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1、Design of Lightly Loaded Steel Column Base Plates THOMAS M. MURRAY One of the least-studied structural elements are column base plates. Even less attention has been paid to lightly loaded base plates, defined here as relatively flexible plates of approximately the same size as the outside dimensions
2、 of the column supported by the plate. Such base plates are found in low-rise conventional construction and in preengineered metal building applications. In this class of construction, relatively small dead loads and low slope roofs commonly result in uplift loads which must be transferred to the fo
3、undation through the base plates. At present, there is no generally accepted practice for the design of such base plates that is not unduly conservative. From results of yield-line analyses and limited supporting experimental data, design procedures for lightly loaded base plates supporting H-shaped
4、 columns are proposed. Both concentric axial compression (gravity loading) and concentric axial tension (uplift loading) are considered. Base plate strength for erection safety is also discussed. GRAVITY LOADING BackgroundTechnical literature concerned with the compressive strength of steel column b
5、ase plates may be treated broadly in two categories: (1) the bearing strength of concrete, and (2) the study of various rigid and flexible plates on elastic foundations.1 The bearing strength of concrete and rock was investigated as early as 1876 by Bauschinger, presented later by Withey and Aston.2
6、 Bauschinger was concerned about the ability of various classes of rock and concrete to support steel bearing piles; his work with concrete was for him less significant. Meyerhof3 found the bearing strength of concrete increases in direct proportion to the ratio of concrete thickness to footing (pla
7、te) width when splitting is present. He demonstrated that when the mass of the concrete is confined to inhibit Thomas M. Murray is Professor of Civil Engineering and Environmental Science and Professor-in-Charge, Fears Structural Engineering Laboratory, University of Oklahoma, Norman, Oklahoma split
8、ting, the capacity is in agreement with the theory of bearing capacity presented by Terzaghi. Shelson4 studied experimentally the behavior of base plates when the ratio of the concrete surface area is large compared to that of the plate bearing area. Apparently, the American Concrete Institutes Buil
9、ding Code Requirements for Reinforced Concrete5 were based on Shelsons work. Hawkins6 reported results of 230 tests using rigid plates. He determined that concrete bearing strength is a function of the plate dimensions and concrete cylinder strength, and showed that Shelsons work is conservative. Th
10、e ACI Code was subsequently liberalized,7 with an increase in allowable stress from 40-87%, depending on the concrete area to plate area ratio. The current AISC Specification8 is based on ACI Code requirements, but in allowable stress design format. More recently DeWolf9 presented the results of 19
11、tests with plates placed on unreinforced concrete cubes and loaded only in the central portion. He has shown the current AISC Specification requirements8 to be conservative. However, he limits his results to base plates which extend beyond the column perimeter. Elastic rectangular plates on elastic
12、foundations have been extensively studied by many authors (Refs. 10-16). However, specific applications to column base plate design are rare. The design procedure found in the 7th and earlier editions of the AISC Manual of Steel Construction17 for determining plate thickness if the base plate extend
13、s beyond the column perimeter is based on the conservative allowable bearing stress permitted by the ACI code at that time and by the assumption of uniform pressure under the base plate. Fling18 has proposed that in addition to the strength requirements suggested by AISC, a relative upward deflectio
14、n limitation of 0.01 in. be imposed. He also presents yield-line and elastic plate bending solutions for determining plate thickness of lightly loaded base plates. A deflection limitation is suggested, with deflection calculated as the maximum free edge deflection of an elastic plate which is fixed
15、on the opposite edge and supported on the other two edges. The elastic strength solution is based on one point at the maximum stress, which occurs at the 143 FOURTH QUARTER / 1983 middle of the fixed edge, set equal to the yield stress of the steel. Fling concedes his requirements are conservative b
16、ecause of the assumptions involved. The elastic plate bending solution has been adopted by AISC19 as one criterion for determining column base plate thickness. It is noted that all of the above solutions assume the base plate remains in contact with the concrete substrate during loading, and the res
17、ulting pressure is uniform over the plate. Stockwell20 presented a design method assuming only an H-shaped area under the column flanges and web to be effective in bearing. His reasoning is based on recognition of the fact that uniform bearing pressure is unrealistic and that maximum pressure would
18、logically follow the profile shape. Resultant stress “redistribution” provides reserve capacity as larger areas of the base plate become effective. Details of Stockwells proposed method will be discussed subsequently. The analyses made of the bearing strength of concrete are primarily based on obser
19、vations of concrete specimens, while the analyses made of the behavior of steel plates on elastic substrates are primarily theoretical in nature dealing with various modelings but without experimental evidence. Of the authors discussed, only Shelson,4 DeWolf,9 Fling,18 and Stockwell20 treat the inte
20、raction of a steel plate and concrete substrate. Only Fling and Stockwell treat the topic of column and base plate of like dimensions. Finally, only Stockwell considers the possibility of uplift at the free edge of a base plate. Finite Element Study The finite element analysis method permits a relat
21、ively easy way of analyzing a base plate, particularly if the plate is subjected to uplift at the boundaries. If the plate is modeled using a bending element supported by elastic springs representing the substrate, the springs can simply be released when uplift occurs. Although the method is iterati
22、ve, results can be obtained fairly quickly. To study the elastic behavior of lightly loaded base plates, the finite element capabilities of the widely accepted computer program STRUDL21 were utilized. Because of double symmetry, only one-quarter of a base plate was analyzed, with support releases us
23、ed to ensure zero slope at the plate centerlines. Each node was supported by a linear spring in the Z-direction. The plate elements under the web and flange of the column were assigned a greater flexural rigidity than the remaining plate elements by using a modulus of elasticity one-thousand times g
24、reater. The STRUDL CPT plate bending element was used exclusively. In each analysis, the plates were first analyzed assuming no uplift, if uplift occurred, the uplifting nodes were released from the substrate and the plate reanalyzed. After several analysis cycles, all uplifting nodes were correctly
25、 released. For each plate, two analyses were performed using both a coarse mesh and a fine mesh to ensure convergence. Figure la shows a typical fine mesh used in the study. For the particular mesh shown, the base plate is 8 in. by 12 in. by 0.375 in. thick. Column flanges are 8 in. by 0.25 in. and
26、the web thickness is 0.25 in. A substrate modulus of 355.4 kips/in.2/in, as determined by experiment, was used in the analysis. Results of the finite element analyses are shown (along with experimental data to be discussed later) in Fig. 1b. The area of the uplifting nodes is shaded for clarity and
27、the deflection values shown have been normalized with respect to the nodes at the tip of the column flange. Approximately 28% of the contact area uplifted. Experimental Study Two gravity load tests were conducted to verify the finite element analysis results. The test specimens consisted of a steel
28、column and base plate section, a reinforced concrete pedestal base, and a layer of expansive grout placed between the steel and concrete to provide a uniform bearing surface. Grout was used to obtain better corroboration with the finite element model, but is not considered necessary for lightly load
29、ed column base plates. The steel column and base plate sections were fabricated from A572 Gr. 50 steel. Specimen BP1 had a 6 in. by 8 in. by 3/8 in. base plate and specimen BP2 a 8 in. by 12 in. by 3/8 in. base plate. Table 1 lists the measured plate thicknesses for each specimen. The reinforced con
30、crete pedestals were cast to a size to provide a 3 in. wide edge distance and the depth was 18 in. Reinforcement consisted of four No. 4 vertical reinforcing bars and three equally spaced No. 3 ties. Two -in. diameter A307 anchor bolts were cast in the specimens. Test cylinder data for concrete and
31、grout are given in Table 2. The assembled specimens were placed in a 200-kip capacity universal type testing machine. Six dial gages were suspended between the column flanges above the base plate on one side of the specimens. The gages were at the quarter points along the length of the plate in two
32、rows, one row at the free edge and one row midway between the web and the free edge. These gages measured the relative upward displacement of the base plate with respect to a horizontal plane through the column approximately 6 in. above the base plate. A seventh dial gage was used to measure the rel
33、ative penetration of one column flange into the grout and concrete body. Sixteen electrical resistance strain gages were attached to one quarter of the base plate upper surface of specimen BP2. Dial and strain gage placement is shown in Fig. 2. After an initial load/unload cycle, loading proceeded i
34、n increments until failure, with gage readings recorded at each increment. Specimen BP1 failed by fracture of the grout at the perimeter of the plate along the flanges of the column section at a load of 187 kips. Specimen BP2 had a capacity exceeding that of the testing machine. Maximum base plate d
35、eflections for either specimen did not exceed 0.05 in. Normalized measured deflections at maximum load for Specimen BP2 are shown in Fig. 1b. Reasonable agreement is found between measured and predicted deflections and the uplift area is verified. Results for Specimen BP1 are similar. Stresses calcu
36、lated from 144 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Fig. 1. Gravity loading analytical and experimental results measured strains and stresses predicted by the finite element analysis were found to be quite small, less than 15 ksi, and are not considered sighificant. An addi
37、tional test was made of the pedestal/grout assembly to determine the composite stiffness. A rigid steel plate two inches square was placed on the grout bed and loaded in the universal testing machine to determine values for elastic stiffness and onset of inelastic strains. The results are shown in F
38、ig. 3. The elastic stiffness was found to be 355.4 kips/in2/in and the onset of inelastic strains at approximately 12 ksi. Table 1. Gravity Loading Specimen Plate Thicknesses Base Plate t (in.) SpecimenFlangeWebNominalMeasured BP10.250 0.17990.3750.367 BP20.2500.2500.3750.375 Application to Design T
39、he analyses proposed by Fling18 seek to satisfy both strength and stiffness criteria. The stiffness criterion limits the relative deflection of the free edge to insure adequate load distribution beneath the plate to avoid overstressing the concrete substrate. However, when the concrete mass is large
40、 enough to inhibit splitting, the necessity of preventing overstress in the concrete substrate is eliminated as the failure mode is not due to brittle Table 2. Concrete and Grout Cylinder Test Results 7 Day Tested CylinderLocationStrength (psi) 1BP11379 2BP11655 3BP23798 4BP23742 5Grout4725 145 FOUR
41、TH QUARTER / 1983 Fig. 2. Dial- and strain-gage placement for gravity loading tests fracture of the concrete base. The experimental evidence does not support the need of a stiffness requirement. Rather the overstress of the substrate encountered with relatively thin plates is highly localized and re
42、sults in redistribution of bearing stress as localized inelastic strains develop. This indicates that a design method need only recognize the ultimate behavior of the base plate (failure mode) and the stiffness criterion can be neglected. From experimental and analytical results, thin base plates li
43、ft off the substrate during loading. Thus, the assumption of uniform stress distribution at the interface is invalid. Further, consideration of only elastic plate strength greatly underestimates the capacity of thin bearing plates. Unfortunately, the current AISC recommended design procedure19 uses
44、both assumptions, resulting in unnecessarily thick column base plates. Stockwell20 has recognized both inadequacies and has recommended the plate be approximated as an H-shaped area under the column as shown in Fig. 4, or in effect cantilevers perpendicular to the column flanges and web. The maximum
45、 allowable bearing stress for the substrate is assumed to be uniformly distributed over the H-shaped area, from which the dimensions of the area can be determined. Constant cantilever length Fig. 3. Steel plate grout penetration for both the flange and web portions is assumed as shown in Fig. 4. Fro
46、m ACI 318-77,7 the allowable bearing stress of concrete pedestals is given by fff pcc =085119 21 ./.AA (1) in which A1 = area of the base plate, A2 = area of the concrete pedestal, = capacity reduction factor = 0.70, and fc = specified compressive strength of concrete. Since the required bearing are
47、a for lightly loaded base plates generally will be small compared to the area of the pedestal, the allowable bearing stress using the ACI procedure will approach 1.19 fc. Furthermore, the research done by Hawkins4 and the testing reported herein, demonstrate that stress distribution occurs under the
48、 base plate and, therefore, it is recommended that 1.19 fc be used for the allowable bearing pressure for lightly loaded column base plates. The resulting proposed design method is then only 146 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Fig. 4. Effective bearing areas a variatio
49、n of the method proposed by Stockwell,20 where bearing stress for allowable stress design is taken as 0.7 fc. Using the proposed method with an assumed plate yield stress of 55 ksi (a 10% increase to reflect typical coupon test results) to calculate the plastic moment capacity, mp, of the base plate and concrete strengths shown in Table 2, the predicted ultimate capacities of the BP1 and BP2 test specimens are 35.6 kips and 148.7 kips, respectively. The H- shaped areas at computed maximum load are shown in Figs. 4b and 4c. The BP1 specimen failed at 187 kips; the strength of
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