Lecture # 06. Design Loads

Transcription

1 Lecture # 06 Design Loads

2 Introduction. The bridge engineer must first list all the possible loads on the superstructure; to wit, A) Permanent Loads: 01. Dead Loads 02. Superimposed Dead Loads 03. Pressures (earth, water, ice, etc.) B) Temporary Loads: 04. Vehicle Live Loads 05. Earthquake Forces 06. Wind Forces 07. Channel Forces 08. Longitudinal Forces 09. Centrifugal Forces 10. Impact Forces 11. Construction Loads C) Deformation and Response Loads: 12. Creep 13. Shrinkage 14. Settlement 15. Uplift 16. Thermal Forces D) Group Loading Combinations.

3 A Brief History of Highway Loading. The primary design parameter for highways are truck loadings. The American Association of State and Highway Transportation Officials (AASHTO), founded in 1914 as AASHO, developed the concept of a train of trucks in the 1935 that imitated the railroad industry s standards. However, as the weight of the trucks grew, the bridges were overstressed. In 1944, AASHTO developed a new concept: hypothetical trucks, called the H (with twoaxles) and the HS (with three-axles) classes of trucks. These were fictitious trucks, used only for design and they did not resemble any real truck on the road. In 1975, the federal DOT upgraded the allowable gross weight for trucks from 73,280 lb to 80,000 lb (although some states increased them to 90,000 lb). A similar standard exists for Canada (the Ontario Highway Bridge Design Code, OHBDC), or the United Kingdom, the BS5400 code. Europe has higher bridge loads, because they are designed to carry heavier loads than the US, primarily military loads.

4 Permanent Loads. Permanent loads are always on the bridge throughout its life. 1. Dead Loads (DL). The dead loads of a bridge are all the loads from the superstructure, such as, the wearing surface, the deck, the stay-in-place forms, parapets, sidewalks, railings, bracing, connection plates, stiffeners, signing and utilities. The table below shows some of the dead load unit weights that are used to calculate the superstructure.

5 2. Superimposed Dead Loads (SDL). In a typical composite superstructure, the deck is formed by an 8 inch thick slab of reinforced concrete, placed upon steel stringers or box girders. The top chord of this composite is in compression, which is ideal for concrete, and the bottom chord is in tension, which is ideal for steel. The superimposed dead loads are those loads placed on the superstructure after the deck has cured, and thus has begun to work with the primary members. These are sidewalks, railings, parapets, signing, utilities and the wearing surface. 3. Pressures. In general, earth pressures upon the back-wall of the abutment is part of the substructure. The same is true of the water pressure (and ice) upon the pier. However, part of the earth pressure can end up affecting the superstructure, and this must be checked in all designs.

6 Temporary Loads. 4. Vehicle Live Loads (LL). A live load is any load that moves along a bridge. AASHO in 1935 came up with the concept of a train of trucks, which is seen below, and identified as the H and H In 1944, the much heavier trucks (due to WWII) were the new five truck categories were, the H10-44 (20,000 lb), the H15-44 (30,000 lb), the H20-44 (40,000 lb), the HS15-44 (54,000 lb) and the HS20-44 (72,000 lb). All of these are still valid except for the H10-44, which has been dropped.

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8 The loading is now performed by placing one HS truck, for example, per lane, per span. The truck is moved along the span, to determine the point where it produces the maximum moment. Some state have very heavily loaded roads (for example, California and Texas, due to NAFTA). These states are using a semi-official class, called the HS25, with a gross vehicle weight of 90,000 lb. Notice the position of the axles of the HS The two rear axles have a variable spacing, that ranges from 14 to 30 feet. This is varies to induce a maximum positive moment in a span. For a simply supported bridge span, that spacing of the axles will be 14 feet. For continuous spans, however, the position of the axles at adjacent supports are varied to create the maximum negative moment. To model the train of trucks, two components are used: (1) a uniformly distributed load, plus (2) a concentrated load.

9 Concentrated loadings generally govern for short simple spans. Lane loading governs for long and continuous span bridges. The concentrated load is moved along the span to determine the point of maximum moment. To determine the maximum positive moment in continuous spans, only one concentrated load is used (which is also true for a simple span bridge). To determine the maximum negative moment in a continuous span, two concentrated loads are used. A reduction of the live load is permitted for bridges with three or more lanes, that have maximum stress caused by fully loading each lane. A reduction to 90% is allowed for three lane structures and to 75% for bridges with four or more lanes (AASHTO 3.12). Reduction is justified on the premise that it is unlikely that all the lanes will be fully loaded to the maximum at the same time.

10 Two additional classes of loading are used by some agencies. One is the AASHTO 3.7.4, which was developed in 1975 by the FHA (Federal Highway Administration), and is known as the Alternative Military Loading. It is represented by two axles separated by only 4 feet, and each carry 24,000 lb. All bridges on the United States Interstate system are required to compare the HS20-44 loading with the Alternative Military Loading, with the configuration that produces the greatest stress being chosen as the design criterion. The second is the P Load class. States like California, that experience a large number of over-loaded trucks, use the P loads (from permit design). The P load design vehicle has a single steering axle in front, and between two to six pairs of loaded axles in tandem.

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12 5. Earthquake Forces (EQ). Earthquake forces are a natural force, that depends on the geographical location of the bridge. These forces are temporary, and act for a short duration of time. The application of these forces to the bridge is usually studied with their effect upon piles, pile caps and abutments, via the Mononobe-Okabe analysis method. These will be studied later. There are four factors that are taken into consideration to determine the magnitude of the seismic forces: 1) The dead weight of the entire bridge; 2) The ground acceleration (all three axes); 3) The period of vibration, and 4) The type of soils or rocks serving as bearing for the bridge. The sum of these factors are reduced to an equivalent static force, which is applied to the structure in order to calculate the forces and the displacements of each bridge element. The first step is to ascertain what is the seismic performance category (SPC), via AASHTO I-A, 3.3 (next two slides). The next step is to determine the type of analysis required, via AASHTO, I-A, 4.2, which are either Method 1 (Single-Mode Spectral Analysis) or Method 2 (Multi-mode Spectral Analysis). Method 1 is the simpler of the two, and can be done by hand-calculations. Method 2 is complex, and requires specialized software. The single-mode spectral analysis uses the same procedure for calculating the longitudinal as the transverse loading. This is done via the principle of virtual displacements, in order to develop a mode shape model for the bridge. An arbitrary uniform static force p o = 1, is applied to the length of the structure in order to produce an initial displacement v s. This displacement, combined with the dead load weight of the superstructure, and part of the substructure, is used to determine the earthquake force.

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15 The next step is to calculate the dead weight value w(x) from the superstructure and part of the substructure. It can also include some live load if the bridge is in a heavily traveled urban area. From these two values, v s and w(x), we can find the fundamental period T of the bridge and the seismic force p e (x).

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18 6. Wind Forces (W and WL). Similar to the earthquake forces, wind forces are extremely complicated, but through a series of simplifications are reduced to an equivalent static force applied uniformly over the exposed faces of the bridge (both super and sub-structures) that are perpendicular to the longitudinal axis. AASHTO specifies that the assumed wind velocity should be 100 mph. For a common slab-on-stringer bridge this is usually a pressure of 50 psf, and a minimum of 300 p/lf. Truss and arch bridges require a pressure of 75 psf, and a minimum of 300 p/lf on the windward and 150 p/lf on the leeward sides. These forces are applied at the center of gravity of the exposed regions of the structure. AASHTO recommends the following for common slab-on-stringer bridges: 1) Wind force on structures (W): a) transverse loading = 50 psf b) longitudinal loading = 12 psf 2) Wind force on live load (WL): a) transverse loading = 100 psf b) longitudinal loading = 40 psf The transverse and longitudinal loads are placed simultaneously for both the structure and the live load (AASHTO ). AASHTO also requires an additional 20 psf of overturning force, to be applied at quarter points on the windward chord.

19 The design wind pressure P D can also be calculated from, For this equation, in S.I. units, V DZ is the design wind velocity at the designated elevation Z in km/h. V DZ is a function of the friction velocity V o, also in km/h, multiplied by the ratio of the actual wind velocity to the base wind velocity both at 10 m above grade, and the natural logarithm of the ratio of height to a meteorological constant length for given surface conditions.

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21 7. Channel Forces (SF and ICE). Channel forces come from the stream flow, floating ice and bouyancy. These forces affect primarily the sub-structure. The force P avg of the stream flow upon the pier, is half the maximum stream flow pressure Pmax measured by a hydrologic study. For floating ice,

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23 8. Longitudinal Forces (LF). Longitudinal forces result from the transfer of momentum from the truck braking or accelerating on a bridge. AASHTO 3.9 specifies that 5% of the appropriate lane load along with the concentrated force for moment be used as the resulting longitudinal force. This force is applied 6 feet above the top of the deck surface. The stiffer or rigid the structure, the greater the effect of the longitudinal force. 9. Centrifugal Forces (CF). A truck turning on a bridge, because of a horizontal curve exerts a centrifugal force, as calculated below, and located 6 feet above the top of the deck surface, using truck loading.

24 10. Live Load Impact (I). Trucks at high speeds may hit the deck with a large vertical force (impact) because of several causes, such as a pot hole, or a large vertical step between the approach slab and the rigid deck, etc. AASHTO defines the impact factor as follows: 11. Construction Loads (I). During the erection of the bridge, some members may be subjected to larger loads than those calculated for normal use. The experienced designer usually consults with the (likely) contractors to obtain information on the method of construction, the heavy equipment that may mount the bridge, staging materials, and other problems in order to add these loads to the bridge analysis.

25 12. Creep. Creep is the deformation of a concrete mass caused by carrying a load over a period of time. When the load is applied, the concrete experiences an instant strain (linearly related to the stress), and an instant deformation. Over time however, an additional strain (creep strain) occurs, which may be from 150% to 300% larger than the instant linear strain. Creep strain is a function of its moisture during curing. If the concrete is left to dry out, creep will be very large. On the other hand, a protected fresh concrete surface that is kept moist, will experience minimal creep strain. Excessive concrete in the deck may deform the length of the members and lead to warping or misalignments.

26 13. Shrinkage. Shrinkage is also, like creep, a deformation due to material properties. It is a consequence of the natural change in volume of concrete, and not related to load. The shrinking is due to the los of moisture during its drying. Steel reinforcing is usually added to absorb some of the tensile stresses induced by the shrinking. The best way to diminish shrinkage is to keep the concrete moist during curing, and using plasticizer to provide workability in lieu of extra water which increase shrinkage (and creep). 14. Settlement. Settlement of the foundations will produce sizable moments in the superstructure, especially differential settlement. Settlement can have one or several causes, including (1) exceeding the bearing capacity of the soils, (2) lowering of the phreatic surface, (3) vibrations, (4) loading the embankments, and (5) changes in the soil properties (for example, shrinkage and swelling). 15. Uplift. Some bridge configurations may produce the lifting of a span with respect to its adjacent elements. For example, high loading a long span, next to a short span. This is called uplift, and its discussed in AASHTO Thermal Forces. The fluctuations in temperature in a bridge may be very high, and produce sizable thermal forces. This force is similar in nature to differential settlement. For example, a bridge in a northern climate, oriented East-West, will always have its southern face heated, and the northern perennially in the shade. This bridge will have a tendency towards thermal forces. Please refer to AASHTO 3.16 on this issue. One common problem of extreme cold weather is brittle fracture of steel, which occurs instantaneously, leading to fatal failure.

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28 Group Loading Combinations. Bridges experience a combination of the previously discussed forces. Experience has generated ten load groups. These are described by the equation below.

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