A generation of frame structure based on Koch curve and an application to spatial frame

The authors have been engaging to apply self-similar forms in nature to architectural form. The self-similarity is one of the characters of fractal. Mandelbrot set, Sierpinski gasket, the Koch curve, and so on are famous as the fractal geometric forms. It seems difficult to apply Koch curve to architectural form because they are complicated in shape. But we can treat numerically because they are composed of a combination of original figures and its self-similar mappings. So, new self-similar frames are generated by adding an angle as a parameter to Koch curve. Here, a parameter is given at the base angle of the equilateral triangles and given at the angle for the line of divided both sides. Though angle 1 varies 0~15 degree and angle 2 does 0~60 degree. However, if angles are raised, the shape is larger obviously and fractal dimension is higher, which varies from 1.00 to 1.28. On a static mechanical characteristic against to vertical load, if both angles are larger, bending moment and displacement are less in a whole. Also, bending moment and vertical displacement are suppressed by increasing of inclination in angle1 or decreasing of angle2 and shapes will be similar to an arch structure. As a result of frame analysis, it was shown that some new Koch curve was superior to a general Koch curve. In addition, some structural examples are shown extending the Koch curve to spatial structures that maintain complexity and self-similarity followed by the fractal characters of Koch curve.