Kleinlogel Rigid Frame Formulas: A Practical Guide for Structural Engineers
If you are a structural engineer who designs statically indeterminate structures, such as single-panel frames, you may have encountered the challenge of finding the internal forces and moments in each member. The elastic equations are dependent on both the form and the substance of the proposed structure, so you need to assume the size of each member in advance and then check if your assumptions are valid. This can be a tedious and time-consuming process, especially if you have to deal with complex shapes and loading conditions.
Kleinlogel Rigid Frame Formulas
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Fortunately, there is a way to simplify this process by using the Kleinlogel Rigid Frame Formulas. These are explicit formulas of all statical quantities for those single-panel frames that occur in practical steel, reinforced concrete, and timber construction. They were derived by Adolf Kleinlogel, a German professor of civil engineering, who published them in his book Rahmenformeln (Frame Formulas) in 1939. The book has been translated into English and has gone through several editions since then.
The Kleinlogel Rigid Frame Formulas cover 114 rigid frame shapes with 1578 figures, showing the internal forces and moments for different load cases, including temperature changes. They are based on the assumption that the frames are perfectly rigid and that the material is linearly elastic. They also assume that the cross-sections of the members are constant and that the joints are either fixed or hinged.
The advantage of using the Kleinlogel Rigid Frame Formulas is that they allow you to find the statical quantities directly from the geometry and loading of the frame, without having to solve any equations or iterate any values. You can simply look up the relevant figure in the book and read off the values from the graphs or tables. This can save you a lot of time and effort in your design work.
However, there are some limitations and precautions that you need to be aware of when using the Kleinlogel Rigid Frame Formulas. First, they are only applicable to single-panel frames with simple shapes and loading conditions. If you have multi-panel frames or more complicated shapes or loads, you may need to use other methods or software tools. Second, they are based on idealized assumptions that may not reflect the actual behavior of the structure in reality. For example, they do not account for deflections, buckling, shear deformations, material nonlinearity, joint flexibility, or connection details. Therefore, you need to check your results with other methods or tests to ensure that they are accurate and safe.
In conclusion, the Kleinlogel Rigid Frame Formulas are a useful tool for structural engineers who design single-panel frames with simple shapes and loading conditions. They can help you find the internal forces and moments in each member quickly and easily, without having to solve any equations or iterate any values. However, they are not a substitute for sound engineering judgment and analysis. You need to verify your results with other methods or tests and consider all the factors that may affect the performance of your structure.
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