**Backgrounds Framework 2 and 3- dimensional**

*View on the user
interface of the Framework program (background picture can be changed)*

The Framework program can be setup in the Dutch, English, German, Croatian and Russian language.

(translators sought for other languages; please do e-mail when you’re interested {around 8000 lines of text to translate})

**What is the purpose of this computer
program?**

**This program can be used to calculate the statical
force distribution and Eigenfrequencies in a 2 and 3 dimensional frame structure.**

**A transient dynamic analysis is also
supported for the 2-dimensional part of the program.**

**The program does try
to combine a high degree of user comfort with rather advanced calculation
techniques.**

The program allows metaphorically speaking peeling off skin for skin.

At each skin layer peeled the substantive difficulty increases, but the program operates at every level of peeling.

For a novice user to the program it’s strongly recommended to start with the two-dimensional part of the program.

The principle of the onion implies that the program makes use of multiple windows, which are successively opened by the user; each onion ring is, as it were,

a separate window which is opened as a descendant of a previously opened window.

For some general background see also Some basic concepts

**Content 2- dimensional**

*Data input main menu
2D
Alternative way for input of data*

*Depiction of 2-dimensional
geometry*

** **

**Content 3- dimensional **

*Data input main menu
3D
Alternative way for input of data*

*Depiction of
3-dimensional geometry*

*Alternative rendering of
3-dimensional geometry with OpenGL
and GLScene*

**Statical**** calculation; linear elastic ****2D**

The program supports the following (calculation) capabilities:

For non-prismatic beams all options are supported as with prismatic beams (all types of beam loads,

eccentrically connections; spring connected beams, hinges etc.).

The stiffness matrix of a non-prismatic beam is determined according exact analytical solutions.

The point load and the point moment as beam loads are also processed exactly following analytical formulas;

at non prismatic beams the other types of beam loads are calculated by way of numerical integration

(100 integration points per load type).

For prismatic beam loads, with the exception of the arbitrary distributed beam load, all types of loads are processed at an exact analytical way.

**Check input data**

The input data for a problem can, next to a numerical input, also be shown and input in a graphical window:

for the case of the GEOMETRY, the BEAM loads and the NODAL loads acting on the framework.

Output of the calculation results (numerical and graphical)

The output is at first given in a numerical form; it concerns the deformations and beam forces near the nodes.

By way of post processing the distribution of the forces along the beam axes can be output.

Next to the numerical output the calculation data can also be shown at a graphical way:

force distribution per base load case and load combination at the whole framework,

separated per beam or per combination beam.

Also by clicking at the tabs the calculated stresses can be shown.

Further from the output data envelopes (maximum and minimum values) of a number of BASE loads

or load COMBINATIONS can be calculated and pictured.

The deformations of the framework can be plot based on nodal displacements.

**Statical**** calculation; GEOMETRIC non-linear 2D**

For a geometrical non-linear calculation the second order terms of deformations are accounted for;

this results in a different force distribution in the framework compared to linear calculation.

Because of the nature of a non-linear calculation the superposition principle does not longer holds.

Each base load case and load combination is calculated apart therefore.

**Calculation of Eigenfrequencies
2D**

With the aid of this option the natural frequencies and the accessory shapes of vibration

(the Eigenvectors) of a framework with fixed beam connections can be calculated.

All shapes of vibration can be thought to consist out of a weighed summation of all Eigenvectors (Fourier analysis).

Acts a load on the framework at a frequency approximately equal to a certain Eigenfrequency

then the appearing deformations are becoming very large (and also the stresses).

The lowest Eigenfrequency is most critical.

Often it will be attempted to keep the load frequency underneath the lowest Eigenfrequencies;

therefore mostly only the lowest Eigenfrequencies (the first Eigenmodes) are of importance.

The frequencies of the maximum of traffic loads at a road bridge lies at about 10 Hz;

the frequency of wind loads on buildings lies at about 0.1 Hz.

Even if there is no danger of strong resonance of the structure the dynamic effect can cause a significant

increase of the deformations and accordingly larger stresses.

The program does not account for material damping; with the majority of building materials this effect can be ignored.

The vibration shapes with the lower Eigenfrequencies are calculates at the largest accuracy

The vibration shapes are calculated in relation to the degrees of freedom at the supplied nodes.

In the case for the need of more detailed information between the nodes, the beams can be divided in parts

with the aid of dummy nodes which should be input extra.

The calculated Eigenvectors are normalized at a maximum value of "1".

The real value is thus the provided value multiplied with an unknown constant;

only the shape of the vibration is calculated.

Next to the beam properties in the nodes extra point masses can be input (mass and moment of inertion).

**Transient dynamical calculation 2D**

In a dynamic analysis, in addition to the stiffness of the structure, the mass and damping of a structure subject

to time-dependent loads is also taken into account.

The total time is divided into time steps.

The entered node and beam loads are multiplied ALL at once by a time dependent factor.

For a selection from the number of calculated time steps, displacements and force effects are displayed both

numerically and graphically.

The program supports 2 different calculation methods:

- Direct dynamic analysis

In this approach, the equation of motion in the program is solved using the Newmark Beta method.

This calculation method is set in the program as the default calculation method, because compared to

MMRA the direct transient response analysis has a greater calculation accuracy.

The reason for this is that in MMRA the accuracy of the determination of the higher Eigenmodes is less.

- Multi modal response analysis (MMRA)

If the equation of motion is transformed to modal coordinates, the equations are decoupled per Eigenmode.

The response in each Eigenmode can be determined independently of the others.

The combination of these responses per Eigenmode gives the total response of the construction.

Each modal response can be determined as a function of time as if it were a single degree of freedom (SDF) system.

Because MMRA is based on the superposition principle, only linear elastic frameworks can be calculated

using this method (however, the program also only supports linear elastic behaviour for direct dynamic analysis).

**Calculation of influence lines ****2D**

With the aid of this option from every framework the influence lines can be calculated of normal forces,

shear forces and moments.

Next to a single point load also influence lines of point load systems can be output.

Except of numerical output (also stresses) a graphical reproduction is possible.

**Available wizards 2D**

In order to make the input easier a number of wizards are available to make this happen

**Statical**** calculation; linear elastic 3D**

The program supports the following calculation capabilities:

**Check input data**

The input data for a problem can, next to a numerical input, also be shown and entered in a graphical window:

for the case of the GEOMETRY, the BEAM loads and the NODAL loads acting on the framework.

It shown through a built in spatial camera model (fully 3- dimensional)

**Output of the calculation results (numerical and
graphical)**

The output is at first given in a numerical form; it concerns the deformations and beam forces near the nodes.

By way of post processing the distribution of the forces along the beam axes can be output.

Next to the numerical output the calculation data can also be shown at a graphical way:

force distribution per base load case and load combination at the whole framework, separated per beam or

per combination beam.

Further from the output data envelopes (maximum and minimum values) of a number of BASE loads or

load COMBINATIONS can be calculated and pictured.

The deformations of the framework can be plot as nodal displacements.

**Calculation of Eigenfrequencies
3D**

The 3D capabilities are equal to the 2D capabilities for the calculation of Eigenfrequencies.

The calculation or Eigenfrequencies is part of the supported earthquake multi modal response analysis

(according to EN 1998-1); see further Earthquake load 3D.

**Statical**** calculation; GEOMETRIC non-linear 3D**

For a geometrical non-linear calculation the second order terms of deformations are accounted for;

this results in a different force distribution in the framework compared to linear calculation.

Because of the nature of a non-linear calculation the superposition principle does not longer holds.

Each base load case and load combination is calculated apart therefore.

**Statical**** calculation; General Method Buckling 3D**

The program does support the “General method” for lateral and lateral torsional buckling

according Eurocode 3 (EN 1993-1-1; art. 6.3.4).

**Available wizards 3D**

In order to make the input easier a number of wizards are available to make this happen.

**Program flow**

a. Input of
data

b. Output of
calculation results

**A general view of the program with some open windows:**

**2-dimensional**

**3-dimensional**

**Educational option for showing of force vectors,
stiffness matrices and displacement vectors:**

*Stiffness matrix of a
single beam*

*Stiffness matrix of
the whole frame*