Beams with linearly varying cross sections are used more often today, because the commercial efficiency is a main part in the daily job of a civil engineer. By matching the grider with internal forces, you can optimize the material utilization. Thus, the material is minimized under warranting the load. Beside the profitability, economizing becomes more important. Therefore conical beams are the perfect elements to unite the advanteges. Especially for halls with articulated bearing on the bottom and on the ridge, beams with linearly varying cross sections are an often used element. In this structure the profile increases until the edge with flexural rigidity. In doing so, the significant bending moment in the edge can be gathered by the cross section and at the same time, the quantity of material is adapted to the less stressed flexible connections. To calculate the stress resultants of conical beams either can be modelised with many elements constantly sectionalised, entailing the disadvantage of an increased system of equation. Or, more precisely, the exact solution can be evaluated by solving the differential equations, adapting thereby the stiffness matrix and the load vector. In this thesis the basics to determinate the element relationships are presented and are examplified by a rectangular cross section with linearily varifying component height. The stiffness matrix on the one hand is derived by the principle of virtual displacements or on the other hand by using the transfer matrix. Both theories are equivalent and can be used. For the practical application of this theory, the tutor „Stiff “ [4] of the chair in statics is upgraded, so that you can compute linearly varying cross sections. The convergence of the solutions can be measured by means of the program. Finally the practical aspect is showed by the calculation of a hall. Also the economic advantage by using conical elements is demonstrated.     «

Beams with linearly varying cross sections are used more often today, because the commercial efficiency is a main part in the daily job of a civil engineer. By matching the grider with internal forces, you can optimize the material utilization. Thus, the material is minimized under warranting the load. Beside the profitability, economizing becomes more important. Therefore conical beams are the perfect elements to unite the advanteges. Especially for halls with articulated bearing on the bottom...     »