TẢI TRỌNG TRÊN CẦU THEO TIỂU CHUẨN 11823

Live Load Placement – Influence Line  Notes   Live Load Placement – Influence Line  Influence line tells you how to place the LL such that the maximum moment at a point occurs; i.e you first pick a point, then you try to find what is the maximum moment at that point when loads are moved around It does not tell you where the absolute maximum moment in the span occurs, nor its value; i.e the maximum moment on the point you picked is not always the absolute maximum moment that can occur in the h span ((which hi h will ill occur at a diff different point i and d under d a diff different arrangement of loads) Live Load Placement – Influence Line   For series of concentrated load (such as the design truck), the placement off lload d ffor maximum i moment, t shear, h or reaction ti may nott be b apparent t The maximum always occur under one of the concentrated loads – but which one? Two methods  Trial and Errors: Move the series of concentrated loads along the span by letting each load on the peak of IL  Use when you have only 2-3 concentrated loads  Can be tedious when you have a lot of concentrated loads Live Load Placement – Influence Line  Train Loading (AREA: American Railroad Engineers Association) Increase/ Decrease Method  This method determine whether the response (moment, shear, or reaction) increases or decreases as the series of concentrated loads move into the span  As the series of loads move into the span, the response increases When it starts to decrease, yyou’ll know that the last pposition was the one that produce the maximum effect Live Load Placement – Influence Line  Increase/ Decrease Method  For shear  Live Load Placement – Influence Line  Sloping Line Jump ∆V = Ps(x2-x1) ∆V = P (y2-y1) Example For moment Sloping Line IL for moment has no jumps! ∆M = Ps(x2-x1)  Note: not all loads may be in the span at the same time Loads that have just moved in or moved out may travel on the slope at a distance less than distance moved between concentrated loads loads Live Load Placement – Influence Line Live Load Placement – Influence Line    For Statically Indeterminate Structures, the Müller-Breslau Principle also h ld holds “If a function at a point on a beam, such as reaction, or shear, or moment, is allowed to act without restraint restraint, the deflected shape of the beam beam, to some scale, represent the influence line of the function” For indeterminate structures, the influence line is not straight g lines! Live Load Placement – Influence Line Live Load Placement - Longitudinal  Methods of finding maximum moment and shear in span    Live Load Placement – Design Equation  Influence Line (IL) – Simple and Continuous spans Design Equation – Simple span only Design Chart – Simple span only Live Load Placement – Design Equation Another Method: Using Barre’s Theorem for simply supported spans  The absolute maximum moment in the span occurs under the load closet l to the h resultant l fforce and d placed l d iin such h a way that h the h centerline of the span bisects the distance between that load and the resultant 0.73 m Resultant 145 kN 145 kN L/2 L/2 HS20 0.73 m Resultant 145 kN 145 kN L/2 35 kN L/2 HS20 Point of Max Moment 35 kN M max  81.25l  Point of Max Moment 172.1  387 kN-m l Mmax occurs at a section under middle axle located a distance 0.73 m from midspan M max  55l  19.8  66 kN-m l Mmax occurs at a section under one of the axle located a distance 0.30 m from midspan Live Load Placement – Design Equation Case Load Configuration 32 32 A Moments (kips-ft) and shears (kips)   x  42  M ( x)  Px 4.51     l l      x  42  V ( x )  P 4.51     l l    x 32 B x 25 25 C 32   x  21  M ( x)  Px 4.51      l l x   x 21  V ( x)  P 4  4.5   l l   x 2  M ( x)  50 x1    l l   x 2 V ( x)  501    l l  Loading and limitations (x and l in feet) Live Load Placement – Design Equation  If we combine the truck/tandem load with uniform load, we can get the f ll i equations following ti ffor maximum i momentt iin spans Truck loading g P = 16 kips MA  MB for: l > 28 x  l/3 x + 28  l VA > VB for any x Truck loading P = 16 kips MB  MA for: l > 28 x > l/3 14  x  l/2 Tandem loading is more severe than truck loading for l  37 ft x 0.64 k/ft D x (l  x) l  V ( x)  0.64  x  2  M ( x)  0.64 x Lane loading Live Load Placement - Longitudinal  Methods of finding maximum moment and shear in span    Influence Line (IL) – Simple and Continuous spans Design Equation – Simple span only Design Chart – Simple span only Live Load Placement – Design Chart Bending Moment in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Moment in kips-ft IM is included ft = 0.3048 m kips = 4.448 kN kips-ft = 1.356 kN-m Live Load Placement – Design Chart Shear in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Live Load Placement – Design Chart  Design chart is meant to be used for preliminary designs  We assume that maximum moment occurs at midspan – this produces slightly lower maximum moment than the Design Equation method method However, the error is usually small  Maximum shear occurs at support However, the chart does not have x = ft The closest is ft from support Shear in kips IM is included ft = 0.3048 m kips = 4.448 kN  Live Load Placement – Design Chart In general, the bridge girder much higher than ft Therefore, shear at ft is still higher than the shear at critical section for shear (at d) so we are still conservative here here Outline   Loads on Bridges Typical Loads       For one lane loading IM is included Live Load of Vehicle Pedestrian Load Dynamic Load Allowance  Fatigue W d Wind Earthquake … Design Lane AASHTO HL93 Loads  Truck  Tandem  Uniform Load   LL Combinations LL Placement  Influence Line  Design Equation  Design Charts O h LLoads Other d  Design Chart for Negative Moment due to Live Load Combination at Interior Support of Continuous Beams with Equal Spans  Dead Load Live Load      Multiple Presence Distribution to Girders Pedestrian Live Load: PL      Analysis Strategy for LL Effect in Bridge Use when has sidewalk wider th 60 cm than Considered simultaneously with truck LL Pedestrian only: 3.6 kN/m2 Pedestrian and/or Bicycle: 4.1 kN/m2 Various V i Live Loads No IM factor (Neglect dynamic effect of pedestrians)    Hammering effect H ff when h wheels h l hit h the h discontinuities d on the h road d surface f such as joints, cracks, and potholes Dynamic y response p of the bridge g due to vibrations induced byy traffic Actual calculation of dynamic effects is very difficult and involves a lot of unknowns To make life simpler, we account for the dynamic effect of moving vehicles by multiplying the static effect with a factor Effect due to Static Load  Dynamic Load Allowance: IM Sources of Dynamic Effects  Dynamic Load Allowance Factor IM Consider dynamic effects Dynamic y Allowance Factor (IM) Dynamic Load Allowance: IM  Place them to get maximum effects on span Effect due to Dynamic Load This IM factor in the code was obtained from field measurements Distribute Load to each girder Moment/ Shear from Live Load to be used in the design of girders Dynamic Load Allowance: IM  Add dynamic effect to the following loads:    Analysis Strategy for LL Effect in Bridge Design Truck D T k Design Tandem But NOT to these loads:   Pedestrian Load Design g Lane Load Table 3.6.2.1-1 ((modified)) Component Deck Joint All limit li i states All other components above ground Fatigue/ Fracture Limit States All Other Limit States Foundation components below ground Place them to get maximum effects on span Various V i Live Loads IM Consider dynamic effects Distribute Load to each girder 75% Moment/ Shear from Live Load to be used in the design of girders M l i l Presence Multiple P off LL Distribution Factors 15% 33% 0% * Reduce the above values by 50% for wood bridges Multiple Presence of LL Multiple Presence of LL       We’ve considered the effect of load placement in ONE lane But bridges has more than one lane It’s almost impossible to have maximum load effect on ALL lanes at the same time The more lanes you have, the lesser chance that all will be loaded to maximum at the same time Number of Loaded Lane Multiple p Presence Factor “m” 1.20 1.00 0.85 >3 0.65   We take care of this by using Multiple Presence Factor 1.0 for two lanes and less for or more lanes This is already included (indirectly) into the GDF Tables in AASHTO code so we not need to multiply this again Use this only when GDF is d determined i d ffrom other h analysis l i (such as from the lever rule, computer p model, or FEM)) Distribution of LL to Girders   A bridge usually have more than one girder so the question arise on how t distribute to di t ib t the th llane lload d tto the th girders id AASHTO Girder Distribution Factor   DFs are different for different kinds of superstructure system DFs are different for interior and exterior beam Two main methods  Using AASHTO’s table: for typical design, get an approximate (conservative) value  roadway width No need to consider multiple presence factor Exterior Distribution Factor DF Lane Moment Girder Moment L Lane Sh Shear Gi d Shear Girder Sh Interior    Refined analysis by using finite element method   DFs are available for one design lane and two or more design lanes (the larger one controls) Must make sure that the bridge g is within the range g of applicability pp y of the equation Need to consider multiple p ppresence factor AASHTO Girder Distribution Factor Factors affecting the distribution factor includes:  Span Length (L)  Girder Spacing (S)  Modulus M d l off elasticity l i i off bbeam and dd deckk  Moment of inertia and Torsional inertia of the section  Slab Sl b Thickness Thi k (ts)  Width (b), Depth (d), and Area of beam (A)  Number of design lanes (NL)  Number of girders (Nb)  Width of bridge (W) DF  Exterior For AASHTO method first we must identify the type of superstructure ( (support beam b & deck d k types) DF  Types (Continued) DFM  Distribution factor for moment in Interior Beams (continued) DFM  Distribution factor for moment in Interior Beams DFM  Distribution factor for moment in Exterior Beams DFV  Distribution factor for shear in Interior Beams GDF  Effects of girder stiffness on the distribution factor DFV  Distribution factor for shear in Exterior Beams GDF – Finite Element Analysis Bridge Model ( ) (a) (b) (c) Boundary (Support) Conditions GDF – Finite Element Analysis Moment and Shear in Typical Girder  At any section, if not using AASHTO’s GDF    MLL+IM, Girder = DFM×(Mtruck/tadem,Lane×IM + Muniform,Lane )×m VLL+IM, Girder = DFV×(Vtruck/tadem,Lane×IM + Vuniform,Lane )×m At any section, if using AASHTO’s GDF   MLL+IM, Girder = DFM×(Mtruck/tadem,Lane×IM + Muniform,Lane ) VLL+IM, Girder = DFV×(Vtruck/tadem,Lane×IM + Vuniform,Lane ) Placed such that we have maximum effects Load distribution in model Live L d Loads (Truck, Tandem and Lane Loads) Place them to get maximum static effects Increase the static load by IM to account for dynamic effects Multiply byy DF Outline   Loads on Bridges Typical Loads      Live Load of Vehicle Pedestrian Load Dynamic Load Allowance      Fatigue W d Wind Earthquake … LL Combinations LL Placement  Influence Line  Design Equation  Design Charts O h LLoads Other d  Design Lane AASHTO HL93 Loads  Truck  Tandem  Uniform Load Dead Load Live Load      Multiple Presence Distribution to Girders O h LLoads Other d Fatigue Wind Earthquake Vehicle/ Vessel Collision Moment/ Shear from Live Load to be used in the d i off girders design id Fatigue g Load   Fatigue Load Repeated loading/unloading of live loads can cause fatigue in bridge components Fatigue load depends on two factors  Magnitude of Load  Use HS-20 design truck with 9m between 145 kN axles for determination off maximum i effects ff off load l d ADT Average Daily Traffic (All Vehicles/ Direction) From Survey (and extrapolate to future) Max ~ 20,000 vehicles/day % of Truck in Traffic ADTT g Daily y Truck Traffic Average (Truck Only/ Direction)  Fraction of Truck Traffic in a Single Lane (p) Frequency of Occurrence:  U ADTTSL = average daily Use d il truck t k ttraffic ffi iin a single i l lane l Wind Load    Horizontal loads There are two types of wind loads on the structure  WS = wind load on structure Wind pressure on the structure itself  WL = wind on vehicles on bridge Wi d pressure on the Wind h vehicles on the bridge, which the load is transferred to the bridge superstructure Wind loads are applied as static horizontal load ADTTSL Average Daily Truck Traffic (Truck Only/ Lane) Table C3.6.1.4.2-1 Class of Hwy y % of Truck Rural Interstate 0.20 Urban Interstate 0.15 Other Rural 0.15 Other Urban 0.10 Table 3.6.1.1.2-1 Number of Lanes Available to Trucks p 1.00 0.85 or more 0.80 Wind Loads (WS, WL)   For small and low bridges, wind l d ttypically load i ll d nott control t l th the design For longer span bridge over river/sea, wind load on the structure is very important  Need to consider the aerodynamic effect of the wind on the structure (turbulence)  wind tunnel tests  Need to consider the dynamic effect of flexible l long-span b id under bridge d the h wind  dynamic analysis WL WS (on Superstructure) WS (on Substructure) Wind Load Earthquake Load: EQ  Horizontal load  The magnitude of earthquake is characterized by return period  Large return period (e.g (e g 500 years)  strong earthquake  Small return period  (e.g 50 years)  minor earthquake  For large earthquakes (rarely occur), the bridge structure is allowed to suffer significant structural damage but must not collapse F smallll earthquakes For th k ((more lik likely l tto occur), ) the th bbridge id should h ld still till bbe iin the elastic range (no structural damage)   T Tacoma Narrows N Bridge B id (Tacoma, (T Washington, W hi USA)   The bridge collapsed in 1940 shortly after completion under wind speed lower than the design g wind speed p but at a frequency q y near the natural frequency q y of the bridge The “resonance” effect was not considered at the time Earthquake Load: EQ  Earthquake must be considered for structures in certain zones  Analysis for earthquake forces is taught in Master level courses Earthquake Load: EQ     The January 17, 1995 Kobe earthquake th k hhad d its it epicenter i t right i ht between the two towers of the Akashi-Kaikyo y Bridge g The earthquake has the magnitude of 7.2 on Richter scale The uncompleted bridge did not have any structural damages Th original The i i l planned l d llength h was 1990 meters for the main span, but the seismic event moved the towers apart by almost a meter! Water Loads: WA    Typically considered in the design of substructures (foundation, piers, abutment) b t t) Water loads may be categorized into:  Static Pressure (acting perpendicular to all surfaces)  Buoyancy (vertical uplifting force)  Stream pressure (acting in the direction of the stream) Loads depend on the shape and size of the substructure Vehicular Collision Force: CT     Vehicular Collision Force: CT   Bridge structures are very vulnerable to vehicle hi l collisions lli i We must consider the force due to vehicle collision and designed for it Vehicular Collision Force: CT Typically considered in the design of substructures (foundation, piers, abutment) b t t) The nature of the force is dynamic (impact), but for simplicity, AASHTO allows us to consider it as equivalent static load load Need to consider if the structures (typically pier or abutment) are not protected by either:  Embankment  Crash-resistant barriers 1.37m height located within m  Any barriers of 1.07 m height located more than m For piers and abutment located within m from edge of roadway or 15 m from the centerline of railway track  Assume A an equivalent i l static i fforce off 1800 kN acting i hhorizontally i ll at 1.2 12 m above ground No protection to the bridge structure Better protection (still not sufficient) Vessel Collision: CV Recap No protection to the bridge piers   Loads on Bridges Typical Loads     Bridge piers are protected  Live Load of Vehicle Pedestrian Load Dynamic Load Allowance      Fatigue W d Wind Earthquake … LL Combinations LL Placement  Influence Line  Design Equation  Design Charts O h LLoads Other d  Design Lane AASHTO HL93 Loads  Truck  Tandem  Uniform Load Dead Load Live Load      Multiple Presence Distribution to Girders ... Design Chart – Simple span only Live Load Placement – Design Equation Another Method: Using Barre’s Theorem for simply supported spans  The absolute maximum moment in the span occurs under the load