9/15/2016 BE05: Design and Construction of Steel Bridges S1 DR TUYEN NGUYENNGOC D E PA RT M E N T O F B R I D G E A N D T U N N E L E N G I N E E R I N G Class website: https://sites.google.com/site/tuyennguyenngoc/courses-in-english-nuce/be05-design-and-construction-of-steel-bridges-s1 Hanoi, 08‐2016 CHAPTER GENERAL CONCEPT ABOUT STEEL BRIDGES OUTLINE FOR CHAPTER 1: INTRODUCTION MATERIALS USED IN STEEL BRIDGES STRUCTURAL TYPES OF STEEL BRIDGES BRIEF HISTORY AND GROWTH TREND OF STEEL BRIDGES 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 3 9/15/2016 1.1 Introduction  STEEL BRIDGES ? • The term “Steel Bridge” means that the superstructure of the bridge is made of steel • Steel bridges are widely used due to the great properties of steel materials including:  High strength,  Relative ductility, and  Reliability  SCOPE OF STUDY • Emphasis in this course is on short (15 m) to medium (60m) simple span girder bridges These girder bridges are readily adapted to different terrain and alignment and can be erected in a relatively short time with minimum interruption of traffic 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 4 1.2 Materials used for steel bridges  STEEL • Steel is an alloy of iron and other elements, primarily carbon, that is widely used in construction and other applications because of its high tensile strength and low cost • Steel contains less than 2% carbon and 1% manganese and small amounts of silicon, phosphorus, Sulphur and oxygen • When compared with iron,  Steel has greater strength characteristics  Steel is more elastic and can withstand the effects of impact and vibration better 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 5 9/15/2016 Materials used for steel bridges (cont.)  STRUCTURAL STEELS FOR BRIDGES • Structural steels for use in bridges generally have more stringent performance requirements compared to steels used in buildings and many other structural applications • Bridge steels have to perform in an outdoor environment with relatively large temperature changes, are subjected to millions of cycles of live loading, and are often exposed to corrosive environments containing chlorides • Steels are required to meet strength and ductility requirements for all structural applications However, bridge steels have to provide adequate service with respect to the additional Fatigue and Fracture limit state • They also have to provide enhanced atmospheric corrosion resistance in many applications where they are used without expensive protective coatings • For these reasons, structural steels for bridges are required to have fracture toughness and often corrosion resistance that exceed general structural requirements 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 6 Materials used for steel bridges (cont.)  TYPICAL STEEL TYPES • Structural Carbon Steel: Grade 250 (Fy=250MPa) Carbon steels have well defined points and generous yield plateau, high ductility Carbon steels are weldable and available as plates, bars, and structural shapes Mostly used as connection plates • High-strength low-alloy Steel: Grade 345, (Fy=345MPa); hot rolled steel with a welldefined yield point and excellent ductility They are weldable and available as plates, bars, and structural shapes Mostly used for main member in small and medium span bridges 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Stress- Strain Curves Slide # 7 9/15/2016 Materials used for steel bridges (cont.) • Heat treated low-alloy Steel: Grade 485 (Fy=485Mpa) The heat treatment removes the well-defined yield point (determined by 0.2% offset), increases the strength, hardness, and toughness Heat treated low alloy steels are weldable and available only in plates • High-yield strength heat treated low-alloy steel: Grade 690 (Fy=690) With higher chemical composition to develop higher strength, greater toughness and good corrosion resistance • High Performance Steel (HPS): improved weldability and toughness in comparison to High strength low alloy steel The goal of HPS is to provide a steel that is forgiving enough to be welded under a variety of conditions without requiring excessive weldprocess 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 8 Materials used for steel bridges (cont.)  STEEL PROPERTIES • Yield strength is the stress at which an increase in strain occurs without an increase in stress • Tensile strength is the maximum stress reached in a tensile test • Ductility is an index of the ability of the material to withstand inelastic deformations without fracture and can be expressed as a ratio of elongation at fracture to the elongation at first yield • Hardness refers to the resistance to surface indentation from a standard indenter • Toughness is the ability of a material to absorb energy without fracture 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 9 9/15/2016 Materials used for steel bridges (cont.) • Fatigue: The mechanism that consists of the formation and growth of cracks under the action of repeated stresses Fatigue failure suddenly occurs at a stress level below the yield stress • Rust / Corrosion: is the primary cause of section loss in steel members and is most commonly caused by the wet-dry cycles of exposed steel 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 10 Materials used for steel bridges (cont.) • Residual Stress: Stresses that exist in a component without any applied external forces  The processes of rolling steel products naturally introduce internal residual stresses due to plastic deformation and differential cooling effects during their production  The resulting residual stress distribution has both tensile(+) and compressive(-) stresses that are always in static equilibrium  Welding, flame cutting, and hole drilling will alter the residual stress pattern for fabricated members  Determining the exact distribution and magnitude of residual stress in fabricated members is a very complicated subject that depends on the shape geometry, processing, and the sequence of fabrication operations  It is possible to measure residual stresses through destructive sectioning and hole drilling techniques and through non-destructive X-ray diffraction and neutron diffraction techniques However, these techniques are impractical except in a research environment 9/15/2016 – NUCE (a) Hot-rolled shape, (b) welded box section, (c) plate with rolled edges, (d) plate with flame-cut edges, and (e) beam fabricated from flame-cut plates TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 11 9/15/2016 1.3 Structural types of steel bridges  GIRDER STEEL BRIDGES • Girder bridge is the most common type of steel bridges In girder system, load from the superstructure are transmitted vertically to the substructure • Simple design, simple fabrication and build • Steel girder bridges can be simple span bridges or continuous span bridges  The girder cross-section could be either I-Section or Box girder • Span length could be up to 200 - 300m  Pontecosta E Silva Bridge in Brazil built in 1974 with span length of 300m,  Neckartalbruecke-1 bridge in German, 1978 with span of 263m 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 12 Structural types of steel bridges (cont.) 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 13 9/15/2016 Structural types of steel bridges (cont.) 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 14 Structural types of steel bridges (cont.)  STEEL TRUSS BRIDGES • Truss members including chords, verticals and diagonals primary carry axial tension and compression loads • Truss members are only subjected to tension and/or compression forces and not bending forces • In most cases the design, fabrication, and erection of trusses are relatively simple • Common types: simple span truss or continuous span truss • The roadway can pass over or though the truss or both • Span length is from 50-60m to 120-150m and even above 500m  Forth Bridge (1890) in Scotland L = 521m, Quebec (1917) in Canada L = 549m, Minato Bridge - Ohashi in Japan L = 510m 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 15 9/15/2016 Structural types of steel bridges (cont.)  STEEL ARCH BRIDGES • Arch bridge is a vertically curved and axially compressed structural member spanning an opening and providing a support for the moving loads above the opening • Reactions at supports always have two components: (1) Vertical force and (2) Horizontal force even if the arch bridge is only subjected to vertical loads 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 16 Structural types of steel bridges (cont.) • To be used with large span • Because of horizontal forces occur in the bearings, it should be used where the ground or foundation is solid and stable • The roadway can pass over the arch or though the arch or both • Common types: hinge-less arch, two-hinge arch and three-hinge arch • The tied-arch can be used if the ground is too soft to deal with the horizontal forces • Span length: over 500m  (Sydney Bridge in Australia L = 503m, Bayonne (1931) in US L = 508m, Fayetterille (1977) in US L = 518m) 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 17 9/15/2016 Structural types of steel bridges (cont.)  STEEL RIGID FRAME BRIDGES • A rigid frame bridge is one in which the piers and girder are one solid structure • Design calculations for rigid frame bridges are more difficult than those of simple girder bridges The junction of the pier and the girder can be difficult to fabricate and requires accuracy and attention to detail 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 18 Structural types of steel bridges (cont.)  SUSPENSION BRIDGES • A suspension bridge has a deck-girder system, which is supported by vertical suspender cables that are in turn supported by main suspension cables The suspension cables are supported by saddles atop towers and are anchored at their ends • Suspension bridges usually use large anchors or counter weights for anchoring suspension cables • Suspension bridges are normally constructed when intermediate piers are not feasible because of long span requirements • Golden Gate Bridge (1937) in US, L = 1280m; Great Belt Bridge (1997) in Denmark, L = 1624m; AkashiKaikyo Bridge (1998) in Japan, L = 1991m Thuận Phước Bridge in Đà Nẵng (2008) L = 405m 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 19 9/15/2016 Structural types of steel bridges (cont.) Golden Gate Bridge (1937) in US, L = 1280m 9/15/2016 – NUCE Akashi Kaikyo Bridge (1998) in Japan, L = 1991m TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 20 Structural types of steel bridges (cont.)  CABLE STAYED BRIDGES • A cable-stayed bridge is another long span cable supported bridge where the superstructure is supported by cables passing over or anchored to towers located at the main piers • Cable-stayed bridges are the more modern version of cable-supported bridges • Span lengths of cable stayed bridges are up to 1000m  Tatara Bridge (1999) in Japan L = 890m; Normandie Bridge (1995) in France L = 856m ; Stonecutter Bridge in Hong Kong L = 1018m; Suton Bridge in China L = 1088m  Bãi Cháy Bridge L = 435m, is recorded as the longest span in the world for cable stayed bridges having only one-plane of cables 9/15/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: http://nguyenngoctuyen.tk/ Slide # 21 10 12/3/2016 Checking limit states (cont.) Illustrative examples of detail categories [AASHTO Fig 6.6.1.2.3-1] 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 250 Checking limit states (cont.)  The effect of changes in the stress range on the number of cycles to failure  Solving Eq (6.6.1.2.5-1) for N and then: • If the stress range is cut in half, the number of cycles to failure is increased by a multiple of • Similarly, if the stress range is doubled, the life of the detail is divided by 12/3/2016 – NUCE Stress range versus number of cycles TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 251 12/3/2016 Checking limit states (cont.) • FATIGUE REQUIREMENT FOR WEB  Purpose: Control out-of-plane flexing of the web due to repeated loadings  To control the web flexing, the maximum elastic stress in flexure or shear is limited by the web buckling stress in flexural or shear  In calculating the maximum elastic stresses, unfactored permanent loads and double the fatigue load combination shall be used  The fatigue truck is doubled when calculating maximum stresses because the heaviest truck expected to cross the bridge is approximately twice the fatigue truck used in calculating stress ranges The distribution factor for the fatigue truck is for one lane loaded without multiple presence [A3.6.1.4] and the dynamic load allowance is 15% TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 252 Checking limit states (cont.)  The flexural web buckling stress is based on elastic plate buckling formulas with partially restrained edges: w  Dc tw • Dc = the depth of the web in compression in the elastic range; • tw = the web thickness • The compressive web depth Dc is the clear height of the web between the compression flange and the point in the web where the compression stress goes to zero [A6.10.5.1.4a] 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 253 12/3/2016 Checking limit states (cont.)  For web with longitudinal stiffeners: • No flexural buckling occur  For web without longitudinal stiffeners: • The maximum compressive elastic flexural stress in the compression flange fcf, which is representative of the maximum flexural stress in the web, is limited by: TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 254 Checking limit states (cont.) Table for calculating C  Shear buckling of the web: • The critical web shear buckling stress vcr is dependent on the overall web slenderness ratio D/tw and is expressed as a fraction C of the shear yield strength Fyv vcr  CFyv  0.58CFyw  Checking formula: vcf  0.58CFyw where:  vcf = maximum elastic shear stress in the web due to the  unfactored permanent load and double the fatigue load k = the shear buckling coefficient: 12/3/2016 – NUCE k  5  / D  TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 255 12/3/2016 4.7 Design shear studs  ROLES OF SHEAR CONNECTORS  To ensure a full composite action, shear connectors must be provided at the interface between the concrete slab and the structural steel to resist interface shear a. Non‐composite girder b. Concrete girder 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 256 Design shear studs (cont.)  SHEAR CONNECTOR ARRANGEMENT  Shear connectors are welded to the top flange of the steel section that are embedded in the deck slab when the concrete is placed  In simple-span composite bridges, shear connectors shall be provided throughout the length of the span  In continuous bridges: If the longitudinal reinforcement in the deck slab is not considered in the composite section, shear connectors are not necessary in negative flexure regions • If the longitudinal reinforcement is included, either additional connectors can be placed in the region of dead load contra-flexure points or they can be continued over the negative flexure region at maximum spacing  Actually, in continuous composite bridges, shear connectors are often provided throughout the length of the bridge Placing shear connectors in the negative moment regions prevents the sudden transition from composite to non-composite section and assists in maintaining flexural compatibility throughout the length of the bridge 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 257 10 12/3/2016 Design shear studs (cont.)  Size of shear studs • Diameter of studs ◦ ds ≥ 5mm • Height of studs ◦ hs ≥ (ds) cex cin • Stud spacing ◦ Longitudinal direction: 6ds ≤ Pitch (P) ≤ 600mm ◦ Transverse direction: ◦ Distance from center to center of studs: cin ≥ 4 (ds) ◦ Clear distance from edge of studs to edge of flange: cex ≥ 25mm ◦ Depth of concrete cover over the top of the studs ≥ 50mm TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 258 Design shear studs (cont.)  LIMIT STATES • Two limit states must be considered when determining the resistance of shear studs: (1) Fatigue limit state and (2) Strength limit state  (1) Fatigue limit state • The relationship between allowable shear stress range Sr and the number of load cycles to failure N: Sr = 1065 N-0.19 • The allowable shear force Zr for a specific life of N loading cycles of the stud: Zr   d S r  (836 N 0.19 ) d or: Zr = α d2 ≥ 19 d2 (6.10.7.4.2-1) where: α = 238 - 29,5 LogN ◦ d = the nominal diameter of the stud (mm) ◦ N = loading cycles 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 259 11 12/3/2016 Design shear studs (cont.) • The horizontal shear per unit of length due to fatigue load vh vh  Vsr Q I (1) where: ◦ Vsr = the shear force range due to the fatigue truck (N) ◦ Q = the first moment of the transformed deck area about the neutral axis of the short-term composite section n (mm3) ◦ I = the moment of inertia of the short-term composite section n (mm4) • The shear force per unit length that can be resisted by n connectors at a cross section with a distance p: nZ vh  r (2) p • From(1) and (2): The center-to-center pitch of shear connectors in fatigue limit state: p 12/3/2016 – NUCE nZ r I Vsr Q TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 260 Design shear studs (cont.)  (2) Strength limit state • Two failure modes: ◦ the studs sheared off the steel beam and remained embedded in the concrete slab ◦ the concrete failed and the connectors were pulled out of the slab together with a wedge of concrete • Nominal shear resistance Qn for a single shear stud connector: Qn  0.5 Asc f c' Ec  Asc Fu (6.10.7.4.4c-1) ◦ ◦ ◦ ◦ where: Asc = the cross-sectional area of a shear stud connector (mm2) f’c = the specified 28-day concrete-compressive strength (MPa) Ec = concrete modulus of elasticity in A.5.4.2.4 (MPa) Fu = specified minimum tensile strength of a shear stud connector • The factored resistance of one shear connector: Qr  sc Asc Fu where: Φsc = 0.85 = resistance factor for shear connectors 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 261 12 12/3/2016 Design shear studs (cont.) • Determine number of shear stud connectors ◦ If sufficient shear connectors are provided, the maximum possible flexural strength of a composite section can be developed ◦ The shear connectors placed between a point of zero moment and a point of maximum positive moment must resist the compression force in the slab at the location of maximum moment: nsQr = Vh ◦ Required number of shear connectors in the length Ls: ns  Vh Qr (6.10.7.4.4A-2) where:  Vh = nominal horizontal shear force at the  interface that must be resisted Qr = factored resistance of a single shear  connector  in Eqs. (6.10.7.4.4a‐1) TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 262 Design shear studs (cont.) ◦ The nominal horizontal shear force Vh: ◦ At location having the maximum moment, the cross‐section could: ◦ have PNA in slab, or ◦ have PNA in steel ◦ Vh is taken as the lesser of either: ◦ Vh = FywD tw + Fyt bt tt + Fyc bf tf ◦ or: Vh = 0.85 f’cbts Nominal horizontal shear force: (a) PNA in slab and (b) PNA in steel 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 263 13 12/3/2016 Design shear studs (cont.) ◦ In negative moment regions of composite continuous beams: The nominal horizontal shear force Vh to be transferred between the point of zero moment and maximum moment at an interior support shall be: Vh = Ar Fyr where: ◦ Ar = total area of longitudinal  reinforcement over the interior support  within the effective slab width  ◦ Fyr = yield strength of the longitudinal  reinforcement 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 264 4.8 Design stiffeners  INTERMEDIATE TRANSVERSE STIFFENERS • Intermediate Transverse Stiffeners work as anchors for the tension field force so that post-buckling shear resistance can be developed • Transverse stiffeners are designed:  to meet the slenderness requirement of projecting elements to present local buckling,  to provide stiffness to allow the web to develop its postbuckling capacity  to have strength to resist the vertical components of the diagonal stresses in the web Bearing  stiffeners Bearing Bearing Elevation of a typical plate girder 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 265 14 12/3/2016 Design stiffeners (cont.) bf • Slenderness:  The width bt of each projecting stiffener element: 50  D E  bt  0.48t p Fys 30 bt  6.10.8.1.2  1 and 16t p  bt  0.25b f  6.10.8.1.2   where: • D = the depth of the steel section (mm) • = thickness of the projecting stiffener element (mm) Transverse stiffener • Fys = specified minimum yield strength of the stiffener (MPa) • bf = full width of the widest compression flange TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 266 Design stiffeners (cont.) • Stiffness:  The requirement for the moment of inertia of any transverse stiffener:  6.10.8.1.3  1 I t  d o tw3 J where  Dp  J  2.5    2.0  0.5    6.10.8.1.3   • It = moment of inertia of 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 (mm4) • tw = the thickness of web(mm) • = the smaller of the adjacent web panel widths (mm) • Dp= the web depth for webs without longitudinal stiffeners or maximum subpanel depth for webs with longitudinal stiffeners (mm) 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 267 15 12/3/2016 Design stiffeners (cont.) • Strength:  The area As of transverse intermediate stiffeners required to carry the tension-field action of the web:    Fyw  V D As  0.15 B 1  C  u  18   tw  tw Vr    Fys   6.10.8.1.4  1 where: tw = the thickness of web(mm) D = the steel girder depth (mm) Vr = factored shear resistance (N) Vu = shear due to factored loads at strength limit state (N) • As = stiffener area (mm2) • Fys = specified minimum yield strength of the stiffener (MPa) • • • • 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 268 Design stiffeners (cont.)  BEARING STIFFENERS  Bearing stiffeners are transverse stiffeners placed at locations of support reactions and other concentrated loads The concentrated loads are transferred through the flanges and supported by bearing on the ends of the stiffeners  The bearing stiffeners are connected to the web and provide a vertical boundary for anchoring shear forces from tension field action • 1/ Rolled Beam Shapes  Bearing stiffeners are required on webs of rolled beams if: Vu  0.75bVn  6.10.8.2.1  1 Where: • φb = the resistance factor for bearing • Vn = the nominal shear resistance determined in Section 8.8 12/3/2016 – NUCE Bearing  stiffeners Bearing Bearing Elevation of a typical plate girder TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 269 16 12/3/2016 Design stiffeners (cont.) • 2/ Plate girders  Bearing stiffeners shall be placed on the webs of plate girders at all bearing locations and at all locations supporting concentrated loads • Slenderness:  The projecting elements of the bearing stiffener must satisfy: bt  0.48t p E Fys  6.10.8.2.2  1 where: • = the thickness of the projecting element (mm) • Fys = the yield strength of the stiffener (MPa) Bearing stiffener cross sections 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 270 Design stiffeners (cont.) • Bearing resistance:  The ends of bearing stiffeners are to be attached for a tight fit against the flange from which it receives its reaction, the bottom flange at supports and the top flange for interior concentrated loads  Bearing Resistance R  Br  b Apn Fys  6.10.8.2.3  1 where: • Apn= the net area of the projecting elements of the stiffener • φb = the bearing resistance factor in A6.5.4.2 Bearing stiffener 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 271 17 12/3/2016 Design stiffeners (cont.) • Axial resistance:  The bearing stiffeners plus a portion of the web combine to act as a column to resist an axial compressive force  The effective area of the column section is taken as the area of all stiffener elements, plus a centrally located strip of web extending not more than 9tw on each side of the outer projecting elements of the stiffener group  Bearing Resistance R  Pr  c Pn where: • Φc = the resistance factor for compression • Pn = the nominal compressive resistance Bearing stiffener 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 272 Determination of shear resistance (cont.)  bf = width of compression  flange  tf = thickness of compression  flange  fc = stress in compression  flange due to the factored  loading  Fys = specified minimum yield  strength of the stiffener  φb = resistance factor of  bearing stiffeners = 1.0  Apn = area of the projecting  elements of the stiffener  outside of the web‐to‐flange  fillet welds, but not beyond  the edge of the flange 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 273 18 12/3/2016 4.9 Design girder connections and girder splices  TÍNH TỐN LIÊN KẾT BIÊN DẦM VỚI SƯỜN DẦM  Khi dầm chịu uốn, tầm biên dầm muốn trượt lên sườn dầm, mối hàn liên kết biên dầm với sườn dầm làm việc với ứng suất cắt dọc dầm Ngoài ra, có bánh xe đặt trực tiếp, mối hàn chịu ứng suất cắt thẳng đứng P  Lực trượt dọc đơn vị chiều dài dầm: V S I L H T B Trong đó: • V = lực cắt • SB = Momen tĩnh biên dầm • I = Momen quán tính tiết diện dầm   Đối với dầm liên hợp BTCT T 12/3/2016 – NUCE V D1S bs V D S b V AD S b  3n  IS I td I tdn TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 274 Design girder connections and girder splices (cont.)  Ứng suất cắt dọc dầm (tác dụng lên đường hàn hai bên sườn dầm):  Ứng suất cắt tổng cộng:  Điều kiện phải đảm bảo: fV  f  T 2 h 1  IM  P P  2 h fV2  f H2 H  Ứng suất cắt thẳng đứng: fH  f  Rr  0, 6e Fexx L  Trong đó: • φexx = 0.8 • Fexx = cường độ mối hàn (MPa) 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 275 19 12/3/2016 Design girder connections and girder splices (cont.)  TÍNH TỐN MỐI NỐI DẦM • Mối nối sườn dầm Mw MW  M IW I Mw n  Dầm làm việc chịu uốn nên tiết diện có momen M lực cắt V, sườn dầm chịu phần M V tiết diện Momen uốn phân cho sườn dầm tỷ lệ với momen quán tính sườn dầm, lực cắt coi sườn dầm chịu toàn thiên an tồn: Vw Vw VW  V • Với I IW mơ men qn tính tiết diện dầm sườn dầm RV  VW R M: RM max  M W ymax  yi2 yi V: ymax  Nội lực truyền cho đinh bu lơng là: • Trong đó: • k = số lượng đinh nửa nối • y = khoảng cách từ trục trọng tâm tiết diện dầm đến tim đinh R M,i R M,Max TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ 12/3/2016 – NUCE Slide # 276 Design girder connections and girder splices (cont.)  Điều kiện kiểm tra: Rmax  R V  RM2 max   Rr K • Với Rr = sức kháng đinh bu-lông làm việc với mặt ma sát RM max  M w rma x  Trường hợp nối rộng, tức số hàng đinh theo phương nằm ngang nhiều: r Mw i rmax  ri2 Trong đó: • rmax = khoảng cách từ trung tâm khu vực bố trí đinh(trên nửa nối) tới đinh xa • Ri = khoảng cánh tới đinh  Nếu kết cấu nhịp cầu dầm liên hợp với mặt cầu thì: M W  M D1 12/3/2016 – NUCE IW I 3n In  M D W3n  M AD Wn I I I VW  V  V D1  V D  V AD TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 277 20 12/3/2016 Design girder connections and girder splices (cont.) • Mối nối biên dầm  Lực biên dầm xác định biểu thức: N = Fr Af Trong đó: • N = sức kháng biên dầm • Fr = cường độ giới hạn cho phép vật liệu biên dầm • Ar = diện tích tính tốn biên dầm  Số đinh bu lông cần thiết để nối biên dầm n N Rr • Với Rr sức kháng đinh làm việc thường với mặt ma sát  Các nối sườn dầm biên dầm có diện tích tiết diện, mơmen qn tính (lấy trục dầm thép) không nhỏ đặc trưng hình học phận tương ứng dầm 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 278 THANK YOU 12/3/2016 – NUCE TS. Nguyễn Ngọc Tuyển – Trường đại học Xây dựng – Website: https://sites.google.com/site/tuyennguyenngoc/ Slide # 279 21