Lecture 06 design loads
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  • 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: • • • – 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: • • • • • – 01. Dead Loads 02. Superimposed Dead Loads 03. Pressures (earth, water, ice, etc.) 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-20-35 and H-15-35. 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.
  • 7. H20-44 8,000 LB H15-44 6,000 LB 32,000 LB 24,000 LB HS20-44 HS15-44 14'-0" :s: . f - - - - - - - ' - - ' - - - - ' ' - - - - - --.;' ~ ,.. d• -- 1 0.1 :s:·.. ~I ,c::) W 8,000 LB 6,000 LB 1-----------10.4W 1 ----- 32,000 LB 24,000 LB 14'-0" c=> I ..... I I :s: co 32,000 LB 24,000 LB .. ·:s: I~ v ~~ c:::i - - - - - I 0.1 w 1 ---- ~ 0.4 w ~ ---- ------- ---- I 0.4 w ~ I I I I -- I o.j w 1- - - -- - - - - - - 1 w 1 -o.4 -- -· W =TOTAL WEIGHT OF TRUCK AND LOAD I I I I I I ----- I 0.1' w 1 ---- ~ o.4 w ~ ----- --------- - I o.4 w ~ - W =COMBINED WEIGHT ON THE FIRST TWO AXLES, WHICH IS THE SAME AS FOR THE CORRESPONDING H TRUCK. V =VARIABLE SPACING-14FT TO 30FT INCLUSIVE. SPACING TO BE USED IS THAT WHICH PRODUCES MAXIMUM STRESSES. 10'-0" CURB 2'-0"_J 6 0 1~--=-·-=---·-~1 1-4... 1.- 2'-0" Standard H T.-ucks 2'-0"_J 6 -0 lt+--=-'-=--" - - + 11 .. .. 1.-2'-0" Standard HS T.-ucks AASHTO Standard H & HS Design Trucks. (Adapted from Standard Specifications for Highway Bridges, 15th Ed., Ref 3.3.)
  • 8. The loading is now performed by placing one HS-20-44 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 HS20-44. 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.
  • 11. ~ I. PS P7 pg P11 P13 18'-0~ 26K 26K 26K 26K -26K !:URJ l13Kl I. .I ~"-wm- ~~~~ '*(fij 18'-0~ 48K 48K 48K 48K · · 48K .1. 18'-0~ 48K 48K 48K 48K 48K I 18'-0" .I 18'-0" 48K 48K 48K 18'- 0" I 18'-0~ .. 48K 48K fiE Em fiE~ tmfm tmtm Em fiE EfE,fm fiE Em I .1. 2'-3~ Min. Veh. 48K 48K 48K 48K fm~ 18'-0" ~-··typ j 18'-0" .I. 18'-0~ I I 48K Em~ ~Em Max. Veh. tmtm Emtm 18'-0" a I I • 18'-0" .I 1 o·-o· clearance Caltrans permit truck. (AASHTO LRFD Bridge Design Specifications 2nd. ed., American Association of State Highway and Transportation Officials. Washington, D.C., 1998. With permission.)
  • 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 po = 1, is applied to the length of the structure in order to produce an initial displacement vs. This displacement, combined with the dead load weight of the superstructure, and part of the substructure, is used to determine the earthquake force.
  • 13. I I ' ' I I ~ -' 3 ' ' R / I I I I I I I I I I I I II $.., / I .; .; I ;4 ' I 6 ~ ' ' 2 I I '5- I I I --' ~ I 'R>" ,~· ,..5, ~',.;-,, I /-- ..... '',A~'"', ·~-1111 ' '« ·~ -...""/I -'I 1.5 '~ Horizontal acceleration (A) values. Divide values on map by 100 to obtain the coefficient used in calculations. (Adapted from Standard Specifications for Highway Bridges, 15th Ed., Ref 3.3.) Consult map in the AASHTO specificationsfor more detail.
  • 14. AASHTO SPECIFICATION DIVISION I·A 3.3 IMPORTANCE CLASSIFICATION 3.4 SEISMIC PERFORMANCE CATEGORY Essential bridges with an acceleration coefficient greater than 0.29 are assigned an importance classification (IC) of "I." All other structures have an IC of "II." An essential bridge is one that is determined to be critical to "social/survival and security/defense" needs (MSHTO, I-A, 3.3). Based on the ICand the acceleration coefficient at the bridge site, a seismic performance category (SPC) can be determined from the table below (MSHTO, 1-A, 3.4). Seismic Performance Categories Acceleration Coefficient A IC A II A B B 0.19<A~0.29 c c 0.29 <A D C 0.09 A~ 0.09 <A~ 0.19 AASHTO SPECIFICATION DIVISION I·A 3.5 SITE COEFFICIENT As stated at the beginning of this section, the type of soil present at the bridge site plays an important role in the forces an earthquake exerts on a structure. The site coefficient is determined by selecting one of three soil profile types that best fits the conditions at the site. (A ASHTO, 1-A, 3.5.1). SOIL PROFILE TYPE 1: S = 1.0 If rock of any type is present, this profile type applies. S Iike orcrystall inetypes hale with a shear wave velocity greater than 2,500 ft/s (762 m/s). Stiff soil on top of rock with adepth less than 200ft (61 m) consisting of stable deposits of sands, gravels, or stiff clays. SOIL PROFILE TYPE II: S =1.2 For stiff clay or deep cohesionless soil conditions along with sites where the soil depth on top of rock is greater than 200 ft (61m) consistingof stable deposits of sands, gravels, or stiff clays. If the soil type is unknown or the soil properties do not fit any of the three types, this site coefficient (S =1.2) is used for all calculations. SOIL PROFILE TYPE Ill: S = 1.5 Soft to medium-stiff clays and sands with adepth of 30ft (9.1m) or greater of soft to medium-stiff clay with or without intervening layers of sand or other cohesion less soils. AASHTO SPECIFICATION DIVISION I·A 3.6 RESPONSE MODIFICATION FACTORS (R FACTOR) For bridges with a SPC = B, C, or D, the seismic design forces for individual members are calculated by dividing the elastic forces by the appropriate Rfactor. Substructure Wall-Type Pier 2 Cone. Pile Bent (Vertical Piles) 3 Cone. Pile Bent (1+ Batter P iles) 2 Single Columns 3 Steel Pile B (Vertical Piles) ent 5 Steel Pile Bent (1+ Batter Piles) 3 Multiple Column Bent 5 Connections Superstructure to Abutment 0.8 Exp. Joints within Span of Super. 0.8 Columns, Piers, or Pile Bents to Cap Beam or Superstructure 1.0 Colums or Piers to Foundations 1.0 AASHTO SPECIFICATION DIVISION I·A 4.2 CHOOSING THE APPROPRIATE SEISMIC ANALYSIS METHOD Once a seismic performance category (SPC) has been assigned, the type of analysis required is identified based on the SPC and whether the bridge is regular or irregular. Regular bridges are those with an unchanging bridge cross section, similar supports, and a uniform mass and stiffness. Bridges which do not satisfy these criteria are irregular. The two methods are applicable to multispan bridges only (AASHTO, 1-A, 4.2). Method 1 = Single-Mode Spoctral Analysis Method 2 =Multimode Spectral Analysis Analysis Procedure SPC Regular Bridge Irregular Bridge A B 1 1 c 1 2 D 1 2 Bridges with 2 or More Spans O nly
  • 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, vs and w(x), we can find the fundamental period T of the bridge and the seismic force pe(x).
  • 16. L = a J Vs( :x;)d:x; 0 L f3 = J UJ(:X)V 5 (:X)d:x; 0 L y = f UJ(:X)Vs(X)2d:x; 0 'QV'"here L length of bridge = "WTith.. iliese factors kno'QV"ll, the fundamental period of the bridge can be computed 'QV'"ith the follo'QV'"i:ng: 'QV'"here p 0 = 1 g = acceleration of gravity (length/tirr1e 2 ) 1.2AS Cs = y 213 where A = Acceleration Coefficient S = Site Coefficient
  • 17. Beam-Girder Bridges ( Table 4 . 6 . 2 . 2 . 1-1 ) No Large deflection theory required per 4.6 . 3 . 8 Nonli near effects included per 4 . 6 .3. 7 No Planar struct. per 4.6.2. 4 Refined anaiysis per 4 . 6 . 3 . 5 ,6 No Refined analysis required ; put load coeficients on plans per 4 . 6 . 3 . 1 No Closed section Strip method 4 .6 .2 . 3 Open section No May not be analyzed as single-spine beam Refined analysis required; put load coefficients on plans per 4 .6 . 3.1 Yes No Refined analysis required; o r put load coefficients on plans per 4 . 6 . 3 . 1 Ok to use load distribution factor tables ; Table 4.6.3. 3 .3a to 3f for moment; Table 4 .6.2 . 2.3a to 3c for shear; Dynamic load allowance per 3 .6 . 2 Yes Number of design lanes per 3 . 6 . 1 . 1 . 1 ; Dynamic load allowance per 3 .6 . 2 ; Multi presence per 3 . 6 . 1 . 1 . 2 No Decimal number of lanes from Table (above) ; Dynamic load allowance per 3 .6.2; Multi presence always included in factors L ive- load distribution for s upers truc ture design.
  • 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 3.15.2.1.3). 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 PD can also be calculated from, For this equation, in S.I. units, VDZ is the design wind velocity at the designated elevation Z in km/h. VDZ is a function of the friction velocity Vo, 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.
  • 20. TABLE Values of Surface Conditions v;, and Z Condition Open Country v., ( km/h) for Various Upstream 13.2 Z , ( mm) 0 70 Suburban 15.2 300 City 19.4 800 Source: AASHTO LRFD Bridge Design Specifications, 2nd. ed., American Association of State Highway and Transportation Officials. Washington, D.C. , 1998. With pernuss1on. TABLE Climate Moderate Cold Temperature Ranges, ° C Steel or Aluminum Concrete Wood -18 to 50 -1 2 to 27 - 18 to 27 -12 to 24 - 18 to 2 4 - 35 to 50 Source: AASHTO LRFD Bridge Design Specifications, 2nd. ed., American Association of State Highway and Transportation Officials. Washington, D.C., 1998. With permiSSIOn. _ Vvz- 2.5~ (v;.o Jln(Zo J Z VB
  • 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 Pavg of the stream flow upon the pier, is half the maximum stream flow pressure Pmax measured by a hydrologic study. For floating ice,
  • 22. AASHTO SPECIFICATION AASHTO SPECIFICATION 3.18.2.2.2 ICE STRENGTH 3.18 .1 3.18.2.2.1 INCLINATION OF NOSE The effective ice strength ranges from 100 lb/in2 to 400 lb/in2 and is dependent on a variety of factors including the temperature of the ice mass at the time of movement and the size of moving ice pieces. Listed below are AASHTO's general guidel ines on selecting the effective ice strength. In general, the lower the temperature the ice moves at, the more damage it can do to apier or other bridge component it comes in contact with. PIER SHAPE CONSTANT The equation for the pressure due to stream flows uses a constant to describe the geometry of the pier in a water channel. The three possible values are listed below: PIERS SUBJECTED TO DRIFT BUILD-UP AND SQUARE ENDED PIERS: K =1.4 CIRCULAR PIERS: K =0.7 ANGLED ENDS: K=0.5 Where the pier ends are angled at 30 degrees or less. The coefficient C varies depending on n the inclination of the nose to vertical (i.e., the pier nose angle inthe vertical plane). Pier noses are often equipped with a steel angle or similar device raked at an angle to act as an ice breaker. 0 to 15 degrees: Cn= 1.00 15 to 30 degrees: Cn= 0.75 30 to 45 degrees: C 0.50 n= p =100 lb/in2 (690 kPa) Ice breaks apart at the melting temperature. Ice pieces are disintegrated and move as small cakes. p = 200 lb/in2 (1379 kPa) Ice breaks apart at the m elting temperature. Ice pieces are solid and move as large pieces. p =300 lb/in2 (2069 kPa) When breaking apart, the ice m oves in large, solid sheets which may impact with the pier. p =400 lb/in2 (2758 kPa) Ice breaks apart or moves at a temperaturewell below the melting temperature.
  • 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 3.8.2 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 3.17. 16. 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.
  • 27. AASHTO SPECIFICATION 3.8.1 WHERE IMPACT APPLIES The impact factor is applied only to certain elements and components. Group A elements include the impact factor. Group B elements do not. GROUP A IMPACT INCLUDED SUPERSTRUCTURE Also includes the legs of a rigid frame. PIERS All features above the ground level. MISCELLANEOUS SUPPORTS Any concrete or steel piles supporting the superstructure and above the ground level. GROUP B IMPACT NOT INCLUDED ABUTMENTS Including any retaining walls or piles (not falling into the Group A category) FOUNDATIONS Pressures and footings. TIMBER STRUCTURES SIDEWALK LOADS CULVERTS In addition to any structures with 3 ft (0.9 m) or greater of cover. AASHTO SPECIFICATION 3.8.2.2 THE LOADED LENGTH The loaded length L varies depending on the element being analyzed. The following lists AASHTO's specification for certain members and calculations. ROADWAY FLOORS Design span length. TRANSVERSE MEMBERS Span length of member from center to center of supports (e.g., afloor beam). 1Rt£K LOAD MOMENT CALCIIAnllt Design span length. For cantilever arms use length from moment center to farthest axle. TRUCK LOAD SHEAR CALCULATION Length of loaded portion of span from point of analysis to farthest reaction. For cantilever arms use I = 0.30. CONTINUOUS SPANS Length of span being analyzed for positive moment plus the average of two adjacent spans loaded for negative moment. AASHTO SPECIFICATION 3.16 TEMPERATURE RANGES AASHTO provides acceptable temperature variations depending on whether the structure is in amoderate or cold climate region. For metal structures, the values are given in the form of extreme hot and cold temperatures. Concrete structures are given temperature rise and fall changes. METAL STRUCTURES From Moderate Climate: 0°F Cold Climate: -30°F CONCRETE STRUCTURES Rise Moderate Climate: 30°F Cold Climate: 35°F Fall 40°F 45°F
  • 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.
  • 29. 13 Factors 0.... ::::> 0 "( a: D CJ (L+I)" (L+I)p CF E 8 SF w WL LF R+S+ EQ ICE 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 /o WORKING STRESS DESIGN I lA IB II Ill IV v VI VII VIII IX X 1.0 1.0 1.0 1.0 1 .0 1 .0 1.0 1.0 1.0 1.0 1 .0 1 .0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 J3E 0 j3E 1 J3E J3E 1 j3E 1 1 1 j3E 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0.3 0 1 0.3 0 0 1 0 0 0 0 0 0 0 1 0 0 0 100 150 ** 125 125 125 140 140 133 140 150 100 LOAD FACTOR DESIGN I lA 18 II Ill IV v VI VII VIII IX X 1.3 1.3 1.3 1.3 1.3 1.3 1.25 1.25 1.3 1.3 1.20 1.30 l3o J3o J3o J3o J3o J3o l3o J3o l3o J3o J3o 1 1.67* 2.20 0 0 1 1 0 1 0 1 0 1 .67 0 0 1 0 0 0 0 0 0 0 0 0 1 .0 0 1 .0 0 1 1 0 1 0 1 0 0 Table l3E 0 l3E j3E J3E J3E J3E J3E J3E j3E J3E l3E 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0.3 0 1 0.3 0 0 1 0 Group Loading Coefficients and Load Factors 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 ..... IIZII 11.1.1 c u :::::; A. A. c b :z
  • 30. p LOAD VALUE J3E Earth Pressure 1.00 f3E f3E Earth Pressure Earth Pressure 1.0 and 0.5 1.3 ELEMENT Vertical and lateral loads on all other structures. Lateral loads on rigid frames (check both and use the one that governs). Lateral earth pressure for retaining walls and rigid frames exclud ing rigid culverts. AASHTO SPECIFICATION 3.22.1 NOTES ON TABLE OF COEFFICIENTS AND FACTORS Live load plus impact for AASHTO H or HS loading. Live load plus impact consistentwith owner's overload criteria. Group X: Pertains to culverts. Wind Load: If member or connection carries only wind load, then no increase in allowable stress is allowed. J3E Earth Pressure 0.5 Lateral earth pressure when checking positive moments in rigid frames. *NOTE: For outside roadway girders, if the governing load combination is f3E Earth Pressure 1.0 Rigid culverts. f3E Earth Pressure 1.5 Flexible culverts. Sidewalk Live Load + Traffi c Live Load with Impact use p = 1.25 f3o Dead Load f3o f3o Dead Load Dead Load Table 0.75 1.0 1.0 Columns, when checking member for minimum axial load and maximum moment or maximum eccentricity. Columns, when checking member for maximum axial load and minimum moment. The capacity of the section should not be less than Traffic Live Load with Impact with p = 1.67 **NOTE: Compute the increase in the normal allowable stress to be Maximum Unit Stress (Operating Rating) x % = _....:.....:_--=-- - = - 100 Allowable Basic Unit Stress Flexural and tension members. Earth Pressure and Dead Load Coefficients %COLUMN: For working stress design method is the percent increase of the basic unit stress.