Modal Behaviors of Spun-Cast Pre-Stressed Concrete Pole Structures

Transcription

1 Modal Behaviors of Spun-Cast Pre-Stressed Concrete Pole Structures Shen-en Chen 1, Choo Keong Ong 2 and Kris Antonsson 2 1 Department of Civil Engineering, University of North Carolina at Charlotte 9201 University City Boulevard, Charlotte, NC Department of Civil and Environmental Engineering, University of Alabama at Birmingham 1075, 13 th Street South, Birmingham, AL ABSTRACT The modal behavior of a spun-cast, prestressed concrete pole is reported in this paper. The goal of this study is to determine the feasibility of using modal frequencies to determine the stability of the pole structure as a monitoring technique. Treating the surrounding soils as stiff springs, a directly-embedded pole structure roughly behaves as a cantilevered beam with strong spring supports. To determine the validity of such assumptions, the pole structure has been tested both simply-supported on railroad ties and directly embedded in the ground. Impact excitations were used in this case. This paper reports the preliminary results of modal testing and finite element modeling that were used to determine the fundamental frequencies of these poles. Since the prestress level within the poles is only a fraction of its buckling load, the contribution of modal frequencies is assumed to be minimal. The results indicate that the numerical cantilevered beams have lower vibration frequencies than the actual beams. Comparative studies of different fixities are also determined using finite element analysis. INTRODUCTION Spun-cast, prestressed concrete poles are unique structural members that are used to support power transmission lines in parts of the southeastern states (Figure 1). The stability of these pole structures is critical to ensure the continuous supply of energy typically to thousands of homes. Direct embedment is a popular technique to stabilize these pole structures and involves creating a cylindrical hole in the ground by auger drill and inserting the concrete pole into the open hole. Annulus materials are then backfilled into the gap between the pole and the augered hole. Such foundations are commonly used with high voltage structures such as single pole or H- frame structures, since they may be subjected to high overturning moments and modest vertical and shear loads. Different from statically-cast concrete poles, the spun-cast, prestressed concrete poles are centrifugally spun with embedded high-strength, prestressed steel strands completely enclosed within the concrete and arranged in a rosette format. The technique allows the poles to be exceedingly strong and impervious to moisture and, hence, corrosion-resistant. Other applications of these concrete FIG. 1 Spun-Cast Concrete Pole for Power Transmission poles include street and highway luminaires. [1] The vibration behaviors of these pole structures are important both for extreme, ice, wind and seismic overload mitigations [2][3] and electric pulse shock wave protection [4]. However, there are very few publications on actual modal tests of these structures. Typical design fundamental period is determined using global stiffness assuming cantilevered structure and is suggested to be in the range of sec. [5-6]. Lantrip (1995) conducted a series of modal tests on several suspended pole structures [7]. He also conducted Finite Element (FE) normal mode analysis to validate the experimental results - due to the tapering shape, stepped plate elements were used. There are some studies of traffic induced vibration of street

2 lights; however, most of these studies only focus on dynamic amplifications and absolute displacements of polelike structures [8]. To ensure the stabilities of directly embedded poles, the vibration testing technique is proposed for monitoring purposes. Treating the surrounding soils as stiff springs, a properly designed pole structure behaves as a cantilevered beam with strong spring supports. To determine the validity of such assumptions, a study has been conducted on a pole structure including modal testing and unsupported standing vibration test (no guy wires). The goals of this study are to: 1) identify the modal behaviors of the prestressed concrete poles; 2) determine the effect of boundary conditions on the modal behaviors; and 3) determine the potential of using vibration measurements to assess the fixity of the direct embedded boundaries. This paper reports the preliminary test results in determining the modal behaviors of a pole structure using impact vibration. Finite Element Analysis (FEA) has also been conducted to confirm the modal test results. Both Modal tests and finite element modeling were used to determine the fundamental frequencies of these poles. MODAL AND SINGLE-POINT IMPACT TESTS Two vibration tests were conducted on a 120 ft tall spun-cast, prestressed concrete pole including full-scale modal testing with free-free boundary conditions and a single impact-point vibration test having a cantilevered boundary condition (direct embedment). The pole structure has a tip diameter of in. and a butt diameter of in. The outer taper of the pole is about in/ft with an inner taper of in/ft. The impact tests were conducted at the site where the pole was to be installed. The free-free boundary conditions are assumed with the pole laid on railroad ties as the pole is too heavy (4,508 lb) to be suspended in the field. Figure 2 shows the schematic test setup. The pole is classified as a wood-equivalent H10S structure and has a tip diameter of in. and a butt diameter of 39.1 in. [9]. The modal test was conducted with the pole lying in a horizontal position. A total of fifteen impact points were applied on the 120 ft pole at approximately 8 ft intervals (Figure 2). Five hits were used to determine the average frequency values. For the free-free conditions, the impact and sensor were placed parallel to the ground. A modal-tuned hammer and seismic accelerometers were used for the modal testing, with a sampling frequency of 2000 Hz. After the modal test, the pole structure was placed in the ground at regular embedment depth of 12.5 ft (10% height + 2 ft). The surrounding soil was replaced with sufficiently compacted gravel. A single-point impact test was conducted to determine the boundary conditions of the directly embedded pole. To conduct the single point test, a sensor was placed at the middle of the pole using a cherry picker (Figure 3) and the impact was applied at the base of the pole. The vibration frequencies determined from the impact tests are summarized in Table 1. The mode shapes of the first three modes are shown in Figure 4, where the first, second and third bending modes are shown. Because of the tapered shape, lop-sided deflections were found to have resulted. (Note: to compare with the cantilevered beam results, the first bending mode is labeled as mode 2) Table 1 Experimental and Numerical Vibration Frequencies Mode Modal Test Free-Free Vibration Test Cantilevered FE Model Free-Free FE Model Cantilevered % Difference Free-Free % Difference Cantilevered 1 N/A 1.83 Hz N/A 0.71 Hz N/A Hz 4.27 Hz 2.26 Hz 3.06 Hz Hz Hz 6.01 Hz 7.58 Hz Hz Hz Hz Hz

3 FIG. 2 Damping compared between two tests along the long axis FIG. 3 Sensor Placement for Single-point Impact Test FIG. 4 Mode Shapes from Modal Tests

4 FINITE ELEMENT MODELING Since closed-form solutions were not available, Finite Element Analyses (FEA) were used to validate the experimental results. The commercially available FEA software, ALGOR, was used to model the pole structure [10]. The pole was approximated as a tapered hollow cylinder using 5,184 four-node plate elements with constant thickness. A normal mode eigenvalue analysis was conducted to determine the modal frequencies and the corresponding mode shapes. Since the prestressed load is significantly lower than the buckling load of the pole, the prestress effect is neglected in the model [11]. Both free-free and cantilevered (fixed-free) boundary conditions are modeled. The resulting frequencies are tabulated in Table 1 and the mode shapes are shown in Figures 5 and 6 for the free-free and cantilevered conditions, respectively. FIG.5 Mode Shapes of Pole with Free-Free Boundaries FIG. 6 Mode Shapes of Pole with Cantilevered Boundary

5 RESULTS AND DISCUSSION Table 1 shows a summary of the first four vibration modal frequencies from both experimental and analytical results. Comparing the results between vibration tests and FE model, the free-free boundary condition is closer then those of the cantilevered condition. For the free-free end condition, the experimental results are consistently lower than the analytical results, whereas, the reverse trend is true for the cantilvered boundary condition. The first mode of vibration, i.e. the cantilevered bending mode, was experimentally determined at 1.83 Hz, which is significantly higher than the finite element result (0.71 Hz). The percentage difference between the experimental and FE results is %. The percentage difference is smaller for the higher modes with the fourth mode being the lowest. For the free-free conditions, the largest percentage difference is 18.8% for the third mode, and the smallest percentage difference is -0.52%, for the fourth mode. The 18.8% difference is deemed acceptable, considering the material complexity of the actual pole structure. It should be noted that Lantrip s results [7] also show large differences between analytical and experimental results. Due to the popular use of these prestressed concrete poles in the utility and communication industries, an understanding of the vibration behaviors of these poles is important. Due to the interaction of the prestessed tendons and the tapered internal and external geometries, theoretical derivation of the eigenvalue solutions is very difficult and has not been completed at this point. The results of this study only showed a glimpse of the complexity of the problem. The discrepancy between the results from the two boundary conditions may be due to a number of reasons: 1) the complex modal behaviors involving the prestressed pole structure; 2) the simplicity in the present analytical models; and 3) the possible inaccuracies in experimental results due to boundary conditions. Since the pole is supported on railroad ties, the assumed free-free boundary conditions may not be precise. Suspension tests (i.e. Lantrip [7]) would be more accurate. Another consideration of possible discrepancies between the experimental and analytical results is the quality of the pole materials. The effect of the pole spun production process typically resulted in a linear densification of the concrete material through the wall thickness - accurate modeling of the pole behavior should include the linear variation of concrete mass density through the pole thickness. This research is part of a project in determining the proper embedment depth for direct embedded pole structures. Current approach of burying the pole at 10% height + 2 ft has been found to be intuitively unsafe due to considerations of the variation in soil properties. It is of interest to know if proper embedment also indicates good fixity of the boundary. However, current results do not yet answer this question. Further developments of this research will include more precise tests and more refined analytical modeling. CONCLUSION Preliminary results of a modal study of the vibration behaviors of a spun-cast, prestressed concrete pole have been presented. First three bending modes of the pole have been identified both by actual test and finite element analysis. The experimental and analytical results are shown to deviate significantly for both free-free and cantilevered boundary conditions with maximum % differences about 18.8% (free-free) and % (cantilevered). This research represents a first attempt in using vibration technique to determine boundary conditions of directly embedded pole structures. However, the complexity of the pole structures makes it difficult to validate the experimentally determined modal frequencies. ACKNOWLEDGEMENT The authors would like to acknowledge the financial support of the Southern Company, the assistance of Mr. Colby Galloway of Alabama Power Co. and the encouragement of the Southern Company wide Transmission Line Design Committee.

6 REFERENCES [1] Fouad, F. H., "Specification Guide for Prestressed Concrete Poles," PCI Committee Report, PCI Journal, Vol. 44, No. 2, March April (1999), pp [2] Building Seismic Safety Council, 2000 NEHRP Recommended Provisions for New Buildings and Other Structures, FEMA 369 (2000). [3] American Society of Civil Engineers, Guide for the Design and Use of Concrete Poles (1987). [4] United States Department of Agriculture, Guide Specification for Spun-Prestressed Concrete Poles and Concrete Pole Structures, RUS Bulletin 1724E-206 (1997). [5] International Code Council, International Building Code (2000). [6] Kalkan, E. and Laefer, D.F., Seismic Based Strengthening of Steel and RC Telecommunication Poles Based on FEM Analysis, Engineering Structures, 25 (2004), p [7] Lantrip, T.B., Identification of Structural Characteristics of Spun Prestressed Concrete Poles Using Modal Testing Methods, M.S. Thesis, Dept. of Civil and Environmental Engineering, University of Alabama at Birmingham (1995). [8] Volkman, C. and Hahin, C., Evaluation of Truck Traffic-Induced Light Pole Vibrations on the I-80 Le Claire Bridge, Physical Research Report No. 151, Illinois Department of Tranportation (2004). [9] Southern Company, Southern Electric System Standard Specifications for Wood Pole Equivalent Spun Prestressed Concrete Poles (SES-PD-024), (1992). [10] Algor, Finite element Analysis Software - User s Manual (2002). [11] Blevins, R.D., Formulas for Natural Frequency and Mode Shape, Krieger Publishing (1995).