Finley Charney; Amber Verma; Maninder Bajwa; Cris Moen
Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA U.S.A
ABSTRACT
The connection at the base of the columns in gable frames used for metal buildings is usually modeled as pinned. However, this connection may have significant rotational stiffness, and including this stiffness in structural analysis may be beneficial. This paper describes the results of two projects related to assessment of the stiffness of the base connections. The first project, which is described in some detail, is the physical testing and related structural analysis of a metal building in Christiansburg, Virginia. The second project, which is described in less detail, is a series of analytical studies in which a computer program was developed which automatically creates a detailed finite element model of a typical connection and reports the moment-rotation behavior and the bearing stress distribution of the connection under gravity load followed by lateral load.
1. INTRODUCTION
Many metal buildings use gable frames for resistance to both gravity and lateral loads. These frames, usually with tapered columns and rafters, are supported at the bottom of the columns with steel base plates that are attached to the concrete foundation with anchor bolts. The column is usually continuously fillet welded to the base plate. In some cases there is a layer of grout between the base plate and the foundation. For the purpose of structural analysis it is usually assumed that the column to foundation connection is pinned, and as such does not resist any bending moment. However, the connection does have some rotational stiffness, and thus it will resist bending moment. While it is generally conservative to ignore this moment when designing for strength, it may be beneficial to include the connection stiffness in analysis for wind and seismic drift serviceability.
2. TESTING OF A METAL BUILDING
In order to assess the influence of the stiffness of the column base connection on the lateral-load response of metal buildings, an existing building was tested (Bajwa, 2010). This building, erected in Christiansburg Virginia in 2007, is 150 ft by 80 ft in plan. The building has five interior gable frames, spaced 25 ft apart. The three most interior frames are of one design, and the two most exterior frames are of a
different design. The building is 18 ft tall at the eave, and has a roof slope of 1/12. The wall and roof decking is attached with metal screws. In this paper only the interior frame is described. Bajwa (2010) provides a detailed description of the entire test building.
An elevation of the interior gable frames is shown in Figure 1. As may be observed, both the column and rafter are web-tapered. The column is 12 inches deep at the base, and 42 inches deep at the haunch. The rafter is 14 inches deep at mid-span, and 42 inches deep at the haunch. The thickness of the flange and web of the column is 0.375 inches and 0.1875 inches, respectively. The width of the column flange is 5 inches. The thickness of the flanges of the rafter varies from 0.375 inches at the haunch to 0.3125 inches at mid-span. The web thickness of the rafter is 0.1875 inches at the haunch, and 0.1345 inches at mid-span. The width of the rafter flanges ranges from 5.0 to 6.0 inches.
The column base plate is 13 inches long and 9 inches wide, with a thickness of 0.375 inches. The concrete slab supports the base plate. There is no grout between the base plate and slab. The plate is affixed to the slab with four 1.0 inch diameter anchor bolts, each with a length of 13 inches. The column is continuously fillet welded to the base plate. The base plate detail is shown in Figure 2.
Figure 1. Elevation of Interior Frame of Test Building
Figure 2. Column Base Plate Connection in Test Building
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 127 128 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
The frame was tested by pulling on a single frame from the interior, as shown in Figure 3. The deflection at the eave height at each end of the tested frames and at the eave height at the ends of the adjacent frames was recorded using linear voltage displacement transducers. The rotation at the base of the columns of the tested frame was measured using inclinometers. Strain gages were positioned on the flanges of the columns near the base, and these were used to determine the applied moment at the base of the column.
Figure 3. Test Set Up 2.1. Preliminary Analysis
A detailed structural analysis was performed on the test structure prior to physical testing. One of the main goals of the analysis was to determine the influence of the rotational stiffness of the column base connection on the lateral drift at the eave of the frame. The frame itself was modeled with SAP2000 (CSI, 2010) using shell elements to represent the columns and rafters. While only one frame was analyzed, this was in fact a three-dimensional analysis because the flanges of the sections were explicitly modeled. Details of the modeling of the frames are reported in Bajwa (2010).
In this analysis, the column base connection stiffness was systematically varied from 1 in-kip/radian (representing a pinned connection) to 109 in-kip/radian
(representing a fixed connection). A simple rotational spring was used to represent the base stiffness. Both of the column base connections were assumed to have the same rotational stiffness. As discussed later, this assumption may not always be accurate.
The results of the analysis are shown in Figure 4. In this figure the computed drift is shown on the vertical axis, and the assumed base connection rotational stiffness is plotted on the horizontal axis. The three curves shown on the figure are for three different assumptions on how the frame is modeled. The curve with triangle symbols is from the finite element analysis (FEA). This is the most accurate analysis and is thereby used for further discussion.
As may be seen from FEA curve the lateral deflection is approximately 0.66 inches for a base stiffness of 1.0 in-kip/radian and reduces only slightly as the stiffness increases to about 1000 in-k/radian. Between a stiffness of 1000 and 1,000,000 in- k/radian there is a sharp reduction in deflection. At a rotational stiffness above 1,000,000 in-k/radian the displacement is again relatively constant, with a minimum value of about 0.28 inches.
Figure 4. Variation in Lateral Displacement with Base Connection Stiffness The curve shown in Figure 4 can be used to estimate the base connection’s stiffness if the deflection at the eave is known. Conversely, the eave deflection can be determined if the connection’s rotational stiffness is known.
To determine the deflection at the eave of the frame the base conditions for the finite element model were modeled explicitly, wherein the base plate and anchor bolts were physically represented. This refined connection replaced the rotational spring from the previous model.
In general, the rotational stiffness of the base connection depends on the following factors:
• Base plate size (plan dimensions)
• Base plate thickness
• Number and arrangement of anchor bolts
• Diameter and length of anchor bolts
• Pretension in anchor bolts
• Thickness and properties of grout
• Size and geometry of the column
• Detail for attaching column to base plate
• Magnitude of initial gravity load
• Magnitude of current lateral load
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 129 130 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
The dependence of the stiffness on load magnitude and direction is a nonlinear effect, and is due to the fact that a portion of the base plate will lift off of the foundation. This lift off and computed bearing stresses after lift off is shown in Figure 5. Lift off can be sudden or gradual, depending on the factors listed above. Note the bending deformation in the base plate in Figure 5a. While both of the column connections in a given (symmetric) gable frame will have the same initial stiffness, the lift off will occur first for the windward column, then (if at all) for the leeward column. In the extreme case the base plate could lift off completely on the windward side if the column goes into net tension, but this is not expected in serviceability calculations.
a) b)
Figure 5. Lift off of Base Plate (a) and Bearing Stress, ksi, after Lift Off (b) For the test building there was no grout below the base plate, and there was no pretension in the anchor bolts. The base plate was modeled using shell elements, and this plate was supported by an array of nonlinear springs. One spring was located at each node point, with edge and corner springs having, respectively, 1/2 and 1/4 of the stiffness of interior springs. The assumed force-deformation relationship for one of these springs is shown in Figure 6a. When in tension the springs have virtual zero stiffness (allowing uplift) and in compression the springs have a large stiffness, thereby preventing the base plate from pushing into the concrete slab.
Figure 6. Force-Deformation Behavior for (a) Foundation Springs and (b) Anchor Bolts
Each anchor bolt is also represented by a nonlinear spring. The stiffness in tension is taken as AE/Leff where A is the cross sectional area, E is the modulus of
elasticity, and Leff is the effective length. The effective length depends on the assumed
bond stress distribution along the length of the bolt. If the bond stress is uniform the effective length is half of the actual length. If the bolt is unbonded and supported only at its embedded end (e.g. via an embedded bearing plate) the effective length is equal to the true length. When the anchor bolt is in compression the stiffness is taken as a very small value because through thickness deformations in the base plate would result in disengagement of the bolt. The force-deformation relationship used for the anchor bolts is shown in Figure 6b.
The results of the analysis are shown in Figure 7 for the case where the effective length of the anchor bolt was taken as 1/2 of the true length. Under a lateral load of 7.5 kips the computed displacement is 0.525 inches, and the resulting base connection stiffness is approximately 20,000 in-k/radian. This value would represent the average stiffness of the two base connections, where the windward side connection (column in tension under wind) would generally have a somewhat lower stiffness than the leeward side connection (column in compression under wind).
Figure 7. Results of Finite Element Analysis
It is of some interest to determine how variations in connection properties would influence the lateral displacement of the frame. Figure 8 shows the influence of both base plate thickness and anchor bolt stiffness. The top curve is for the base plate thickness of 3/8 inch, which is used in the test building. For this base plate thickness the stiffness of the anchor bolt has a definite influence on behavior when the bolt stiffness is less than about 5,000 kips/inch. However, the influence on anchor bolt stiffness is much greater when the base plate is thickened to 0.75 inches and again to 1.5 inches. For a 1.0 inch diameter anchor bolt the stiffness is 3,500 kips/inch, and it appears for the test building that doubling the thickness of the base plate from 3/8 to 3/4 inches would reduce the lateral drift by a factor of 2. This is a remarkable influence in behavior given the small additional cost related to the thicker plate.
The influence on initial dead load on the behavior of the test frame is shown in Figure 9. In this analysis the anchor bolt stiffness was kept constant at 3,500 kips/inch, and the dead load and the base plate thickness was varied. As may be observed the influence of dead load is small, and is more significant for thinner base plates.
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 131 132 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
Figure 8. Influence of Base Plate Thickness and Anchor Bolt Stiffness on Drift
Figure 9. Influence of Dead Load Magnitude and Base Plate Thickness on Drift 2.2. Test Results
While not directly related to column base stiffness, it is interesting to note that the two columns in one frame shared almost equally in resisting the lateral load, and that only a small portion of the lateral load was shed to adjacent frames. This indicates that the roof diaphragm (the screwed on metal deck and supporting purlins) was ineffective as a load transfer mechanism. Additionally, the fact that the columns almost equally shared in loads indicates that the effective rotational stiffness at the two column bases was nearly the same. This behavior is reasonable given the relatively light lateral load applied during tests, but could change as one of the columns begins to lift off.
Measurements from the strain gages on the columns and the inclinometers placed near the base of the columns gave estimates of column base stiffness that ranged considerably, but several of these values were in the range of 25,000 inch-kip per radian. A typical plot is shown in Figure 10. Note from this figure that the noise in the data acquisition system was rather large compared to the values being read. However the measured stiffness was in the range of that predicted from analysis (see Figure 7 above).
Figure 10. Moment-Rotation Plot from Frame Tests 3. SUMMARY AND CONCLUSIONS
The research reported herein indicates that the base connections in metal buildings can have a significant influence on computed behavior of gable frames under lateral loading. While several factors influence the stiffness of the connection, the most important factors appear to be the thickness of the base plate and the axial stiffness of the anchor bolts. The influence of other parameters such as anchor bolt location, pres- ence of pretension, and presence of grout, is somewhat less important (Verma, 2012). Determining a realistic rotational stiffness for a base plate connection is not trivial however, and generally requires a detailed finite element analysis of the type described in this paper. A utility for estimating the connection stiffness was developed by Verma (2012). This utility includes an easy-to-use graphical user interface, and uses either SAP2000 or OpenSEES (PEER, 2012) as the analytical engine. This tool is currently being used by the authors to provide a better understanding of the influence of column base stiffness on the performance of metal buildings under lateral load.
ACKNOWLEDGEMENTS
The Metal Builders Manufacture’s Association, headquartered in Cleveland, Ohio, supported the research presented in this paper.
REFERENCES
[1] Bajwa, M. (2010), “Assessment of Analytical Procedures for Designing Metal Buildings for Wind Drift Serviceability”, Master of Science Thesis, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA.
[2] CSI (2010), “SAP 2000”, Computers and Structures, Inc., Berkeley, CA.
[3] PEER (2012), OpenSEES Computer Program, Version 2.3, Pacific Earthquake Engineering Research Center, Berkeley, CA.
[4] Verma, A. (2012), “Influence of Column Base Fixity on Lateral Drift of Gable Frames”, Master of Science Thesis, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA.
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 133 134 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012