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In order to form a consistent basis for design, organizations like AASHTO, American Association of State Highway and Transportation Officials, have developed a set of standard loading conditions which are applied to the engineer's design model of the structure. Other nations maintain their own set of design loads like the BS 5400 loads utilized in the United Kingdom or the Ontario Highway Bridge Design Code, OHBDC, loads utilized in the Canadian province of Ontario and elsewhere in that nation. (1) Permanent loads, as the name would imply, are those loads, which always remain on a bridge throughout its life. Although the term dead load is often used synonymously with permanent loads, there are distinctions, which need to be made. Permanent loads are divided into the following three major categories: dead load, superimposed dead load, and The dead load on a superstructure is the aggregate weight of all superstructure elements (i.e. those elements above the bearings). This would include, but not be limited to, the deck, wearing surface, stay-in-place forms, sidewalks and railings, parapets, primary members, secondary members (including all bracing, connection plates, etc.), stiffeners, signing, and utilities. One of the first steps in any design of a superstructure is to compile a list of all the elements, which contribute to dead load. Table 1.1 ,at the end, provides a list of some dead load unit weights that are used in computing the overall superstructure In composite construction superimposed dead loads are those loads placed on the superstructure after the deck has cured and begun to work with the primary members in resisting loads. From the table 1.1 the designer would separate items such as sidewalks, railings, parapets, signing, utilities, and the wearing of the surface. Pressures due to earth and water are also considered permanent loads. While these loads primarily affect substructure elements, they have the potential of impacting superstructure elements as well at points where these two components interface (e.g., at the abutment backwall). This gives us a good reminder that while we are discussing the structure's individual components, we can not lose sight of the structure as a whole. Temporary loads are those loads, which are placed on a bridge for only a short period of time. Just as dead loads are the permanent loading condition, live loads represent the major temporary loading condition. There are, however, several other classes of temporary loads, which the designer must consider. The temporary loads are: vehicle live load, earthquake live load, wind loading, channel forces, centrifugal forces, impact forces, The term live load means a load that moves along the length of a span. Therefore, a person walking along the bridge can be considered live load. Obviously, a highway bridge has to be designed to withstand more that pedestrian loading. To give designers the ability to accurately model the live load on a structure, hypothetical design vehicles based on In 1935, what was then called the AASHO issued a loading scheme based on a train of trucks. These are identified as H-20-35 and H-15-35 in figure 2.1.(4) To meet the demands of heavier trucks, the introduction of five new classes were made in 1944. These classes have the following designations and gross vehicle weights: * H15-44 (30,000 lbs. - 13,608 kg) * H20-44 (40,000 lbs. - 18,144 kg) * HS15-44 (54,000 lbs. - 24,494 kg) * HS20-44 (72,000 lbs. - 32,659 kg) Today, all but the H10-44 vehicles are still in included in the AASHTO specifications. To load a structure one such truck per lane, per span is used. The truck is then moved along the length of the span to determine the point of maximum moment. Recently, to account for higher load conditions, some states have begun using the HS25 design vehicle, which represents a 25 percent increase in loading over the standard HS20-44 truck for a total gross vehicle weight of 90,000 lbs. (40,824 kg).(1) It is important to stress that the H and HS trucks do not represent an actual truck being used to transport goods and materials. They are approximations used to simulate the greatest Replacing the train of trucks in the 1935 circa design code are laneloading configurations, which approximate a 40,000 lb. truck, followed by a train of 30,000 lb. truck. To model this, a uniform distributed load is used, combined with a concentrated force. This force varies for moment and shear computations. Where truck loading generally governs for short, simple spans, lane loading typically hods for long continuous span bridges. Like truck loading, the concentrated load is moved along the span to determine the point of A reduction in the live load intensity is permitted for bridges with three or more lanes that have maximum stress caused by fully loading each lane.(1) A 90 percent reduction of three land structures and 75 percent reduction for bridges with four or more lanes is allowed. The reduction is permitted given the rarity of the situation where simultaneously While I have discussed the legal load limits for trucks, there is also the issue of providing for those trucks which are overweight. In an attempt to deal with extralegal loading conditions, the California Department of Transportation developed a live loading configuration known as the permit design loads or P loads. Like their H and HS cousins, P loads are hypothetical design vehicles. The P load design vehicle consists of a steering axle and between two to six pairs of tandems. The number of tandems used is based on the configuration that produces the maximum stress in a span. The abbreviation LL is used to reference live load in the text. The abbreviation DL is used in reference to dead Earthquake loading is a product of natural forces which are dependent on the geographic location of the bridge. In general, there are three major forces with which the bridge engineer must be concerned: Seismic Forces, Wind Forces, and Channel Forces. Like the vehicle live loads discussed before, seismic, wind, and channel forces are temporary loads on a structure which act for a short duration. Superstructure elements, though are affected by seismic forces in many ways. An earthquake exerts forces on a bridge that are defined as a function of the following These factors are used to determine the response of the bridge to an assumed uniform loading on the structure. This response takes the form of an earthquake loading which is applied to the structure to calculate forces and displacements on bridge elements. The AASHTO specifications provide two methods for calculating this loading. The method used is dependent of whether the bridge is single span or multispan and the geometric characteristics of the structure. Since single span structures can be considered to be extremely stiff and their ability to withstand earthquakes is deemed adequate, AASHTO decided to segregate their analysis from bridges with two or more spans.(1) The analysis of multispan bridges varies depending on the type of geometry present and the degree of seismic activity at the bridge site. The regular bridges are those with consistent and similar superstructure cross sections and intermediate support structures. Bridges with varying cross section and different types of support are considered irregular. The degree of seismic activity is based on the acceleration coefficient at the bridge site. The acceleration coefficient is a dimensionless constant used to describe ground motion.(2) Bridges with an acceleration coefficient greater that 0.19 are considered to be in an area of high seismic activity. This coefficient, along with whether the bridge is classified as essential or not, are used to assign the bridge a seismic performance category Based on the SPC and the number of spans, one of two different analysis methods are chosen to calculate the loading on the bridge due to earthquake forces. The two methods In general, regular bridges in area of low seismic activity utilize the less involved single-mode analysis method, while irregular bridges in high seismic risk locations require the multimode spectral analysis. The former can be performed using conventional hand calculation method, but the latter demands more rigorous computer-aided solutions. The single-mode spectral analysis method assumes loading in basic transverse and longitudinal directions as illustrated in figure 2.2(4) The multimode approach, however, is required because of the irregular bridge geometry which necessitates analysis to determine the effects of coupling in three coordinate directions for each vibration mode. For regular multispan bridges the single-mode spectral analysis method for calculating equivalent static earthquake loading is shown below. The single-mode spectral analysis procedure uses the same method for calculating both longitudinal and transverse earthquake loading. This method utilizes the principle of virtual displacements to develop a mode shape model of the bridge. An arbitrary, uniform static loading po is applied to the length of the structure to provide an initial displacement vs. This displacement, combined with the DL weight of the superstructure, can be used to The first step is to calculate the initial displacement of our generalized model. Figure 2.2 shows the longitudinal loading of the structure. The initial displacement vs is illustrated at the piers and at the end of the last span. This value varies depending on the type of piers in place. The displacement is calculated assuming an arbitrary unit load of po = 1. The next step is to calculate the DL value w(x). This represents the DL of the superstructure and contributing substructure elements. It is even possible to include live load values for structure in high traffic urban area where large numbers of vehicles may be present on the structure during an earthquake. Once the values of vs and w(x) are known the following three factors can be calculated: With these factors known, the fundamental period of the bridge can be computed Now it is almost time to compute the resultant horizontal earthquake loading on the structure. This loading can be described as a function of AASHTO provides an elastic seismic response coefficient which quantifies these parameters into dimensionless value. This single coefficient greatly simplifies the analysis since it does not require the designer to calculate an overall site period. The coefficient is Where A = Acceleration Coefficient (see figure 2.3) S = Site Coefficient (see table 1.2) With the values from these equations in place, the intensity of the earthquake loading can be computed. This loading is an approximation of the inertial effects resulting from the dynamic deflection of the structure and is defined as Pe(x) = [((Cs)/(()] w(x) vs (x) Eq. 6 This load can now be applied to the structure in a fashion similar to the one in which the initial unit loading of po = 1 was at the beginning of the process. Now, though, the value of Pe(x) is substituted to determine displacement, shears, and moments due to Like earthquake loading, wind loading offers a complicated set of loading conditions which must be met in order to provide a workable design. Although the problem of modeling wind forces is a dynamic one, with winds acting over a given time interval, these forces can be approximated as a static load being uniformly distributed over the exposed The exposed region of the bridge is taken as the aggregate surface areas of all elements as seen in elevation. The loading on a bridge due to wind forces is specified by AASHTO based on an assumed wind velocity of 100 miles per hour. For conventional girder/beam type bridges this translates into an intensity of 50 pounds per square foot with the minimum total force being 300 pounds per foot. Trusses and arches require wind loads applies with an intensity of 75 pounds per square foot with the minimum total force of either 150 or 300 pounds per foot, depending on whether the affected member is windward or leeward chord. The windward chord is that chord exposed to the prevailing wind and the leeward chord is located away from the wind. With regard to the superstructure, wind forces are applied in a transverse and longitudinal direction at the center of gravity of the exposed region of the superstructure. AASHTO offers a set of wind loading values for truss and girder bridges based on the angle of attack of wind forces. Conventional slab-on-stringer bridges, however, with span lengths less that or equal to 125 ft can utilize the following basic loading: Transverse loading = 50 lb/ft² (2.39 kN/m²) Longitudinal loading = 12 lb/ft² (0.57 kN/m²) Transverse loading = 100 lb/ft (1.46 kN/m) Longitudinal loading = 40 lb/ft (0.58 kN/m) The transverse and longitudinal loads are to be placed simultaneously for both the structure and love load. Another loading consideration is the effect of overturning. To account for this, AASHTO specifies a 20 lb/ft² overturning force to be applied at quarter Channel forces are those loads imposed on a structure due to water course-related features. These forces include, but are not limited to, stream flow, floating ice, and buoyancy. Channel forces, similar to seismic forces, primarily affect substructure When a bridge is subject to loads, its constituent elements develop internal forces which resist those loads. In general, the resisting of loads of When a load is placed on a structural member, the member will respond by bending. This bending is resisted by an internal rotational force or moment. These rotational forces are equal and opposite couples which act in a common plane. From basic statics, it is known that a moment can be quantified as a force times a distance. Since the loads on bridges are relatively large, U.S. values are typically given as ft-kips where a kip is a 1000-pound force. The SI equivalent unit is kN-m. Stresses in a member that result from bending forces are referred to as bending stresses or sometimes as flexural stresses. In bridges design, primary members are the elements that are most affected by bending forces. As the load acts downward the effects of which are compression at the top most part of the beam and tension at the bottom. It is at the top and bottom of the girder where stresses are the greatest. Stresses decrease to zero approaching the neutral A shear force will cause an internal force in a member which acts in the plane of the section. The shear stress will be referenced according to the particular plane in which it acts. In a wide flange girder, vertical shear occurs in the beam cross section if the beam is loaded vertically. Horizontal shear acts along the length of a girder if the member is loaded longitudinally. One can visualize the effects of shear stress as one cross-sectional piece moving in the opposite direction and another, adjacent cross-sectional piece moving An internal shear force is induced by a load acting in the opposing direction. In a bridge, the greatest danger for shear occurs at supports where a load, combined with a beam reaction, can result in high shear stress. From basic strength of materials, we can find that average shearing stress is defined as the load divided by the resisting area. Taking a wide flange girder as an example, vertical shear would be computed as the load It is know from basic engineering physics that torsion is a twisting about the longitudinal axis of a member. When the effects of torsion are severe, box girder structures are used because of their ability to resist torsional forces. Torsional forces are caused by eccentric loads (i.e. loads that are not placed on top of the member).(3) In highway bridge, torsional forces could result from wind forces, eccentric wheel loading, or other overturning type loads. When a torsional force is applied to a member, the maximum stresses will occur at the outer face of the element. Similar to bending, where stress is zero at the neutral surface, torsional stresses are zero along the longitudinal An axial force is one which acts along the longitudinal axis of a member. Depending on the direction of the force, the axial force will induce either compression or tension. If the load is acting toward the member, it will be compressed, and if it acts away from it, the member will be in tension. An example of an element under compression axial force would be a pier column. A tensile axial force in a cable, for example, of a As one would expect, compression members have a large cross-sectional area with respect to their length. This geometry is required to resist loads and avoid buckling of the member. Beyond buckling, there is also the concern of crushing of an axially loaded member in compression. Members more susceptible to tensile axial forces, have a cross-sectional area which is small when compared to its length. So far, I have discovered that bridge loads are transmitted from the deck to the superstructure and then to the supporting substructure elements. Exactly how are these loads transmitted through? If a truck is traveling over the top of a primary member, it is logical to say that this particular beam is resisting the truck load. This stringer, however, is connected to adjacent primary members through some form of secondary member. In addition to this, the bridge deck itself acts as a connection between longitudinal girders. This connectivity allows different members to work together in resisting loads. Returning to the example of the truck traveling over the top of a specific primary member, it would be logical to assume that this specific beam is carrying most of the load. As a result of being connected with the girder is question, adjacent members assist in carry part of the load. Exactly how much load they carry is a function of how the load is transmitted or distributed to them. Determining the fraction of load carried by a loaded member and the remainder distributed to other members is what I will discuss now. The highway bridge, as mentioned previously, is not a collection of elements, each performing a specific function, but rather an integrated unit. The modeling of how a load is actually dispersed from the deck down through the substructure is not a trivial undertaking. A wide variety of parameters which range from the structure's geometry to element material properties influence exactly how loads are distributed. Where defining a precise mathematical model of what happens to a bridge load in a structure is complicated, it is possible to examine the variables which influence the distribution. The influencing parameters are a function of the bridge superstructure cross-sectional properties. The following parameters determine how loads are distributed in a bridge superstructure. It should be kept in mind that this is a general list and that other variables could potentially affect the distribution on loads. With this in mind, the Table 1.3 shows the AASHTO wheel load distribution factors for various floor type and spacing configurations. Distribution will also vary depending on whether longitudinal or transverse members are being analyzed. It is important to note that these factors are applied to wheel loads. When computing the bending moment due to the LL, a fraction of both the front and rear wheel loads is taken to act on a given interior stringer. Consulting table 1.3(4), for concrete deck with two or more lanes and a stringer spacing of less than 14 ft, the resultant distribution factor will be DF = S/5.5 = 7.0 ft/5.5 = 1.27 Eq. 7 This value would be multiplied by half the weight of the design truck. The total weight of an H20-44 truck is 8,000 lb. (front axial) + 32,000 lb. (rear axle) or 40,000 lb. Therefore, one set of from and rear wheels would be half this amount or 20,000 lb. or 20 kips. When computing bending moments the distributed load used would be(2) Distributed Load = DF•One set of wheels This means that 25.4 kips of the 40 kip H20-44 truck acts on any given interior stringer and the remaining 14.6 kips are distributed amongst the other girders. If the spacing between the stringers had been greater than 14 ft, the concrete deck between the two adjacent interior stringers would be assumed to act as a simple beam. The wheel loads would then act on this simple beam and the resulting reactions taken as the load on any individual stringer. If the bridge were carrying only one design traffic lane, then the distribution factor would have been S/7.0 rather than S/5.5.(2) In addition to floor type and stringer spacing, the criteria governing load distribution vary depending on the orientation of the member being analyzed and its position. The following offers a general overview of some of the major types of floor systems and the related AASHTO requirements for distribution of loads. As discussed before, the live load distribution factor is determined from table 1.3. This accounts for lateral distribution of loads only. No longitudinal distribution of wheel loads is allowed. Live load bending moments are computed using on set of front and rear wheels multiplied by the distribution factor. Unlike an interior girder, outside girders are often subject to dean loads over and above those caused by the deck and superstructure frame. Loads such as curbs, sidewalks, railings, barriers, etc., which are placed on an exterior girder can be distributed equally among primary members. For slab-on-stringer bridge with four or more stringers, the following distribution factors are used(1) DF = S/5.5 (S( 6 ft) or DF = S/ (4.0 + 0.25S) (6(S(14ft) Where S = distance between exterior and adjacent interior stringer From that equation it is shown that the distribution factor will vary depending on the spacing of stringers. As is the case with many interior stringers, when the spacing between an exterior and adjacent interior stringer exceeds 14 ft, the flooring between the two stringers is taken to act as a simple beam with the load on each stringer being the resulting wheel load reaction. This is also the general load distribution approach taken for When an exterior stringer is also intended to carry live load, the allowable stress may increase by 25 percent, provided that the stringer possesses the capacity which would be required even if there were not a sidewalk present. If a load factor design approach is being used and the condition exists where sidewalk plus traffic LL controls, a ( factor of 1.25 is used in lieu of the 1.67 value specified.(2) The AASHTO specification does not allow for any lateral distribution of loads for transverse members. When there are no longitudinal members present and the deck is supported entirely by floor beams, the distribution factors are used. The distribution factors for transverse members are dependent on floor type and the spacing between floor A multibeam concrete deck can be either conventionally reinforced or prestressed. Precast prestressed concrete panel decks were discussed earlier. Briefly, these types of decks consist of concrete panels which run longitudinally and are placed next to one another. The panels are connected together with a shear key and lateral bolts. As with other longitudinal members, no longitudinal distribution of wheel loads is allowed. The AASHTO approach takes into account the stiffness of the deck panels through use of a stiffness parameter C is given as(1) C = (W/L)(((I/J)(1 + ()) = (W/L)(K Eq. 8 Where W = width of entire bridge perpendicular to beams, ft L = Span length taken parallel to longitudinal girders, ft ( = Poisson's ration (referred to in most texts as v) for concrete, poisson's ratio The boundary within which the stiffness parameter C falls and its value are used to define D = (5.75 -0.5NL) +0.7 NL(1-0.2C)² for C(5 Eq. 9 Therefore, like other members, the resultant distribution factor can be calculated as a function of the spacing between stringers using the equation If the value of ((I/J) is great than 5.0, AASHTO recommends that a "more precise method" such as grillage analysis, be used. From the above, it can be seen that the value of the distribution factor is greatly dependent on the cross-sectional geometry of the precast panel. Both the moment of inertia and torsional constant are functions of the type of panel/beam used. AASHTO provides a list of general constant values for use in the preliminary design of a multibeam bridge.(1) As can be seen from the design perspective, the approach which AASHTO takes for the distribution of loads has fostered some debate as to whether or not the method is too conservative. Regardless of the merits of such arguments, the subsequent text will utilize the AASHTO load distribution specification, when appropriate. The AASHTO code places the distribution of loads for concrete slabs within the same section as that which describes the general design criteria for this element. For load distribution criteria pertaining to other less common flooring, such as timber flooring (wood), you can be referred to the AASHTO specifications directly for information. Bibliography: References: 1. American Association of State Highway and Transportation Officials (AASHTO): Standard Specifications for Highway Bridges, Washington, D.C., 1977 2. Bakht, B. and Jaegar, L.G.: Bridge Analysis Simplified: 1985 3. Serway: Physics for Scientists and Engineers: Vol. 1, 4th ed. 1996 4. Hoelsher, R.P. and Springer, C.H. and Dobrovolny, J.S.: Graphics for Engineers: Visualization, Communication, and Design, New York, New York, 1968 Word Count: 4268
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