3.6.10: Resultant Section Forces

The “Beam Resultant Forces”-component retrieves axial forces “N”, resultant bending moments “M” and shear forces “V” for all beams and load cases. Force and bending moment components are positive in the direction of the local coordinate axes. The sequence of element results corresponds to the sequence of beams. Thus the data can be used for cross section design of radially symmetric elements. The output values are organised with a data tree structure where the load-cases take hierarchy over the individual beam elements.

Fig. 3.6.10.1 shows a beam with two load cases presented in one picture. The beam consists of two elements and has a total length of eight meters. In load case zero a vertical force of magnitude $1 kN$ acts vertically downwards in the middle of the beam. Load case one consists of a point-load of $3 kN$ directed parallel to the undeformed beam axis. The results at the output-plugs “N” and “M” in fig. 3.6.10.1 are trees that hold the beams normal force, shear force and resultant bending moment. If the input-plug “LCase” has a value other than the default of “-1” the output in “N”, “M”, and “V” is limited to the load-case with the corresponding index. With “BeamIds” the result output may be confined to a subset of the beams in the model.

Tensile normal forces come out positive, compressive normal forces have negative sign. The resultant moment yields always positive values as it is the length of the resultant moment vector in the plane of the cross section.

Fig. 3.6.10.1: Beam under axial and transverse point-load

The input-plug “NRes” sets the number of equidistant points along the beam axis where resultant forces are calculated in order to determine the maximum values for output. In case of zero gravity and in the absence of uniform beam loads the maximum values of M and N occur at the endpoints. Otherwise these maxima may lie inside the elements. The default value of “NRes” is three which means that values are checked at the beams end-points and in the middle.

As “M” is always rendered positive the maximum along an element is unambiguously given. Under gravity normal forces in a beam may change sign. In such a case Karamba3D returns that “N” which gives the maximum absolute value.

Fig. 3.6.10.1 shows the results of a simply supported beam consisting of two elements under two load-cases: In load case zero both elements return zero normal force because there acts no external axial load. The maximum moment of both elements is $2 kNm$. For a simply supported beam under a mid-point transverse load the maximum moment occurs in the middle and turns out to be $M= F \cdot L/4 = 1kN \cdot 8m/4 = 2kNm$.

The axial force of $3 kN$ in load case one flows to equal parts into both axial supports. It causes tension ($1.5 kN$) in the left element and compression ($-1 kN$) in the right one.