PC-BASED FINITE ELEMENT ANALYSIS REVEALS DANGEROUSLY LOW RESONANCE IN COASTAL TOWER

Plot of the deformed tower model displayed on top of the original illustrates the bending that occurs.

Finite element analysis (FEA) on a personal computer has enabled a marine engineering firm to determine the natural frequencies of a 110-foot-tall data transmission tower in Key West. The General Offshore Corp. of Fort Lauderdale, Florida recommended the tower not be used since FEA showed that these frequencies were so low that the tower could be affected by the coastal wind gusts of 80 to 130 mph, potentially causing the structure to resonate and crash.

The United States Navy intended to use the 110-foot-tall data transmission tower for a project in Key West. The Navy wanted to place the tower on a pier then attach transmission equipment atop it; they thought this would save money over building a new tower, according to Bert Gillenwater, a General Offshore engineer. The tower's structure was square and symmetrical, composed of five-foot pipe sections. For protection against the 80 mph to 130 mph wind gusts, there was bracing around the top, lateral support on all sides, along with concrete reinforcement at the base. The Navy had made durability studies of the tower, Gillenwater says, but they wanted further analysis of its dynamic behavior, the culprit of most vibration problems in elastic structures.

Gillenwater's approach to determine the tower's dynamic behavior was to use the Algor Supersap Full Stress/Dynamic Modeling & Analysis package on a Compaq 386 to determine the tower's basic strength via static analysis, and then find the natural frequencies using modal analysis.

The finite element package from Algor utilizes interactive graphics coupled with high-speed processors that make modeling, meshing and analysis quick and easy. "Since we bought Supersap a year ago, I've used FEA hundreds of times; it's a regular part of my analysis of shell-type structures and hydraulically actuated frames. I can test a lot of configurations much faster than I could by hand."

Relates Gillenwater, "We picked Supersap among the other PC-level FEA systems primarily because it is a comprehensive package and its mesh generators are better than the others. For example, it enabled me to build a spline inside a flange drum. I wouldn't have known how to do this with other systems, but with Supersap, I just drew a cross-sectional view of it using SuperDraw II (Algor's full-featured CAD system); and with their radius brick generator I made a 90 degree arc and it automatically generated the boundary conditions for me."

To create a complete model of the tower, Gillenwater used Algor's Beam Design Editor to graphically generate a section of the tower and then Substruct, an Algor pre-processor, to "glue" together the sections, placing every juncture according to corresponding nodes. He created 500 beam elements.

Engineer Bert Gillenwater of General Offshore Corp., whose analysis using Supersap prevented the failure of a Navy coastal tower.

With mesh completed, Gillenwater used Algor's AEdit to establish the boundary conditions on the model, applying loads based on a 0.8 drag coefficient with a wind speed of 125 mph using the South Florida Building Code. The code stipulates the use of 55 pounds-per-square-foot wind loading for structures above 100 feet.

The next step was to run the static analysis and then the modal analysis. Modal analysis characterizes a structure's dynamic properties by identifying its modes of vibration. Each mode has a specific natural frequency and damping factor, which can be identified from practically any point on the structure. In addition, it has a characteristic mode shape, which defines the resonance spatially over the entire structure. A structure is "dynamically weak" when it can be easily excited at or near the frequency of a resonance peak. With the properties characterized, the behavior of the structure can be predicted - and then controlled and optimized.

Once the modes of vibration were identified, Gillenwater was able to predict how the model behaved at each of its resonant frequencies and ascertain the source of the disturbance, its propagation path, and how it is radiated into the environment. After the analysis, Algor's POST, which creates an output file from the processed model, gave Gillenwater a listing of the stresses and deflections.

The fundamental frequency was 0.086 Hertz (cycles per second), which is equivalent to a period of 11.6 seconds. Among the first five modes, the shortest period was two seconds (0.5 Hertz). "There's a good chance the structure will resonate since there are significant structural modes in the same range of periods as the wind gusts, which hit every 5-6 seconds," states Gillenwater. "Coupled with the static loads I applied to it, the tower would come crashing down. The results of the analysis confirmed my suspicions that the tower would not withstand the high winds. I recommended that the Navy buy a tower from an actual tower manufacturer."

"Without FEA," explains Gillenwater, "it would have been very difficult to get accurate estimates of the tower's natural frequencies. I wouldn't have been able to get the perspective on the model's behavior. FEA allows you to see very quickly where all the stresses are coming from and what the relationship is between several elements or between a certain section and another. Gillenwater concludes that Algor's Supersap Full Stress/Dynamic Modeling & Analysis package opens the door to a level of analysis not possible with hand calculations by integrating analysis with superb graphics, modeling and meshing, giving the engineer an actual 3-D picture of stress and insight into the model's behavior.