Design of smoke stacks for electrical utilities presents a wide range of challenging design issues. Traditionally, these issues are addressed by looking up appropriate equations in a handbook such as Roark's and generating a manual solution. Geometries, which are too complex to fit a formula, are normally addressed with general-purpose finite element packages. In the last several years, I have been using two software packages, which provide dramatic improvements over these methods. For simpler problems which are normally handled by solving an equation, I switched to The Desktop Engineer, a computerized engineering handbook from Desktop Engineering Int'l Inc., Woodcliff Lake, New Jersey, which provides the solutions to virtually any handbook problem in a few minutes simply by plugging in the required input parameters. For complex geometries, I now use the SAP90 finite element analysis package from Computers & Structures, Inc., Berkeley, California, which provides many modeling and analysis features that specifically address structural engineering. This combination of programs saves time; helps produce more accurate designs and minimizes the need for testing.

Killion Engineering is a small structural engineering firm founded in 1982 and operates as a sole proprietorship. The company specializes in the design of large cylindrical structures including water towers and grain bins as well as smoke stacks. In 1987, Killion and a colleague patented a hydraulic derrick that builds smoke stacks between 60 and 80 feet in diameter and up to 1500 feet tall. The device has been used for the construction of smoke stacks at a number of electric power plants throughout the country and abroad. Killion Engineering typically takes responsibility for both structural design and detailing. Despite its small size, the company handles a large volume of work by taking full advantage of computer-aided engineering and design. The design and drafting portion of the job is performed with the assistance of AutoCAD computer-aided design software from AutoDesk, Inc.

Smoke stacks are typically constructed of an outer concrete shell with an interior brick or steel liner. Fiberglass liners are sometimes used but have become less popular recently because their durability has come into question. Three different methods are commonly used to build smoke stacks. With the jump form method, each section of stack is poured 7'6" at a time. A derrick is raised on the previously poured sections. Typically the derrick is supported several sections below the section that was poured the day before. The slip form method involves a truss arrangement with the concrete forms being slipped and jacked up continuously as pouring proceeds at a 12 inch per hour rate. The third and newest method is called the jump jack system. This approach is similar to the jump form method except that instead of using a derrick, jump beams are attached to the wall of the stack. As the jack clears a beam, the lowest beam on the structure is removed and reattached above the highest beam. This new method is gaining in popularity because it requires less labor than the other methods, although it is limited for use on relatively small diameter chimneys.

Each construction method presents its own unique analysis challenges. The work deck used in the jump jack system to support the workmen and inside forms is a good example. The work deck is a grid-type structure with a timber beam grid and a plywood shell. The primary design issues are membrane stress on the deck and bending stresses in the beams that support the deck. The deck faces tremendous lateral pressure from the forms. In the past, these stresses were approximated with a Roark formula for buckling of a circular plate. This approach took about half a day and provided only maximum stress in the plate without determining the stresses at particular areas. This made it necessary to over-design the deck to a considerable degree. Each deck section had to be designed for the maximum stress, which was actually experienced only in one small area. To design a lighter deck, it would have been necessary to build a test frame as a prototype prior to constructing the actual structure - an expensive undertaking.

About five years ago, I began using the personal computer version of a popular general-purpose mainframe finite element analysis program. This was a major improvement over hand or plane frame (2D) analysis but the company I bought it from soon stopped supporting the program. So I purchased the SAP90 program. I selected SAP90 because it contains many unique features useful in structural analysis such as providing the ability to model the more difficult aspects of the structure. Unlike other structural analysis software on microcomputers, which are based on 20-year-old solution technology, SAP90 is fast and efficient, and makes use of the modern element technology, element formulations, equation solution algorithms and Eigen solution methods. Compared to the program I used before, it takes much less time to produce the model and the analysis also runs much faster. The end goal in analyzing the deck is to determine buckling strength. However this cannot be directly calculated with any currently available software. The buckling strength can be estimated reasonably well by comparing the stresses on the plate calculated by the SAP90 program with formula buckling stress on a plate of equivalent thickness. This greater accuracy makes it possible to optimize the design to a level that greatly reduces its cost and also eliminates the need to build a test deck for further substantial savings.

Another important issue in designing smoke stacks is determining the torsional effects on the steel ring girders that support the steel liners on the inside of the structure. The ring girder supports the weight of the entire steel liner. In the past, I used Roark's reference manual to find the proper formula to fit the structure of interest and then calculated the answer by hand. Approximately 20 variables were typically involved in the formula and each of these variables usually required one or more calculations. Determining the stress for a particular set of boundary conditions thus would generally take several hours. Nearly always the first design iteration was unsatisfactory which meant repeating the entire process several times. The process was prone to errors because of the large number of hand calculations involved.

For this type of problem, finite element analysis may not be appropriate or necessary so I used a computerized engineering handbook called The Desktop Engineer. Since I began to use The Desktop Engineer, I have drastically reduced the amount of time required to design ring girders. I now select the curve beam module and enter the required information based on the prompts provided by the program. This method produces the answer in just a few minutes, including the time spent gathering the necessary information. With the first iteration completed, I can solve for different boundary conditions in even less time thus making it possible to simulate the structure for various sets of boundary conditions in about 10 minutes. This is typically sufficient to establish a worst case scenario upon which to base the design.

In some situations, I have used the dynamic analysis capabilities of The Desktop Engineer to determine the natural frequencies of walls supporting vibratory equipment. In one case, the existing walls were 24 feet high by 40 feet long and supported conveyors that were powered by reciprocating motors. The analysis determined that the walls had been designed at the natural frequency of the equipment and thus explained why they were shaking. Using The Desktop Engineer, the problem was solved in just 15 minutes, which is far less time than would have been required with either hand calculations or finite element analysis. In reality, the wall was fixed at one side and at its bottom and would have been very difficult to solve at all by hand analysis. For this particular problem The Desktop Engineer was much faster than finite element analysis programs and avoided the need to create a finite element model.

The Desktop Engineer also is a wonderful tool for the host of smaller issues that often arise during smoke stack design. For example, I have used the program's circular arches module to look at the eccentric loads on smoke stacks. Sometimes there is a knee brace that supports the boiler duct and in that situation I use the program to look at the concentrated loads on the stack walls. Another application is designing steel free-standing stacks, which have three sections with each section decreasing in diameter up the structure. It is possible to calculate global buckling failure on this type of stack by plugging in the appropriate areas and moments of inertia of each section using the beams and columns module. One of the more desirable things about the program is that many modules are based on the common engineering formulas with which most of my clients are already familiar. Thus, there is almost never any need to explain the graphical and tabular output produced by the program since it is easily understood by almost everyone and rarely questioned.

The Desktop Engineer, of course, does not replace finite element analysis, but can be used to calculate input parameters, to perform preliminary or parametric studies and to verify results of more complex analyses. For more detailed analysis of the 3D steel frames of smoke stacks, I use SAP90. In the past I handled problems like this with a plain frame and truss program whose accuracy was limited. The next version of SAP90, I have been told, will provide a tension-only element that will make it possible to model derricks that are suspended from cables. When the derrick moves slightly due to wind pressure, the current software output shows that some cables go into tension while others go into compression. The ones in compression do not contribute to maintaining the load of the derrick. Currently, I handle this problem in SAP90 by removing the members which are in compression and simulating large displacement analysis on the other members.

In summary, smoke stack design provides an excellent example of how finite element analysis and a computerized engineering handbook can work together to reduce design time requirements while providing performance gains.