Dead Loads. Load Resistance ηγ i Q i ΦR n. Design Criteria. EGCE 406 Bridge Design III. Loads on Bridge Summary of Concepts.

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1 Design Criteria We want the load effects to be less than the resistance EGCE 406 Bridge Design III. Loads on Bridge Summary of Concepts This Section Load Resistance ηγ i Q i ΦR n Load Multiplier Nominal Resistance Load Factor Resistance Factor Nominal Load Effect Praveen Chompreda Mahidol University First Semester, 2007 Loads on Bridge DD = downdrag (wind) DC = dead Load of structural and nonstructural components DW = dead load of wearing surface EH = earth pressure (horizontal) EL = secondary forces such as from posttensioning ES = earth surcharge load (vertical) EV = earth pressure (vertical) BR = breaking force of vehicle CE = centrifugal force of vehicle (at curves) CR = creep of concrete CT = vehicle collision force (on bridge or at piers) CV = vessel collision force (bridge piers over river) EQ = earthquake FR = friction IC = ice IM = dynamic load of vehicles LL = live load of vehicle (static) LS = live load surcharge PL = pedestrian load SE = settlement SH = shrinkage of concrete TG = load due to temperature differences TU = load due to uniform temperature WA = water load/ stream pressure WL = wind on vehicles on bridge WS = wind load on structure Dead Loads DC, DW

2 Dead Loads: DC, DW Tributary Area for Dead Loads Calculated from Density Material Concrete (Normal Weight.) Asphalt Density (kg/m 3 ) w DC or w DW M=wL 2 /8 Distribute to girder through Tributary Area Different load factor for DC and DW V=wL/2 DC, DW Section for maximum moment is not the same as the section for maximum shear For simply-supported beams Maximum M occurs at midspan Maximum V occurs over the support As we shall see in the designs of girders, the Critical Section for shear is about d from the support.(where d is the effective depth of section, approximately 0.8h) At this point, shear is slightly lower than at the support. If we use shear at the support for the design of stirrups, we are conservative. Live Loads LL+IM, PL

3 Live Loads: LL+IM, PL LL LL 3 basic types of LL in AASHTO LRFD, called HL-93 loading (stands for Highway Loading, year 1993) Design truck (HS-20) Design tandem Uniform loads IM (sometimes called just I ) PL Dynamic Allowance Factor, which applies to: Design Truck Design Tandem Pedestrian only: 3.6 kn/m 2 Pedestrian and/or Bicycle: 4.1 kn/m 2 LL in AASHTO are specified as Static Lane Loading HS-20 We need to consider dynamic effect of this LL We also want to know how much, at most, each girder has to carry this load, under worst possible loading patterns Analysis Strategy for LL Live Various Live Loads Design Truck Design Tandem Uniform Lane Load Transverse Placement (for slab design) Longitudinal Placement (for girder design) Place them to get maximum effects on span Consider dynamic effects Dynamic Allowance Factor (IM) Distribute Load to each girder Multiple Presence of LL Distribution Factors Moment/ Shear from Live Load to be used in the design of girders Design for 3 combinations of LL (per 1 Design Lane) Combination 1: Truck + uniform lane load Combination 2: Tandem + uniform lane load Combination 3: (for negative moments at interior supports of continuous beams) place two HS20 design truck, one on each adjacent span but not less than 15 m apart (measure from front axle of one truck to the rear axle of another truck), with uniform lane load. Use 90% of their effects as the design moment/ shear Use maximum effect of these cases for design

4 Live Load Placement - Longitudinal Live Load Placement Influence Line Methods of finding maximum moment and shear in span Influence Line (IL) Simple and Continuous spans (most general) Design Equation Simple span only Design Chart Simple span only Influence line is a graphical method for finding the variation of the structural response at a point as a concentrated live load moves across the structure We can sketch this IL by Placing Unit Load, calculate the response using statics, plot the response considered as the unit load moved along the span Use Müller-Breslau Principle IL for determinate structure consists of straight lines IL for indeterminate structure will have curved lines Influence line tells you how to place the LL such that the maximum moment at a point occurs; but not where the absolute maximum moment in the span occurs; i.e. the maximum moment on the point you picked is not always the absolute maximum moment that can occur in the span (which will occur at a different point and under a different arrangement of loads) Increase/ Decrease method for series of concentrated loads Live Load Placement Design Equation Live Load Placement Design Chart If we combine the truck/tandem load with uniform load, we can get the following equations for maximum moment in spans Bending Moment in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Moment in kips-ft IM is included 1 ft = m 1 kips = kn 1 kips-ft = kn-m

5 Live Load Placement Design Chart Live Load Placement Design Chart Shear in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Shear in kips IM is included 1 ft = m 1 kips = kn 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. However, the error is usually small. Maximum shear occurs at support. However, the chart does not have x = 0 ft. The closest is 1 ft from support. In general, the bridge girder much higher than 1 ft. Therefore, shear at 1 ft is still higher than the shear at critical section for shear (at d) so we are still conservative here. Analysis Strategy for LL Dynamic Load Allowance: IM Transverse Placement (for slab design) Longitudinal Placement (for girder design) Effect due to Static Load Dynamic Load Allowance Factor IM Effect due to Dynamic Load Various Live Loads Design Truck Design Tandem Uniform Lane Load Place them to get maximum effects on span Consider dynamic effects Dynamic Allowance Factor (IM) Distribute Load to each girder Multiple Presence of LL Distribution Factors Moment/ Shear from Live Load to be used in the design of girders Table (modified) Component Deck Joint All limit states All other components above ground Fatigue/ Fracture Limit States All Other Limit States Foundation components below ground IM 75% 15% 33% 0% Add dynamic effect to the following loads: Design Truck Design Tandem But NOT to these loads: Pedestrian Load * Reduce the above values by 50% for wood bridges Design Lane Load

6 Analysis Strategy for LL Multiple Presence of LL Various Live Loads Design Truck Design Tandem Uniform Lane Load Transverse Placement (for slab design) Longitudinal Placement (for girder design) Place them to get maximum effects on span Consider dynamic effects Dynamic Allowance Factor (IM) Distribute Load to each girder Multiple Presence of LL Distribution Factors Moment/ Shear from Live Load to be used in the design of girders Number of Loaded 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 Multiple presence factor is included in the Distribution Factor from AASHTO. We will need this only when we calculate the distribution factor from Lever Rule or other analyses (such as FEM) > 3 Multiple Presence Factor m AASHTO Girder Distribution Factor DF DF for Moment Interior Exterior DF for shear Interior Exterior Distribution Factor Lane Moment DF Lane Shear roadway width Girder Moment Girder Shear For AASHTO method first we must identify the type of superstructure (support beam & deck types) (Example) Exterior Interior Exterior DFs are available for one design lane and two or more design lanes (the larger one controls) Must make sure that the bridge is within the range of applicability of the equation

7 DF M DF M Distribution factor for moment in Interior Beams (Example) Distribution factor for moment in Exterior Beams (Example) Summary of LL+IM Calculation At any section, if not using AASHTO s GDF M LL+IM, Girder = DF M (M truck/tadem,lane IM + M uniform,lane ) m V LL+IM, Girder = DF V (V truck/tadem,lane IM + V uniform,lane ) m At any section, if using AASHTO s GDF M LL+IM, Girder = DF M (M truck/tadem,lane IM + M uniform,lane ) V LL+IM, Girder = DF V (V truck/tadem,lane IM + V uniform,lane ) Dead Load + Live Load Load Combination and Limit States Placed such that we have maximum effects

8 Design Criteria We need to consider several possible combinations of loads under different conditions Load Multiplier Load Factor Nominal Load Effect Load Resistance ηγ i Q i ΦR n Nominal Resistance Resistance Factor STRENGTH I: Basic load combination relating to the normal use of bridge. Maximum combination is used when LL produces the same effect as DC. Minimum combination is used when LL produces opposite effect to DC. STRENGTH II: load combination for special vehicles specified by owner STRENGTH III: load combination where the bridge is subjected to high wind (> 90 km/h) and traffic is prevented STRENGTH IV: load combination for long span bridges (>67 m span) which has large ratio of DC to LL STRENGTH V: load combination where bridge and traffic on the bridge is subjected to wind velocity of 90 km/h Load Factors for DC, DW EXTREME EVENT I: load combination for structural survival under major earthquake EXTREME EVENT II: load combination for structural survival under combination of events such as flood and vessel collision SERVICE I: load combination for normal operation of the bridge and for checking compression in prestressed concrete SERVICE II: load combination for steel bridges to control yielding SERVICE III: load combination relating to tension in prestressed concrete during service FATIGUE: load combination for fatigue and fracture due to repetitive LL and IM

9 Load Factors for DC, DW Consider Maximum case for Gravity load designs Load Factors for LL Notes on For slabs and girders designs under gravity loads, we normally have only DC, DW, and (LL+IM) 1.25DC DW (LL+IM) (Strength I) 1.50DC DW (Strength IV) 1.00DC DW (LL+IM) (Service I) 1.00DC DW (LL+IM) (Service II, Steel) 1.00DC DW (LL+IM) (Service III, Prestressed) Note that the sections for maximum moment of dead load and live load are not the same!!! Dead Load: midspan Live Load: some small distance away from midspan If we add them together, we are conservative! Critical moment for shear is d away from the support. We can calculate shear at this location for both dead load and live load IF we know the height of the section We estimate the height from past experiences of similar projects If we don t know, we calculate shear at the support. This is conservative but may not be economical.