Introduction. Crossarm Design

Transcription

1 SUBJECT BCTC 287kV H-Frame Crossarm Finite Element Analysis Report AUTHOR Jeremy Mostoller DATE August 4, 2008 Introduction This report details the analysis and optimization of the glass fiber reinforced polymer (GFRP) pultruded crossarm for the BCTC 287kV and 230kV transmission line structures. This investigation concentrated on the crossarm attachment to the poles and the conductor attachment to the crossarms. The load and geometric data for the 287kV structure was provided on International Power and Engineering Consultants LTD drawing # T08C186. The geometric data for the 230kV structure was provided on the BCHydro drawing # 2LGS-TO8- D657. Finite element analysis was used for this project due to the problematic nature of both the load condition as well as the attachment scheme. The proposed FRP profile used to replace the timber and/or steel crossarm is a C-channel section 14 x 6 x 0.5 and is manufactured using a two part urethane resin system. The urethane resin system has been proven to provide significantly higher mechanical properties when compared to properties achieved by more traditional pultrusion resin systems such as polyester or vinylester. Mechanical testing has been conducted on previously manufactured lots of a similar profile. Table 1 shows the average values attained across four lot samples manufactured within the 2007 calendar year. Note these values represent tests performed at room temperature, dry conditions; environmental conditions can have a significant effect on the mechanical data. Mechanical knockdowns for the service environment have been included in the factor of safety calculations. Crossarm Design The historical design of the timber 287kV transmission line H-frame structure uses two 4 x 14 x 46 Douglas Fir members or a single 10 x 6 x 0.25 x 46 steel rectangular tube as the crossarm section of the structure. Two poles are used to support the crossarm, one 12 ft from each end of crossarm. The two members are attached to the pole using a single through bolt in conjunction with spiked steel grids and large washer, which was estimated to be 4 square. A 1

2 shelf gain (Josyln Manufacturing Co. part # PX249AG) is used in place of the steel grid for any installation using the steel crossarm. The 230kV structure is installed using the same hardware as the 287kV structure. The crossarms for the 230kV structures are a double arm of 4 x 12 x 37 9 Douglas Fir or a single steel crossarm of 8 x 6 x 0.25 rectangular tube section. The poles of the 230kV structure are located 9 10 from each end of the crossarm. The conductors for the double crossarm configurations are suspended from an adjustable tie plate which connects the two timber crossarm members together. The crossarm can be used to support up to three conductors, one mounted at the center and one mounted 1ft from either end of the crossarm. The 287kV reference drawing (listed above) indicates the forces exerted on the crossarm by the conductors are 4440lbs vertical, 1600lbs transverse, and 1120lbs longitudinal at each conductor location. The 230kV loading has been provided by BCHydro as 3600lbs vertical, 1575lbs transverse. These load values are considered the extreme operational loading of the crossarm, but do not include any safety factors based on material components. The drawing also indicates the loads should be applied simultaneously at any one, two, or three locations. The profile design of the GFRP crossarm was developed based on the desire to maintain the same overall stiffness of the timber design and shall be mounted in a two crossarm configuration similar to the timber crossarm. Using 1.9Msi as the flexural modulus of the timber crossarm, the GFRP moment of inertia was manipulated to provide a stiffness (EI) in both the X- and Y- axis that is similar to that of the timber crossarm. Table 2 shows this correlation. Figure 1 shows the resulting profile and section properties Table 1. Average property results from mechanical testing of the CH997 (11.5 x 2.75 x 0.5 channel) profile performed during the 2007 calendar year Mechanical Properties Test Method Average Units Tensile Strength Lengthwise ASTM D638 75,698 psi Tensile Modulus Lengthwise ASTM D E+06 psi Tensile Strength Crosswise ASTM D638 27,554 psi Tensile Modulus Crosswise ASTM D E+06 psi Flexural Strength Lengthwise ASTM D790 78,533 psi Flexural Modulus Lengthwise ASTM D E+06 psi Flexural Strength Crosswise ASTM D790 50,093 psi Flexural Modulus Crosswise ASTM D E+06 psi Compressive Strength Lengthwise ASTM D695 59,884 psi Compressive Modulus Lengthwise ASTM D E+06 psi 2

3 Compressive Strength Crosswise ASTM D695 37,465 psi Compressive Modulus Crosswise ASTM D E+06 psi In-Plane Shear Lengthwise ASTM D2344 9,044 psi Bearing Stress Lengthwise ASTM D953 78,623 psi Bearing Stress Crosswise ASTM D953 75,129 psi Izod Impact Lengthwise ASTM D ft.-lbs./in. Izod Impact Crosswise ASTM D ft.-lbs./in. Physical Properties Water Absorption ASTM D % Full Section Bending Axis Tested: Y-Y ANSI E+06 psi Table 2. Calculated stiffness comparison of the GFRP, timber, and steel crossarms Crossarm Material Flexural Modulus (psi) Cross-Section Dimensions Construction 14 x kv Timber 1.9* x 6 230kV 10 x 6 x kv Steel 29.0* x 6 x kv Axis Moment of Inertia (in 4 ) Stiffness (EI) (lb-in 2 ) X *10 9 Y *10 9 X *10 9 Y *10 9 X *10 9 Y *10 9 X *10 9 Y *10 9 3

4 GFRP 4.3* x 6 x 0.5 Both X *10 9 Y *10 9 Figure 1. GFRP crossarm profile with section properties. Analysis The finite element analysis was performed using the commercial finite element software code COSMOS DesignSTAR. A solid element model was created using linear, 4-node tetrahedral elements with a global mesh size of 2.0, with 0.5 elements used near the bolted connections. The shelf gain and the tie plates were explicitly modeled using the 0.5 element size. The existing tie plate geometry (BCHydro drawing # G-T08-B495) was used as the basis for the geometry with minor modifications to aid with meshing ability. The tie plates were centered vertically on the web of the crossarm section. Both the crossarm and the tie plates had through holes for the bolt connection. Load between the two crossarm members was transferred through a contact surface and bolt connecters which used a 4 square surface for the bolt head on the crossarm and a 2 square surface on the tie plate. A contact surface was also modeled between the two parts of the tie plate with a bolt connecter at the top bolt hole and the bottom bolt hole of the tie plate. Hardware used with the tie plates is 5/8 diameter, which is consistent with the timber installation. The forces representing the conductor/ice loading were applied to 4

5 the bottom bolt hole of the tie plates. All three vector loads were applied at the three potential conductor locations of the crossarm, simultaneously. The pole connection was also modeled using the bolt connector with a 4 square surface defining the bolt head. This bolt was tied to a rigid surface to represent the pole. The surface of the guy bracket in contact with the pole was held in the radial direction. Another bolt connecter was used at the lower slot of the guy bracket and was also tied to a rigid surface. A shelf gain was used in the model, however early design attempts indicated contact between the channel and the shelf could cause high stresses in the channel. Therefore, the model was modified to have the channel mounted with a 0.25 space between the shelf and the crossarm. Orthotropic material properties were used to characterize the stiffness response of the channel section. The values listed in Table 3 were used in the construction of the FE model. Figure 2 shows the model geometry used for the analysis of the crossarm. Figure 2. Finite element model geometry used for the 230kV analysis of the crossarm. The 287kV geometry differed only by the length between the pole and conductor attachments. Table 3. Material properties used in FE analysis Stiffness Properties Property Value Units EXX 4.30 Msi EYY 2.75 Msi EZZ 1.00 Msi!XY 0.28!XZ,!YZ 0.34 GXY 0.75 Msi GXZ, GYZ 0.50 Msi Strength Properties 5

6 Property Value Units F11 T 75,000 psi F11 C 59,000 psi F22 T 27,000 psi F22 C 37,000 psi F33 T 7,000 psi F33 C 20,000 psi F12 9,000 psi F13, F23 7,000 psi FBearing 75,000 psi Results and Discussion Deflection and stress distributions were extracted from the model for discussion purposes. A maximum stress failure criterion was used when comparing the predicted stress values to the allowable values listed in Table 3. A linear buckling analysis was also conducted to determine the load at which the profile will buckle. The global coordinate system used throughout the discussion section is as follows: X- Axis is the transverse direction Y- Axis is the vertical direction Z- Axis is the longitudinal direction Deformation The profile of the GFRP crossarm was sized to match the deflection of the timber crossarm based on an average modulus of the timber being 1.9 Msi. The maximum deflections predicted by the model for the vertical, longitudinal and transverse directions are given in Table 4. Contour plots of the deflection predictions were generated and are shown in Figures 3-6. Table 4. Deflection predictions for each principal direction Configuration Transverse Deflection Vertical Deflection Longitudinal Deflection Resultant (Parallel X), in (Parallel Y), in (Parallel Z), in Deflection, in 287 kv kv

7 Figure 3. Predicted transverse displacement of the crossarm. 7

8 Figure 4. Predicted vertical displacement of the crossarm. Figure 5. Predicted longitudinal displacement of the crossarm. 8

9 Figure 6. Predicted resultant deflection of the crossarm, deformed at 1.0 scale. Stress Material properties were assigned to the part model based on the orientation of each portion of the channel, i.e. the inplane properties of channel legs are in the global X-Z plane whereas the inplane properties of the channel web are in the global X-Y plane. Note the global X- axis is in the transverse direction, the global Y- axis is in the vertical direction, the global Z- axis is in the longitudinal direction. The stress distributions for the GFRP channels are shown in Figures As can be seen in the figures much of the high stresses predicted by the model are local effects occurring at either at the pole attachment or at the tie plate locations. A comparison of the peak values predicted by the model and the allowable stresses listed in Table 3, indicates the structure is well 9

10 within the acceptable design guidelines. The minimum factor of safety calculated for the structure is 3.0, which includes a 0.90 factor for long term degradation and a 0.90 factor for environmental temperatures. Figure 7. Normal stress acting parallel to the X-axis (lengthwise of the part). 10

11 Figure 8. Normal stress acting parallel to the Y-axis (crosswise of the part web). 11

12 Figure 9. Normal stress acting parallel to the Z-axis (crosswise of the part flanges). Figure 10. Shear stress acting in the X-Y plane (inplane shear stress of the part web). 12

13 Figure 11. Shear stress acting in the X-Z plane (inplane shear stress of the part flanges). 13

14 Figure 12. Shear stress acting in the Y-Z plane (interlaminar shear stress of the part cross-section). Hand calculations were performed to determine the shear and bearing stresses associated with the bolt connections within the assembly. The peak resultant shear force was extracted from the FE model and used in the Equations 1-2 below. Equation 1 Equation 2 where "Bearing is the bearing stress acting in the GFRP channel. #bolt is the shear stress acting in the bolt. P is the peak shear reaction force from the FE model, which is 3,650lbs for the pole attachment. 14

15 d is the bolt diameter, which is 0.75 for the pole attachment. t is the channel thickness, which is 0.5in. The calculations indicate the bolt connections are sufficient for the design. The minimum factor of safety is calculated to be 4.90 for FRP bearing and 1.96 for bolt shear. Buckling A linear buckling analysis was performed using the same finite element model as used for the stress analysis. Note a buckling analysis can not be performed in conjunction with a contact solution. Therefore, the buckling analysis was modeled with the tie plates rigidly connected to the crossarm, the shelf gain was removed and boundary conditions were applied to the bolt hole to represent the fastener. Figure 14 shows the deformed shape of the model for the first positive buckling mode. The predicted factor of safety resulting from the buckling analysis is No added stiffeners are required beyond the standard installation of the timber crossarm. Figure 13. FE model predicted critical buckling mode at a load factor of 2.23, deformed at a scale of

16 Summary This investigation was conducted as a final analysis of the pultruded GFRP channel section for use as a crossarm for a 287kV and 230kV transmission line H-frame structure. The analysis indicates that all components of the structure will have factors of safety greater than 3.0 for the given load condition. The crossarm can be installed using similar hardware as is currently used with the timber and/or the steel crossarms. Minor changes, typical for FRP use in utility applications, are required in the hardware. They are as follows: 4 (minimum) square washers are recommended at each bolt location on the composite surface. A curved shelf gain is recommended at the pole attachment for support redundancy in case of non-catastrophic failure. The crossarm shall be installed such that the lower flange of the crossarm is a minimum of! above the shelf. This will result in the load being transferred from crossarm to the pole via the through bolt. The 1 tab on the tie plates would need to be removed or altered to allow for uniform contact between the mating surfaces. Tables 4 and 5 show a summary of the results generated from the analysis. The tables show only the peak values when considering nodal results for an installation similar to that of the timber crossarm. The GFRP profile was designed to provide similar stiffness characteristics to that of the timber crossarm with limitation of the cross-section envelop being 14 x 6. While the FE analysis detailed within this report shows the GFRP channel will meet the design criteria for both the 287kV and the 230kV structures, ultimately full scale testing is necessary to validate the design. 16

17 Table 5. Summary of the 287kV structure design values generated through the FE analysis. 17

18 Table 6. Summary of the 230kV structure design values generated through the FE analysis. 18