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HEAT STRAIGHTENING DAMAGED STEEL PLATE ELEMENTS
By R. Richard Avent,1 David J. Mukai,2 Paul F. Robinson,3 and Randy J. Boudreaux4
ABSTRACT: The fundamental element of any structural steel shape is the flat plate. Damage to bridge structures consists of these plate elements, in combination, bent about their strong and/or weak axes. The purpose of this paper is to describe experimental and analytical research on heat straightening as applied to plates and to present related engineering criteria for its use. An experimental program was conducted to evaluate the response of plates to heat straightening and to identify important parameters influencing behavior. Over 300 heats were applied to a variety of plates. The primary factors influencing straightening were the angle of the vee heat, steel temperature during heating, and external restraining forces. The plastic rotation after heating was directly proportional to these parameters. To aid engineers in predicting plate movements during heat straightening, a simple mathematical formula was developed. This equation relates the average plastic rotation per vee heat to vee angle, steel temperature, magnitude of restraining force, coefficient of thermal expansion, and yield stress. The formula compares well to the experimental data and is the first simple formula available that includes the parameters of heating temperature and magnitude of restraining force. The form of this analytical approach also will lend itself toward extensions, including the behavior of rolled shapes, axially loaded members, and composite and noncomposite girders.
INTRODUCTION
The fundamental element of any structural steel shape is the flat plate. Damage to bridge structures consists of these plate elements, in combination, bent about their strong and/or weak axes. The purpose of this paper is to describe experimental and analytical research on heat straightening as applied to plates and to present related engineering design criteria for its use. This work forms the basis for extensions to heat straightening of rolled shapes.
Several detailed studies have been conducted for vee heats applied to plates. The vee heat is the usual heating pattern for straightening plates bent about their strong axis and is explained in detail in a later section. These studies have attempted to identify parameters that influence vee heats and to develop predictive models based on this data. Nicholls and Weerth (1972) described the bends produced by 211 vee heats whose apex angle varied from 247 to 607 in 67 increments applied to 10-mm (3/8-in.) thick A36 steel plate. The vee depth was also varied over full depth, three-fourth depth, and onehalf depth. No attempt was made to evaluate the effect of these parameters other than the general result that the greater the vee angle and depth, the greater the bend produced. Roeder (1986) also conducted a study on undamaged vee heated plates. He employed sophisticated monitoring equipment such as thermocouples, contact pyrometers, and strain gauges, as well as more conventional tools such as vernier caliper and a steel ruler. His work is particularly significant as the first attempt to both experimentally and analytically quantify heatstraightening behavior for plates over a wide range of parameters. The parameters included vee geometry, specimen geometry, heating temperature and rate, steel grade, restraining force, initial residual stresses, and quenching. Roeder’s conclusions were based on approximately 60 heats over a wide range of parameters. As a result there were relatively few re-petitive heats using identical parameters. Although trends could be drawn from this data, its sparseness limited the quantitative value of the results. However, his research provided the initial basis for much of the experimental work reported here. Roeder’s most significant conclusions were
? A practical and safe upper heating treatment limit is 6507C (1,2007F).
? Changes in material properties are small when the heating temperature remains below the phase transition temperature of approximately 7207C (1,3307F).
? The rotation produced by a vee heat is directly proportional to vee angle and heating temperature.
? The rotation produced by a vee heat is directly proportional to restraining forces that produce compression in the open end of the vee during heating.
? Quenching is effective and may increase vee heat rotations, but heating temperatures should be kept below the phase transition temperature [although some practitioners recommend quenching only if the steel temperature is below 7007F or (3707C)].
? Plastic strain occurs primarily within the vee heat region.
? Plastic strain is somewhat sensitive to geometry of the plate. However, much of this sensitivity can be attributed to differences in rate of heating and heat flow. The research described in this paper extends Roeder’s work and includes enough repetitive data points to quantify these and other conclusions.
Literature on heat straightening has been available for many years as reviewed in a state-of-the-art paper by Avent (1989). However, engineering quantification of the process has been lacking. The handful of practitioners currently using the method rely extensively on their many years of experience to guide them through a repair. An engineer lacking this wealth of experience needs a set of analytical procedures to determine how best to apply the heat-straightening process to a particular repair. These analytical tools, for reasons of economy, should be relatively fast, easy to apply, and allow for such considerations as different vee geometries, temperature ranges, external loadings, and support restraints. At present, two extremes exist: (1) Overly simplistic models (Holt 1965, 1971; Moberg 1979) that cannot take into account the effect of either temperature variations or internal and external restraint; and (2) comprehensive computer models (For Chin 1962; Burbank 1968; Weerth 1971; Horton 1973; Roeder 1985, 1986, 1987) based on elastic-plastic finite-element or finite-strip stress analysis combined with a similar thermal analysis. Whereas the former is too simplistic to accurately predict behavior, the latter requires such lengthy computational effort as to not be practical for design office use. As a result, there is a need for an analytical model that offers both practicality and comprehensive inclusion of all important variables to accurately predict behavior.
An important consideration not included in the more simple formulations is the influence of external and internal restraining forces. External forces typically are applied to produce bending moments tending to straighten the member. The external forces, producing compression on the open end of the vee during heating, will increase the available confinement and, therefore, increase the rotation produced per heat. The field applications cited by both Holt and Moberg involved the use of restraining forces. Because in most cases the material restraint alone will be less than perfect confinement, it seems likely that any correlation between the predicted and actual movement in the structures being repaired, as noted by both Holt and Moberg, is primarily due to the influence of the external forces. An improved analytical model should include the effects of both internal and external restraints.
The purpose of this paper is to quantify the parameters influencing the heat straightening of plate elements and to develop simple yet efficient procedures for predicting the response of deformed steel plates during the heat-straightening process. The approach chosen was to first identify all parameters that have an important influence on the heat-straightening process. This phase was accomplished by studying the experimental data available from previous research as well as by conducting an extensive experimental program to provide additional data. After synthesizing this experimental data, an analytical procedure for predicting member response was developed.
EVALUATION OF RESULTS OF EXPERIMENTAL PROGRAM
Vee Angle
Researchers agree that one of the most fundamental parameters influencing the plastic rotation of a plate is the vee angle (Holt 1971; Roeder 1986; Avent 1989). The data shows a fairly linear relationship between plastic rotation and vee angle. For this reason, most data will be plotted with the vee angle as the ordinate and plastic rotation wp as the abscissa. A first-order least-squares curve fit will sometimes be shown. Plots in succeeding sections show a consistent proportional relationship between these variables.
Depth of Vee
Past researchers (Holt 1971; Roeder 1985) have concluded that the plastic rotation is proportional to the depth ratio Rd, which is the ratio of vee depth dv to plate width W. A review of Roeder’s test data in the range of 6507C (6807) [1,2007F (61507)] is inconclusive as to vee depth effect. Recognizing that the data was sparse, neither the depth ratio of 0.75 nor 0.67 produced plastic rotations that were consistently hiearchial. To further evaluate this behavior, a series of tests was conducted for depth ratios of 0.5, 0.75, and 1.0 and vee angles ranging from 207 to 607. At least three heats were conducted on initially straight plates for each case and the results averaged. The results are shown in Fig. 2 for a combination of three depth ratios, three vee angles, and two jacking ratios.
The jacking ratios reflect that a jacking force was used to create a moment at the vee heat zone equal to either 25 or 50% of the ultimate bending capacity of the plate. As can be seen from Fig. 2, the depth ratios of 75 and 100% track each other well. In fact the 75% depth ratio resulted in slightly larger plastic rotations in all but one of the six cases. The 50% depth ratio resulted in an erratic behavior when compared to the other two. In three of the six cases the 50% depth ratio produced much smaller plastic rotations. In the other three cases, the plastic rotations were similar.
To further verify this behavior, a series of plates was damaged and straightened. The degree of damage was large enough that at least 20 heats were required for most of these plates. Therefore, more statistically significant average plastic rotations were obtained from these tests. Results are compared in Fig. 3 for a jacking ratio of 0.5 and two vee depth ratios, 0.75 and 1.0. Again the pattern of plastic rotations does not have a direct correlation to the vee depth ratios.
Therefore, although it would seem intuitive that increasing the vee depth would increase the plastic rotation, there is no experimental justification for such a general statement. It can be concluded that the variation of vee depth ratios between 0.75 and 1.0 has little influence on plastic rotation. However, a vee depth ratio of 50% may reduce the plastic rotations.
Plate Thickness and Width
Researchers have generally considered plate thickness to have a negligible effect on plastic rotation. The only reservation has been expressed that the plate should be thin enough to allow a relatively uniform penetration of the heat through the thickness. The practical limiting value is on the order of 19–25 mm (3/4–1 in.). Thicker plates can be heated on both sides simultaneously to ensure a uniform distribution through the thicknesses, or a rosebud tip can be used. The results from tests involving different plate thicknesses are shown in Fig. 4.
Each bar represents the average of at least three heats on a single plate. No jacking forces were used in these tests. The results illustrate the level of variability that may occur among groups of heats. However, there is no discernable pattern among the plate thicknesses for the three different vee angles used. The randomness of these results indicates that plastic rotation is not a function of plate thickness. A similar trend was found in earlier tests with fewer variables (Roeder 1985).
In addition to thickness, three plate widths were studied, as shown in Fig. 5.
The plastic rotations are the average of three heats. An unusually low average was observed for the 102-mm (4-in.) width. However, little difference was found between the 203-mm (8-in.) and 302-mm (12-in.) widths. The results of these tests show no clear relationship between plastic rotation and plate width. Tests by Roeder (1985) also indicated a similar trend.
In summary, the parameters of plate thickness and width show little definitive influence on plastic rotations. The test results do illustrate the variability of response typically found in heat straightening. It is probable that the fluctuations shown here reflect this variability characteristic rather than effects of plate geometry. Thus, plate geometry is considered to be a minor factor influencing plastic rotation behavior.
Temperature
One of the most important and yet difficult to control parameters of heat straightening is the through-thickness temperature of the heated metal. Factors affecting the temperature include size of the torch orifice, intensity of the flame, speed of torch movement, and thickness of the plate. In his experiments Roeder (1985) made careful temperature measurements of the heats produced by knowledgeable practitioners. He found that these individuals, when judging temperature by color, commonly misjudged by 567C (1007F) and, in some cases, as much as 1117C (2007F). Thus, there are considerable variations in temperature control, even with knowledgeable users.
To more clearly define the behavior suggested by a limited number of data points in Roeder’s study, a series of heats were applied to plates in which the heating temperature was varied from 3707 to 8157C (7007 to 1,5007F) in increments of 567C (1007F). The results are shown in Fig. 6, where each data point represents three heat cycles, and the points are connected by lines for clarity in identification.
A clear and regular progression of increased plastic rotation with increasing temperature is shown. Part of the reason for the regularity of the curve fits is that the same technician conducted all heats and varied the temperature in consistent step increments.
The maximum temperature recommended by most researchers (Holt 1971; Shanafelt and Horn 1984; Roeder 1986) is 6507C (1,2007F) for all but the quenched and tempered high strength steels. For carbon steels, higher temperatures may result in greater rotation; however, out-of-plane distortion becomes likely and surface damage such as pitting will occur at 7607–8707C (1,4007–1,6007F). Also, temperatures in excess of around 7007C (1,3007F) may cause molecular composition changes that could result in changes in material properties after cooling. The limiting temperature of 6507C (1,2007F) allows for a safety factor in this regard. For the quenched and tempered steels, the heat-straightening process can be used, but the temperature should be limited to 5937C (1,1007F) for A514 and A709 (grades 100 and 100W) and 5667C (1,0507F) for A709 (grade 70W) to ensure that the tempering temperature is not exceeded and that the properties are not adversely affected. Permitting quenched and tempered steels to be heat straightened is contrary to the recommendations of Shanafelt and Horn (1984); however, no adverse effects have been noted in the literature (Avent 1989).
To control the temperature, the speed of the torch movement and the size and type of orifice must be adjusted for different thicknesses of material. However, as long as the temperature quickly reaches the appropriate level, the contraction effect will be similar. This conclusion was verified by two test series on plates in which the intensity of the torch was varied. In one set, a low intensity torch moved slowly to achieve a 6507C (1,2007F) temperature, and in the other a high intensity torch was moved more quickly while again attaining the same maximum temperature. The rotations in both cases were similar.
Restraining Forces
The term ‘‘restraining forces’’ can refer to either externally applied forces or internal redundancy. These forces, when properly utilized, can expedite the straightening process. However, if improperly understood, restraining forces can hinder or even prevent straightening. The basic mechanism of heat straightening is to create plastic flow, causing expansion through the thickness (upsetting) during the heating phase, followed by elastic longitudinal contraction during the cooling phase.
Although practitioners have long recognized the importance of applying jacking forces during the heat-straightening process, little research has been conducted to quantify its effect. A series of tests designed to evaluate this parameter involved applying a jacking force to a plate such that a moment is created about the strong axis in a direction tending to close the vee. This moment (at ambient temperature) is nondimensionalized for comparison purposes by forming a ratio of the moment at the vee due to the jacking force Mj to the plastic moment Mp of the cross section, that is Mj /Mp. This term is referred to as the jacking ratio. The tests included jacking ratios ranging from zero to 50% with four different vee angles and the vees extending over either three-fourth depth or the full depth of the plate. The results are shown in Figs. 7 and 8.
It can be concluded from this data that the variation of plastic rotation is generally proportional to the jacking ratio, and the proper use of external loads greatly expedites the heat straightening process. Roeder (1985) also studied the effect of the jacking ratio variation and found a similar pattern of behavior. However, the number of data points was limited.
The results shown in Figs. 7 and 8 are based on undeformed plates that were heated either three or four times with each data point representing the average. The total number of data points for any fixed set of parameters was typically six or less. Although such data illustrate the trends associated with variations of basic parameters, the data set is too small to obtain statistically meaningful average values. To fill this void, a test series was conducted on similar size 6-mm (1/4-in.) thick plates that were initially damaged and then heated until straightened. Ten damaged plates were straightened with the number of heats required per plate ranging from 20 to 100. A summary of the test parameters and resulting plastic rotations is given in Table 1.
The heating temperature was 6507C (1,2007F). Some of the results are also plotted in Fig. 9, illustrating the jacking ratio effect. The mean values are plotted for three cases.
The range corresponding to the 95% confidence interval for the mean is also shown, providing a measure of the scatter of the test data that is typical of heat straightening. Again, the plastic rotation is found to be proportional to the jacking ratio.
An interesting phenomena that had not been noted in previous research was the relatively high (statistically significant) plastic rotations resulting after the first few heats, particularly the first. After these first few heats, the plastic rotations were consistently lower and showed no significant statistical variation with respect to heat number in the later heats. A similar, but much less pronounced trend was noted on the undamaged plates. This behavior is attributed to the initial residual stresses induced during the damage process. The implications of this result is that theoretical formulations should be evaluated on experimental data with a large number of data points rather than on tests involving only a few heats. In all data presented here, the average of all heats in a sequence was used. As expected, the movement per heat of initially straight plates and damaged plates were similar when 3 or more heats were averaged for straight plates and 10 or more averaged for damaged plates.
A second type of constrai