 0.45fc′ Nonsegmental bridge during shipping and handling 0.60fc′ Segmental bridge during shipping and handling 0.45fc′ Precompressed tensile zone assuming uncracked sections Nonsegmental bridges Longitudinal stress in precompressed tensile zone Segmental bridges Stress ksi (MPa) Area and condition Transverse stress... painting is high but is essential to the continued good condition of the bridge The color of the paint is also an important consideration in terms of its public appeal or aesthetic quality c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.10: Tension-type connection 10.3 Concrete Bridges 10.3.1 Introduction For modern bridges, both structural concrete and steel give satisfactory performance The choice... as 1.5 times the structural depth The most commonly used spacings are between 6 and 10 ft (1.8 to 3.1 m) 3 Cast-in-Place Box Girder Box girders like the one shown in Figure 10.12c, are often used for spans of 50 to 120 ft c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.12: Typical reinforced concrete sections in bridge superstructures (15.2 to 36.6 m) Its formwork for skewed structures is simpler... Generally, concrete structures require less maintenance than steel structures, but since the relative cost of steel and concrete is different from country to country, and may even vary throughout different parts of the same country, it is impossible to put one definitively above the other in terms of “economy” In this section, the main features of common types of concrete bridge superstructures are briefly... slip-critical (friction) bolt is most commonly used in bridge construction as well as other steel structures because it is simpler than a bearing-type bolt and more reliable than a tension bolt The force is transferred by c 1999 by CRC Press LLC tailieuxdcd@gmail.com FIGURE 10.8: Types of welding joints (From Tachibana, Y and Nakai, H., Bridge Engineering, Kyoritsu Publishing Co., Tokyo, Japan [in... concrete sections commonly used in highway bridge superstructures 1 Slab A reinforced concrete slab (Figure 10.12a) is the most economical bridge superstructure for spans of up to approximately 40 ft (12.2 m) The slab has simple details and standard formwork and is neat, simple, and pleasing in appearance Common spans range from 16 to 44 ft (4.9 to 13.4 m) with structural depth-to-span ratios of 0.06