STE 003 Modules 3 5 6 PDF

1 Design limit states A limit state is a condition beyond which a bridge system or bridge component ceases to fulfill the function for which it is designed. 2 tHe gOal OF stRUCtURal DesIgn The primary go...

1 Design limit states A limit state is a condition beyond which a bridge system or bridge component ceases to fulfill the function for which it is designed. 2 tHe gOal OF stRUCtURal DesIgn The primary goal of structural design is to size members and components of a system to adequately and safely sustain loads. Designers aim to prevent these conditions while balancing the goals of functionality, appearance, and economy. In engineering practice today, there are two main philosophies used: Allowable stress/strength design (ASD) - Based on safety factors Load and resistance factor design (LRFD) - Probabilistic (reliability-based) approach allOWaBle stRess DesIgn ASD is a more historic method of structural design. - It involves the use of safety factors selected based on experience and judgment. For example: - Let's say a member has a computed (or nominal) axial capacity of 100 kips. - An engineer might then employ a safety factor of 2.0. - Therefore, its allowable strength would be 50 kips. allOWaBle stRess DesIgn The main disadvantages of ASD are: It does not take into account the uncertainties associated with design. It treats dead and live load with equal statistical certainty.. Uncertainties: lOaD anD ResIstanCe FaCtOR DesIgn When employing LRFD, we modify the nominal loads and resistances by statistically calibrated factors. For resistances: -Nominal resistances (Rn) are multiplied by "ϕ" to obtain factored resistances. For loads: - Nominal loads (Qi) are multiplied by load factors ( ) to obtain factored loads.In addition, loads are amplified by load modifiers (ηi), which will be discussed later. -Instead of lumping all loads together, we typically keep them separate. Differentiates levels of probability (i.e., dead vs. live) -We then combine these loads using statistically calibrated load combinations. lOaD anD ResIstanCe FaCtOR DesIgn Therefore, the ultimate goal of LRFD is to meet the following criterion: Where = load modification factor =resistance factor =load factor lOaD anD ResIstanCe FaCtOR DesIgn lOaD anD ResIstanCe FaCtOR DesIgn lOaD anD ResIstanCe FaCtOR DesIgn limit states There are essentially four classes of limit states that we need to assess: 1. Strength limit states 2. Service limit states 3. Fatigue & fracture limit states 4. Extreme event limit states 11 limit states Strength Limit State - These are taken to ensure that strength and stability, both local and global, are provided to resist the specified statistically significant load combinations that a bridge is expected to experience in its design life. - These limit states are statistically calibrated using reliability-based methods previously discussed. - Strength limit states include the evaluation of resistance to bending, shear, torsion, and axial load. 12 limit states Service Limit State - These are taken as restrictions on stress, deformation, and crack width under regular service conditions. - The service limit state provides certain experience-related provisions that cannot always be derived solely from strength or statistical considerations. 13 limit states Fatigue Limit State - The fatigue limit state shall be taken as restrictions on stress range as a result of a single design truck occurring at the number of expected stress range cycles. - Intended to limit crack growth under repetitive loads to prevent fracture during the design life of the bridge. - The fracture limit state shall be taken as a set of material toughness requirements (AASHTO Materials Specifications). - Unchecked fatigue can lead to the development and propagation of cracks. 14 limit states Fatigue Limit State 15 limit states Extreme Event Limit State - These are taken to ensure the structural survival of a bridge during a major earthquake or flood, or when collided by a vessel, vehicle, or ice flow, possibly under scoured conditions. - Extreme event limit states are considered to be unique occurrences whose return period may be significantly greater than the design life of the bridge. - Ensures that the bridge can survive and remain functional during and after such events, minimizing the risk of catastrophic failure. 16 lOaD DesIgnatIOns Permanent and transient loads and forces that must be considered in a design are designated as follows: 17 lOaD COmBInatIOns anD lOaD FaCtORs Strength Limit States Strength I:Basic load combination relating to the normal vehicular use of the bridge without wind. Strength II:Load combination relating to the use of the bridge by Owner- specified special design vehicles, evaluation permit vehicles, or both without wind. Strength III:Load combination relating to the bridge exposed to wind velocity exceeding 55 mph. Strength IV:Load combination relating to very high dead load to live load force effect ratios. Strength V:Load combination relating to normal vehicular use of the bridge with wind of 55 mph velocity. 18 lOaD COmBInatIOns anD lOaD FaCtORs Service Limit States Service I:Load combination relating to the normal operational use of the bridge with a 55 mph wind and all loads taken at their nominal values. Service II: Load combination intended to control yielding of steel structures and slip of slip-critical connections due to vehicular live load. Service III: Load combination for longitudinal analysis relating to tension in prestressed concrete superstructures with the objective of crack control and to principal tension in the webs of segmental concrete girders. Service IV: Load combination relating only to tension in prestressed concrete columns with the objective of crack control. 19 lOaD COmBInatIOns anD lOaD FaCtORs Fatigue and Fracture Limit States Fracture I: Fatigue and fracture load combination related to infinite load- induced fatigue life. Fracture II: Load combination intended to control yielding of steel structures and slip of slip-critical connections due to vehicular live load. Fractured components can lead to an unstable structure, posing significant safety hazards and potentially leading to catastrophic collapse. 20 lOaD COmBInatIOns anD lOaD FaCtORs Extreme Even Limit State Extreme Event I: This limit state covers load combinations related to earthquakes, including water load (WA) and friction (FR), with considerations for partial live load coinciding with an earthquake. Extreme Event II: This limit state includes load combinations related to hydraulic events, which can encompass flooding caused by typhoons, as well as ice load and collisions by vessels and vehicles. 21 lOaD COmBInatIOns anD lOaD FaCtORs 22 lOaD COmBInatIOns anD lOaD FaCtORs 23 lOaD COmBInatIOns anD lOaD FaCtORs Simplifying Load Combinations Identify Relevant Load Types: For specific bridge types (e.g., composite steel girder bridges), focus on the most relevant loads such as dead load, live load, and wind load. Exclude loads that do not significantly impact the structure, such as prestressing forces, extreme event forces, and thermal loads (if not critical). Consider maximum and minimum envelopes for loads to capture the most critical effects. 24 lOaD COmBInatIOns anD lOaD FaCtORs Composite Steel Girder Bridges (No earthquake and typhoon) Strength I: 1.25DC + 1.50DW + 1.75(LL + IM)1.25DC Strength III: 1.25DC + 1.50DW + 1.40W Strength IV: 1.50DC + 1.50DW Strength V: 1.25DC + 1.50DW + 1.35(LL + IM) + 0.40WS + 1.0WL Service II: 1.00DC + 1.00DW + 1.30(LL + IM) Fatigue I: 1.50(LL + IM) Fatigue II: 0.75(LL + IM) 25 sHORt QUIZ PaRt 1 (10 mInUtes) You will be asked to provide a short commentary on a question related to bridge engineering design principles. 3 points each. STUDENT ID NUMBER ENDS IN EVEN NUMBER OR 0 1. Discuss briefly why suspension bridges are favored for spanning long distances. 2. Give 1 reason why LRFD is more advantageous than ASD. STUDENT ID NUMBER ENDS IN AN ODD DIGIT 1. Why do we multiply the resistance with a reduction factor Φ in engineering design? 2. Why is a service limit state necessary for bridge structures? 27  IntenDeD leaRnIng OUtCOme At the end of this discussion, the student shall be able to: 1. Understand the differences between permanent and transient loads and their significance in bridge design. 2. Able to calculate for dead loads common to slab deck/ steel girder bridges. 3. Understand the design truck, design tandem, and lane load seen in a bridge structure. 28 BRIDge lOaDs A limit state is a condition beyond which a bridge system or bridge component ceases to fulfill the function for which it is designed. 29 BRIDge lOaDs The primary goal of structural design is to size members and components of a system to adequately and safely sustain loads. Designers aim to prevent these conditions while balancing the goals of functionality, appearance, and economy. In engineering practice today, there are two main philosophies used: Allowable stress/strength design (ASD) - Based on safety factors Load and resistance factor design (LRFD) - Probabilistic (reliability-based) approach BRIDge lOaDs Bridge loads may be divided into two broad categories: The permanent loads remain on the bridge for an extended period, usually for the entire service life. Such loads include the self-weight of the girders and deck, wearing surface, curbs, parapets and railings, utilities, luminaries, and pressures from earth retainment. Transient loads typically include gravity loads due to vehicular, railway, and pedestrian traffic as well as lateral loads such as those due to water and wind, ice floes, ship and vehicular collisions, and earthquakes. PeRmanent lOaDs Loads that remain on the bridge throughout its entire service life. 1. Self-weight of Structural Components or Nonstructural Attachments (DC) - These are loads that represent the inherent weight of the bridge’s primary structural elements, which are part of the load-resisting system including the weight of bridge girders, bridge deck, primary and secondary beams, piers, and columns, abutments and diaphragms and cross beams. PeRmanent lOaDs Many of the components of DC loading are applied before the concrete deck becomes composite. Therefore we split DC into two components: DC1 : Noncomposite dead loads applied to steel section only. DC2 : Composite dead loads applied to long term-composite section. PeRmanent lOaDs 2. Wearing Surface (DW) - This category covers the elements related to the top layer of the bridge deck that directly interacts with traffic. It includes asphalt or concrete overlay, road markings, anti-skid treatments and drainage structures. PeRmanent lOaDs 3. Earth Loads - These loads are associated with earth materials interacting with the bridge structure. Dead Load of Earth Fill (EV): The weight of earth or other fill material that rests on or around the bridge structure. Earth Pressure Load (EH): Lateral pressure exerted by the surrounding soil on bridge abutments, retaining walls, or piers. Earth Surcharge Load (ES): Additional load due to structures, vehicles, or other materials placed on the surface above the natural ground level adjacent to the bridge. PeRmanent lOaDs 4. Locked-in Erection Stresses (EL)- These stresses arise during construction and remain in the structure after completion. Pre-tensioning Stresses: Residual stresses from pre- tensioned tendons or cables before the concrete is cast. Post-tensioning Stresses: Stresses from post-tensioned tendons or cables after the concrete has hardened. Construction Stages: Stresses from temporary loads during construction stages that may become locked in the structure. PeRmanent lOaDs 5. Downdrag (DD) - These stresses arise during construction and remain in the structure after completion. Foundation Settlement: Movement of the foundation due to consolidation or compaction of underlying soils. Pile Settlement: The downward movement of piles driven into the ground due to long-term soil creep or other subsurface changes.Negative Skin Friction: Additional downward drag on piles or shafts from surrounding soil that settles at a slower rate than the pile or shaft. InDIVIDUal aCtIVItY 11.5 m 11.1 m 0.6 m 0.1m 225 mm Conc. Slab (23.5 kN/m3) 20 mm wearing surface = = 21.5 kN/m^3 Stay in place concrete = 0.65 kPa 0.4m Misc Details = 4% of girder weight Barrier = 18 kN/m^3 0.2m 75mm 0.8m 3 @ 3.3 m 0.8m A = last digit of W1200x300 your student ID Bf=3A0 mm number 50 m sYstem analYsIs The slab and slab–girder bridges are the most common types of bridge. The principal function of the slab is to provide the roadway surface and to transmit the applied loads to the girders.  sOlVIng DC anD DW 10.8 m 10.5 m 0.6 m 210 mm Conc. Slab (23.5 kN/m3) 15 mm wearing surface Stay in place concrete = 0.7 kPa Misc Details = 5% of girder weight Barrier = 2 kN/m Bituminous Wearing = 22 kN/m^3 50mm 0.75m 3 @ 3.1 m 0.75m W1000x222 Bf=300 mm 50 m tRansient lOaDs (ll + Im) Of course, we need to design highway bridges for some sort of vehicular loading.  However, it should be noted that "cars" really do not induce any appreciable load demand on highway bridges.  It is "truck" loading that produces the effects for which engineers design highway bridges. tRansient lOaDs (ll + Im) Specifically, the vehicles in question are exclusion vehicles, such as concrete mixers, short-haul vehicles, and high-impact vehicles.  In other words, those vehicles that produce the extreme effects. This presents a problem, though:  Do we have to design for ALL of these loads? tRansient lOaDs (ll + Im) Instead, AASHTO has developed a live load model that simulates the effects of the extreme loading on highway bridges. The HL-93 vehicular live load. The load model consists of the traditional HS20-44 truck and other components. When compared to the traditional truck, the new HL-93 model better captures highway bridge loading tRansient lOaDs (ll + Im) Specifically, the components of HL-93 live load model (LL) are the following: The design truck load. The design tandem load. The design lane load (Equal to 640 lb/ft=-0.64 kip/ft= 9.4 kN/m) tRansient lOaDs (ll + Im) HL-93 vehicular live load (design truck) 36 kN 144 kN 144 kN Varies from 4.27 m 4.27 m to 9m 1.8 m tRansient lOaDs (ll + Im) HL-93 vehicular live load (design tandem) 111 kN 111 kN 1.2 m 1.8 m tRansient lOaDs (ll + Im) HL-93 vehicular live load (design lane load) tRansient lOaDs (ll + Im) In addition to live load model, the engineer must account for the dynamic effects of vehicular loads. In particular, due to varying surface roughness, vehicular loads experience dynamic amplification. We account for this by employing dynamic load allowance (IM), commonly known as impact factors. For deck joints IM = 1.75 For the Fatigue IM = 1.15 It should be noted that these factors Limit State are only applied to the truck and tandem. For all other limit IM = 1.33 states InDIVIDUal aCtIVItY 11.5 m 11.1 m 0.6 m 0.1m 225 mm Conc. Slab (23.5 kN/m3) 20 mm wearing surface = = 21.5 kN/m^3 Stay in place concrete = 0.65 kPa 0.4m Misc Details = 4% of girder weight Barrier = 18 kN/m^3 0.2m 75mm 0.8m 3 @ 3.3 m 0.8m A = last digit of W1200x300 your student ID Bf=3A0 mm number 50 m gROUP aCtiVitY maximUm mOments OF Hl-93 mOVing lOaDs FOR simPle sPan maximUm mOments OF Hl-93 mOVing lOaDs FOR simPle sPan maximUm mOments OF Hl-93 mOVing lOaDs FOR simPle sPan maximUm sHeaRs OF Hl-93 mOVing lOaDs FOR simPle sPan maximUm sHeaRs OF Hl-93 mOVing lOaDs FOR simPle sPan maximUm sHeaRs OF Hl-93 mOVing lOaDs FOR COntInUOUs sPans Loading for Maximum Negative Moment maximUm sHeaRs OF Hl-93 mOVing lOaDs FOR COntInUOUs sPans maximUm sHeaRs OF Hl-93 mOVing lOaDs FOR COntInUOUs sPans PeRmIt VeHICle lOaDIng PeRmIt VeHICle lOaDIng PeRmIt VeHICle lOaDIng PeRmIt VeHICle lOaDIng sUPeRstRUCtURe FRaming Plan 72  steel tRUsses The steel truss system consists of vertical trusses, struts, sway and portal braces, top wind braces, transverse floor beams and floor stringers.  steel tRUsses The main steel trusses are made up of the top chord, bottom chord, diagonal and vertical members. Steel trusses function similarly as I-beam where the top and bottom chords act like the top and bottom flanges of an I-beam, respectively. The main advantage of using trusses is the considerable truss height serves as the lever arm resulting into a very high moment capacity.  steel tRUsses The compression chord (For simple span trusses, this is the top chord) is subject to buckling and therefore must be braced (to reduce unbraced length). The bottom chord is the tension resistance and the most efficient member requires smaller sizes than the top compression chord. The web members (vertical and diagonal), are tasked to resist the shear force and highest at the support. Some are in tension and some experience compression. h FlOOR FRamIng sYstem The deck is commonly a concrete slab but in certain cases, metal decking is used. The use of metal decking makes for a very light superstructure, can be installed quickly but can be annoyingly noisy used by vehicular traffic. The deck can be supported by longitudinal stringers that are in turn supported by transverse beams that transmit the loads to the trusses. In the figure, the concrete deck is a one-way slab with the main reinforcements in the transverse direction (perpendicular to traffic). lOaD CalCUlatIOns A. Permanent loads - The stringers and transverse beams are usually made with the concrete deck. As such, the non-composite dead loads DC (stringers, beams and attachments, miscellaneous details, haunch and slab) are accounted separate from the composite dead loads DW (curb, railings, medians and wearing surface). B. Transient Loads B.1 Vehicular Traffic Load for Longitudinal Stringers B.2 Vehicular Traffic Load for Transverse Beams lOaD CalCUlatIOns lOaD CalCUlatIOns The vehicles in a multi-lane bridges are positioned within the traffic lanes and the wheels of the HL-93 vehicles are placed at a distance of 0.6 m from the traffic lane boundaries. lOaD CalCUlatIOns The loads from the floor live load will not be equally distributed to the trusses when the live loads are not positioned symmetrically with the bridge centerline. This unbalanced distribution can be expressed as the ratio of maximum support shear over twice of the total live load. 𝑉 𝐹𝑎𝑐𝑡𝑜𝑟 = 2𝑃 lOaD CalCUlatIOns C. Pedestrian Live Loads - To maximize the loading on the transverse beams and truss system, the pedestrian live load of 3.6 kPa is applied as well simultaneous with the vehicular traffic live loads, if sidewalks for pedestrians or bicycle lanes are present. However, the pedestrian live loads are considered to have no dynamic load effect. - The pedestrian live load is not applied in the design of the slab. tRUss DesIgn examPle lOaD analYsIs A steel truss superstructure with a composite floor system is to be designed using A-50 steel, A490 bolts, 300 mm thick concrete slab with compressive strength of 28 MPa. Additional Data Asphalt Thickness = 50 mm Sidewalk Thickness = 200 mm Haunch Thickness = 100 mm Miscellaneous Details = 5% of the beam weight Add 50 mm on each sides of the bridge for barriers and construction allowance. examPle lOaD analYsIs 8 @ 6m = 48 m 9 @ 6m = 54 m 9 @ 6m = 54 m