We provide hints and tips to help you get started with the main programs RFEM and RSTAB.
We will illustrate the meaning of this option by means of the simple example of a loaded cantilever (see picture).
The loading of the cantilever causes a small rotation at node 3. If you calculate according to second order analysis by using this check box, you can also decide whether the internal forces at this node are related to the original or the rotated coordinate system. If the system is calculated according to first order theory, the following internal forces result (RO 101,6×3.6, S235):
Nx = 0
Vy = 0
Vz = 3,00 kN
Mx = 0
My = 9,00 kNm
Mz = 0
The forces and moments can be understood as vectors (Equation 1 and Equation 2). At node 3, a rotation results according to Equation 3.
Thus, the local member axes system is rotated by the angle φy. Now, the internal forces are converted to the rotated coordinate system. This is done by multiplying the vector by the so-called rotation matrix (http://en.wikipedia.org/wiki/Rotation_matrix). The rotation matrix for the rotation about the y-axis is given in Equation 4. The conversion is carried out by using the Equatione 5 and 6. Equation 7 is obtained by substituting the numbers.
The calculation shows that a small part of the transverse force becomes a tensile force:
Nx = 0,4326 kN
Vy = 0
Vz = 2,969 kN
The moment vector does not change.
The calculation of this simple example can be checked as shown in Equation 8.
Thus, we can see the effect of this calculation option. But what are the “right” internal forces? The internal forces related to the rotated coordinate system are certainly more exact. Preconditions for the second order calculation, however, are small torsions. Therefore, the results may not differ significantly. If they do, the large deformation analysis is necessary and the results are always related to the rotated coordinate system. In first order analysis, the internal forces are always related to the original coordinate system.
internal forces, deformed structure, second order, P-Delta
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