APM WinMachine | APM Beam

APM Beam

The beam represents a bar of an arbitrary cross section, which dimensions are significantly less than the bar’s length. The main mode of stress for beam structures is a bend in the majority of cases. It does not mean, however, that other modes of loading are not allowed, but for beam structures they are more likely to be an exception. When designing such structures it is essential that the stressed-strained state of the beam should be determined and its dynamic characteristics should be calculated, which proves to be possible for the given geometry. Besides, the important parameters are reactions in supports, which are necessary to calculate and design the beam mating components.

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APM Beam is intended to perform a complex checking calculation of the beam under conditions of arbitrary loading and fastening. In this case the beam can consist of several sections of different length and different cross-sections

APM Beam capabilities

The following results can be achieved by means of the APM Beam:

reactions in the beam supports;
distribution of moments and bend angles along the beam length;
distribution of transversal and longitudinal deformations;
distribution of equivalent stresses along the beam length;
distribution of transversal forces;
stresses distribution maps in any arbitrary cross-section along the beam length;
characteristic oscillation frequencies.

Besides, results of calculations offer an opportunity to plot self-configuration of the beam on the corresponding characteristic frequency.

Creation of the beam model, loading it and setting the cross-section

Fig. 1. Creation of the beam model, loading it and setting the cross-section

Specialized graphic editor

The APM Beam specialized graphics editor of beams and their cross-sections specification is used at the preparation initial data stage for further calculations. The editor having a complete set of all necessary procedures offers the user convenient means to:

setting and editing the length of the cross section of the beam part;
entering the loads effecting the beam;
setting of different kinds of supports and their location;
setting of external lumped masses and inertia moments in case of calculation of transversal and torsion beam structures.

When entering the parameters it is possible to use the both built-in graphics editor and APM graph services, as well as the AMP Mechanical Data database.
The graphics editor is easy to operate; it fully preserves the succession with other products being developed by APM Ltd.

Solution Methods

When carrying out the check calculations the combined methods are used. The calculation of displacements is performed by the energy method also known as the More’s method. Static indeterminacy expansion if any is performed by the flexibility method, the canonical equations coefficients of the flexibility method being calculated by use of the More integral.
The calculation of stresses and torsions in cross-section is performed by the finite element method, and the bend and shift stresses by the inertial moments method. When carrying out calculations by the finite element method, fragmentation into triangular finite elements is performed automatically.
Values of equivalent normal and tangent stresses are calculated based on the energetically strength theory.

Calculation results

APM Beam permits to perform a complex calculation of the beam and in case of necessity to choose the most appropriate cross-section for it. Besides, the module possesses the possibility to perform a dynamic calculations complex by the initial parameters method, allowing determining the characteristic oscillation frequencies and self-forms of the beam.

Stress in cross-sections maps

Fig. 2. Stress in cross-sections maps

2-th natural shape of the beam, and beam critical frequencies

Fig. 3. 2-th natural shape of the beam, and beam critical frequencies

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