Some basic concepts as used in the program

- Types of calculations

In addition to linear static calculations, geometric non-linear calculations (incl. 2nd order effects) are also possible.

In linear calculations, the various base load cases can be calculated in one operation; for geometrically non-linear calculations this must be done separately (the superposition principle is then not valid).

Furthermore, the calculation of Eigen frequencies is supported.

A base load case is a collection of associated member and/or node loads.

The geometry, member properties, prescribed displacements, eccentric beam connections and spring-supported nodes remain unchanged.

In a calculation, the following equation is solved: k = [S].v

with

k is the load vector, containing the load present on the nodes

[S] is the stiffness matrix of the total structure

v is the displacement vector, containing the displacements occurring at the nodes (degrees of freedom)

k and [S] are the known quantities; v is the unknown quantity to be solved.

In a linear calculation, the superposition principle applies, which makes it possible to calculate several base load cases in one step.

k = ki ..….kn

with

v = ­vi ..….vn as associated unknown displacements.

[S] is then equal in all base load cases

A load combination is a collection of associated base load cases . Each base load case is multiplied by a multiplication factor to be entered.

This is a form of post-processing and is performed after v from k = [S].v has been solved.

- Nodes

A framework consists of straight beams that together form the geometry of the framework. Both ends of a beam are called nodes.

The location of these nodes is determined by the nodal coordinates to be entered.

Several beams can be connected to a node.

Degrees of freedom are present at the nodes: translations and rotations.

- Beams

A beam forms the straight connection between 2 nodes; No more and no less. The length of the beam is determined from the distance between the two connecting nodes.

In principle a beam can transfer normal forces, shear forces and moments. Some tines called ‘beam-column’ elements in literature.

By arranging hinges on both sides of a beam, a beam can possibly be limited to the transfer of normal forces only.

In the case of trusses, however, this is a somewhat dated method of schematization.

- Beam properties

In [S] the beam properties are included. This concerns quantities such as E-modulus (E), area (A), moment of inertia, etc.

If the stresses also have to be calculated during post-processing, additional properties such as e.g. moments of resistance are entered.

A database with steel sections is available.

The relevant Eurocodes are also supported.

- Prescribed displacements (including supports)

Equation k = [S].v can  be solved if there is a connection with the outside world only.

This means that displacements at some of the nodes must be prescribed.

If the magnitude of this prescribed displacement is equal to zero, then the relevant degree of freedom is fixed (support).

If the magnitude of this prescribed displacement is unequal to zero, then the respective degree of freedom undergoes a fixed value prescribed at the input (a settlement).

- Beam connections (including hinges)

By default a beam is rigidly connected to the two connecting nodes.

A beam can also be spring connected to one or both nodes. If the stiffness of the bending spring is equal to zero then it functions as a hinge (simplified input for hinges is provided).

- Eccentric beam connections

By default, the centreline of a beam is directly connected to both nodes. By entering an eccentric connection, the centreline may be shifted with respect to the nodes (offset).

The shifted part is not part of the elastically deforming beam; is infinitely stiff as it were.

Point shaped loads can be directly introduced in the direction of the respective degrees of freedom.

Internally entered beam loads are converted to nodal loads to solve for k = [S].v

Different types of beam loads can be entered on the various beams present; acting along the longitudinal direction of the respective beams.

Internally entered beam loads are converted to nodal loads to solve for k = [S].v

The force acting in the longitudinal direction of the beams is a form of post-processing after solving k = [S].v

- Spring supported nodes

Using this option, a node can be spring connected to the outside world.

This is a variant of the option of 'Prescribed displacements'

- Spring-supported beams

Using this option, a spring-supported bed acting along the beam axis can be entered.

- Influence Lines (2D only)

Using this option, the influence of a mobile load can be calculated (principle: Maxwell's reciprocity law; Müller-Breslau method).

This option uses the option of 'Linked nodes' internally.

- Tyings (2D only)

Using this option, dependency relationships between different nodes can be entered.

This is a fairly advanced option.

- 'Wizards'

With the help of various 'wizards', certain construction types can be entered relatively quickly and easily using a type of template.

Such as for continuous beams, spring supported beams, trusses, beams and columns, grillages and space frames.

It is not a fundamentally new option, but is intended to aid in data entry for a particular type of construction.