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1、Cambering Steel Beams DAVID T. RICKER DEFINITIONS A dictionary definition of the verb camber is: “to arch slightly, to bend or curve upward in the middle.“ The noun camber is defined as “the curve resulting from the camber process.“ The noun sweep is defined as “a widely or gently curving line, form
2、, or part.“ As applied to steel beams, it usually pertains to the gentle curve of a beam about its weaker axis. The term camber generally applies to the curve about the strong axis of the member. This paper deals primarily with camber. The camber process as applied to steel beams can be expressed as
3、: “the pre-deforming of a member so that, in a loaded state, it more nearly approximates its theoretical presumed shape.“ TYPES OF CAMBER Natural mill camber is the out-of-straightness remaining after the initial rolling, cooling, and straightening of the member at the mill. Tolerances for natural m
4、ill camber are listed in the AISC Manual of Steel Construction.1 Induced camber is that which is applied subsequent to the initial rolling and straightening process. Induced cambering can be done at either the rolling mill or the fabricating shop. Tolerances for induced camber are also listed in the
5、 AISC Manual of Steel Construction. THE CAMBER CURVE The deflection curve for a horizontal uniformly loaded member of constant cross section theoretically approximates a parabola. However, since the sag ratio for beams, that is, the ratio of mid-ordinate to chord, is so small, it is generally accept
6、ed that adequate accuracy results if the camber curve is considered to be a segment of a circular curve. Some camber calculations are based on circular curves. Camber is usually expressed in terms of the maximum ordinate at midspan. If it is desired to find the camber at other locations along the sp
7、an, a handy method is shown in Fig. 1. Divide the span into an even number of equal segments as desired. This example shows eight equal segments. Number the points as shown starting with zero at David T. Ricker is vice-president-engineering, The Berlin Steel Construction Company, Berlin, Conn. This
8、paper was developed as part of the ASCE Committee on Design of Steel Building Structures chaired by Mr. Robert O. Disque. the support. Multiply the points as shown to form a “factor fraction.“ If the centerline camber is, say, 1.5 in., the camber at the other points is found as follows: Point #1 ord
9、inate = 7/16 (1.5) = 0.65 in. = 5/8 in. Point #2 ordinate = 12/16 (1.5) = 1.125 in. = 1 1/8in. Point #3 ordinate = 15/16 (1.5) = 1.4 in. = 1 3/8 in. The resulting camber curve is shown in Fig. 2. This method is especially useful for calculating the camber at truss panel points. If six segments were
10、laid out, the factors would be as shown in Fig. 3. The AISC Manual of Steel Construction, 8th ed., pages 2-130, gives various co-efficents for determining the centerline deflection for various load combinations. Once the deflections are determined, the desired amount of camber can be selected. The s
11、election of camber is often arbitrary. The methods of cambering are relatively crude, and the results are less than precise. There is little need nor justification in meticulous mathematical manipulation or methodical multifarious meditation when it comes to determining camber requirements. METHODS
12、OF CAMBERING At one time, cambering was done at the rolling mills during the rolling process by means of adjusting (gagging) the rollers. Most mills are now reluctant to use this method. Instead they use presses and/or offset rollers and cambering (or straightening) is done subsequent to the shaping
13、 process. The method most popular at this time is cold cambering utilizing brute force. Steel members can be purchased with the cambering performed at the mill, or the fabricator can order the straight beams and do the cambering in his own shop. Beams can also be cambered by the application of heat
14、at various points along their length. This will be discussed later on. A combination of heat and force can be used to induce camber. Figure 1 136ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication
15、 or any part thereof must not be reproduced in any form without the written permission of the publisher. A recent development in curving methods is the use of induction benders. In this process the steel is heated by electricity while being forced into precise bending guides. This is the most accura
16、te method of bending. It is used extensively to curve pipes and tubes. When camber is required in plate girders, the web plate is usually cut to the desired camber profile before assembly. METALLURGY 3 Whether we cold camber using force or apply heat, we must be aware of important metallurgical chan
17、ges in the steel. Cold Cambering Using Force: The types of steel used for structural purposes are ductile, that is, they have the property of deforming extensively under substantially constant stress. This deformation is about 10 to 20 times the amount of deformation exhibited in the elastic range a
18、nd is represented by the horizontal portion of the classic stress- strain curve for mild ductile steel (see Fig. 4). When we cold camber a beam, the extreme fibers reach stresses and deformations which are on the horizontal portion of the stress-strain curve. With most cold-cambering devices, it is
19、impossible or difficult to maintain a constant stress. The rams which deliver the force advance when the button is pushed and halt when the button is released. When the ram is halted, the deformation and stresses come to balance in a brief moment and equilibrium is reached. When the ram is retracted
20、, the beam relaxes and some residual deformation is evident by the fact that the beam is no longer straight. This essentially is the cold-cambering process. We all know that bending a wire back and forth enough times will weaken it to the point that it will fail with very little effort. What about t
21、he cold-cambered beam which we bent in one direction to make the camber curve and are now loading in the opposite direction with its service loads? Another of the seemingly endless wonderful properties of structural steel is that, if allowed to rest for a few hours at room temperature, steel has the
22、 tendency to recover its elastic properties. The application of mild heat, about 225F for a Figure 2 Figure 3 few minutes, will accelerate the period of recovery. Mention should be made here of the term “strain hardened.“ This consists of an alteration of the elastic properties of cold-worked steel,
23、 and a raising of the proportional-limit stress, as a result of the aforementioned aging or application of mild heat. Two facts emerge from this brief discussion of cold- bending. 1.The same allowable stresses (or load factors) can be applied to cold-cambered beams as to uncambered beams provided th
24、ey are allowed to “age“ for a few hours. 2.Never attempt to reduce the camber in an over- cambered beam by immediately applying force in the opposite direction. If this caution is ignored, strain- weakening will result and the elastic-limit will be lowered. If normal, allowable stresses are subseque
25、ntly assigned to the member, the factor of safety will be reduced. Cambering Using Heat: The heat application must not exceed 1100F for ASTM A514 steel nor 1200F for other structural-type steels. The temperatures should be monitored by heat-sensitive crayons or other suitable means. There is no reas
26、on to exceed these temperatures. In fact, most cambering can be done at temperatures lower than these maximums. (Heat-cambering methods will be discussed later on.) MEMBERS TO CAMBER Members Which Lend Themselves to Cambering a.Filler beams b.Girder beams c.Composite floor beams d.Members with unifo
27、rm cross section Members Which Do Not Lend Themselves to Cambering a.Crane beams or crane girders b. Spandrel beams, especially those supporting facia materials Figure 4 FOURTH QUARTER / 1989137 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part
28、thereof must not be reproduced in any form without the written permission of the publisher. c.Beams with single or double cantilevers d.Beams braced with knee braces e.Beams with full moment connections or significant semirigid moment connections f.Beams with welded cover plates, especially if the c
29、over plate does not extend full length g.Members of non-uniform cross section h.Beams with significant non-symmetrical loading i.Short beamsless than 20 ft in length j.Shallow beamswide flange shapes less than nominal 14 in. depth and standard beams less than 12 in. depth k.Beams subject to signific
30、ant torsion loads l. Beams which would require less than 1 in. of camber. (Small camber requirements can often be satisfied by natural mill camber.) ESTABLISHING THE AMOUNT OF CAMBER Beams may be cambered to accommodate part of the dead load deflection, the full dead load deflection, or dead load de
31、flection plus part of the live load deflection, at the discretion of the engineer. He may be influenced by the relative percentages of dead and live load, the probable frequency and intensity of live load, the performance history of similar members, aesthetics, or other pertinent factors. As stated
32、before, the AISC Manual of Steel Construction lists maximum amounts of natural mill camber permitted in various sizes and lengths of rolled sections. Also listed are maximum and minimum amounts of induced camber which the mills will agree to supply and the tolerances for this camber. (It should be n
33、oted that all mills do not follow AISC camber recommendations. The mills should be consulted regarding their individual practices.) The manual also lists camber ordinate tolerances. Camber tolerances are always on the plus side. When beams are cambered at the mill, some of the camber is lost by the
34、time the members reach the fabricator. This is due to the aging process or relaxation of stresses. The vibration associated with rail or truck travel, whether the members are shipped standing up or lying down, and the positioning of the dunnage are also contributing factors. If a beam is ordered wit
35、h 1 in, camber, the mill will probably provide about 2 in. camber. By the time the member reaches the fabricator, the camber may be approximately 1 to 1 in. Most mills will not provide camber less than 1 in. Figure 5 Camber amounts greater or less than those available from the mills can be supplied
36、by most fabricators using heat-and/or cold-cambering processes. As previously mentioned, the determining of the amount of camber is a very inexact process. After the cambering process, the performance of the member is often not according to the script. In general, the anticipated amount of beam defl
37、ection does not occur. This probably is due to some degree of end fixity of the beam connections. Strain- hardening should not be a factor because the service stresses are or should be well within the elastic range. WHEN TO CAMBER Usually the cambering, if performed by the fabricator, is done after
38、the member has been cut to length and punched or drilled. Beams which require square and parallel ends, such as for end plate or welded moment connections, must be cut after cambering (see Fig. 5). Any interior hole groups will be perpendicular to the flanges at their locations. The fact that the be
39、ams which frame to these hole groups will not be exactly vertical is of small consequence. CAMBERING BY HEAT APPLICATION 3,4,7 As previously stated, A514 steel should not be heated above 1100F, and other structural type steels should not be heated above 1200F during the cambering process. The conseq
40、uences of overheating are not readily apparent to the naked eye but nonetheless they are present in the form of microstructure changes in the steel. Most heat cambering is accomplished by heating wedge-shaped segments at intervals along the length of the member. If the member is over-heated beyond t
41、he transformation temperature of approximately 1350F, there will occur “islands“ of altered microstructure; in other words, the steel will be non-homogenous. This is to be avoided. The number of wedge-shaped heated segments varies depending on length and size of the member and the amount Figure 6 13
42、8NGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. of camber required. For starters, try tw
43、o heated areas at the 3/8 and 5/8 locations. Experience will be the best teacher. Before heating, install a plumb line or other device so that the movement can be monitored. Once the heating starts, it should not be interrupted until the serpentine path described below is completed. As the heating p
44、roceeds, the member will start to bend in the direction opposite to that intended. However, after the heating is finished and the beam starts to cool, the beam will commence to straighten and then continue to bend in the desired direction. The following procedure will produce camber about the strong
45、 axis. (ASTM A36 steel is assumed.) Refer to Fig. 6. Start the flame spreader at point A. Heat spot A to a light red color (1110F). Proceed slowly in a serpentine path in the direction of the arrow. Direct the torch toward that direction, moving slowly, bringing each area to a light red color. The a
46、rea B A C should be roughly the shape of an isoceles triangle with the angle at A varying from 20 to 40, the larger number producing more movement. It is not necessary to return to point A to reheat. When the web heating is finished, start the flange heating at point D and proceed toward the center.
47、 (The flange heating may be started, using an additional torch, as the web heating is nearing completion.) Thick material, say over 1 in., may be heated simultaneously at both the near and far surfaces. Always advance the torch along the path bringing the steel to a light red color as it proceeds. T
48、he flange to be heated is on the concave side of the camber curve; consequently, point A should be about 2 in, in from the convex side of the camber curve. For best results, let the heated member cool by itself. The heat cambering process can be enhanced by positioning the member so that gravity wil
49、l aid in producing the curve. Note that the heat wedges do not necessarily have to be equally spaced, but they should be symmetrical about the centerline of the span (see Fig. 7). The following procedure will produce camber about the Figure 7 weak axis. Refer to Fig. 8. Start the flame at point E and move in a serpentine path bringing each area to a light red (1110F). The heated area is about 3 in. wide. Heat each flange simultaneously starting at point F and weaving an expanding path toward points G and H very near the eventual concave edge of the flange. The area G F H
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