An initial estimate is made of N/N uz, the section is designed, a corrected value of N/N uz can then be estimated, and the process repeated until a correct solution is obtained.Ī much simpler, but considerably more approximate method to the design of biaxial columns has been adopted in BS 8110. It, therefore, has to be used iteratively.
The difficulty with the approach from the practical point of view is that it cannot be used as a direct design method since N Rd can only be established once the reinforcement area has been found. In the Table above, N Rd is the squash load of the column, and may be calculated from The proximity to the squash load can be defined using the N/N uz ratio parameter, and EN assumes the relationship between this parameter and the exponent ‘ a‘ given in the Table below. Clause 5.8.9(4) adopts the equation below as a means of describing the complete interaction surface At loads approaching the squash load, the M x – M y interaction diagram approaches a circle, while in the region of the balance point it is close to a straight line. If a = 2, this equation becomes a circle, while if a = 1 it describes a straight line. A super-ellipse has an equation of the form This is based on the observation that the form of the M x – M y interaction diagram can conveniently be represented by a super-ellipse. An example is the approach given in clause 5.8.9(4) of EN for the design of biaxially bent sections in slender columns. There are however simplified methods of dealing with biaxial bending in reinforced concrete structures. The force and moment at each strip in the x and y-axis can be summed up in the ultimate limit state to find the moment and axial force developed by the concrete in compression. To develop such a program, one can divide the compression zone into strips that are parallel with the neutral axis of the section, and calculate the stress in each strip using the parabolic-rectangular diagram. This may not be very easy to achieve without the use of charts or computer programs. The columns circled in red are biaxially loadedĮN 1992-1-:2004 (Eurocode 2) did not give an express method of designing biaxial columns other than working from the first principles.
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