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Beam ModellerNumber Of Elements =10U D L =0NotesNumber Of Nodes =11Node Data: Left Of Column FConstraintsForcesNodeNode/ElementElement PropertiesElement Data : Right Of Column FDispRotForceMomDistanceNumberEIYNumber Of Nodes = Number Of Elements + 11012.00E+054.62E+08347.5122.522.00E+054.62E+08347.5Constraints Must = 1, 0 or Blank, (1 = Applied 0 or Blank = Not Applied)24532.00E+054.62E+08347.5UDL: Uniformly Distributed Load = Force per Unit Distance367.542.00E+054.62E+08347.5UDL: Is proportionally applied to all nodes49052.00E+054.62E+08347.5All Element Properties Must Be Stated for the last element100000050062.00E+054.62E+08347.551072.00E+054.62E+08347.5The last Node Diastance Must Be stated632.582.00E+054.62E+08347.5Any Node distances left blank will be calculated Automaticaly75592.00E+054.62E+08347.5877.5102.00E+054.62E+08347.5Loads must not be apllied on constrained Nodes1010001112131415161718192021222324252627282930313233343536373803940414243444546474849505152535455565761312.5585960616263646566676869707172737475767778798081828384858687888990919293949596979899100

Compile

Data FileBEAM FINITE ELEMENT PROGRAM (USING MATRIX DISPACEMENT)Number of Elements =10.00Number of Nodes =11.00ConstraintsNode NumberDisplacementRotation1.001.000.0011.001.000.00Element PropertiesElement NumberLengthIEYbar1.00122.50462000000.00200000.00347.502.00122.50462000000.00200000.00347.503.00122.50462000000.00200000.00347.504.00122.50462000000.00200000.00347.505.0010.00462000000.00200000.00347.506.0010.00462000000.00200000.00347.507.00122.50462000000.00200000.00347.508.00122.50462000000.00200000.00347.509.00122.50462000000.00200000.00347.5010.00122.50462000000.00200000.00347.50ForcesNode NumberForceMoment6.001000000.00RESULTSElement NumberLengthStressMomentDisplacement

RUN

I Value CalculatorSecond Moment Of Area CalculatorEstablish a datum PointBreak object into individual componentsMaximum of 4 components can be calculatedYELLOW cells are for data inputDatumb = Width of Componentd = depth of componenty = Distance from centre of component to Datum PointMaximum Depth Of Section =520Section 1IAreaArea *YBarb=300d=20y=51020000060003060000Section 2b=20d=500y=250208333333.333333100002500000Section 3b=d=y=000Section 4b=d=y=000Totals160005560000From Datum PointY Bar =347.5Maximum Ybar =347.5For Beam CalculationsI xx =462033333.333333

Ybd

MBD0001E46C.docReducing Model Size

It is very rare that an FE model is made of a complete object; most models are constructed so that they only consider the area of interest. However the constraint applied to the area of interest by the main object have to be known or accurately assumed.

Consider a simply supported beam with a point load in the centre. The rotation of this beam in the middle changes from positive to negative; at its exact mid point the rotation is theoretically zero. Therefore this beam can be represented by two cantilever beams, simply supported at one end and constrained against rotation at the other, thus reducing the size of the FE model.

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Force

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Force

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MBD00007704.docBEAMS

A finite element program for calculating bending stress and displacement in beams subject to point loads.

Basics

Beam structures are broken up into elements, the beam elements used by this program are flexible, and therefore increasing the number of elements does not improve accuracy. However the program is currently set up to calculate up to 100 elements.

Elements are joined together by nodes.

Constraints are applied to nodes to fix the beam. A built in beam will have its end node constrained from both displacement and rotation. A beam with a point support will have its node constrained against displacement only

Point loads can only be applied to nodes. Uniformly distributed loads must be represented a series of point loads; this may require more elements to model this type of load accurately. The program will, if required, automatically apply a given uniformly distributed load or pressure load across the entire beam.

The displacement of the beam caused by bending is calculated at each node point.

Bending stresses can only be calculated in the middle of elements. However a good approximation of the stress at a node point can be obtained by using a very small adjoining element.

Using the program

1. Enter beam details on the Beam Modeller sheet

2. Click the compile button. This copies the data on to the Data File sheet.

3. Click the Run button on the Data file sheet to run the program

4. The calculated results appear below the data and a separate data file is created called Beamsdat.txt, which is saved in the C: directory.

Example:- Cantilever Beam

FE Model

Enter Data in the Data Modeller Sheet

Node and element numbers are in column F . The left hand side of this column is node properties and the right hand side is element properties.

Enter distance along the beam, the first node is 0, the next node is 0.001 and the third node 50. (Note the maximum stress will be a node 1, therefore to evaluate the stress at this point element one must be small.)

Enter a one in the constraints column for Displacement and a one in the column for rotation for node 1. (Note 1 denotes a constraint, a blank cell no constraint.)

Enter 1000 N force, in force column for node 3

Enter Youngs modulus E, Second Moment of area Ybar, and I, for element 2 only.

Note; Any element property cell left blank will assume the value of the next cell below that contains data. Values can be changed for each element if required, but no account is taken of the stress concentration effect caused by discontinuities in the beam.

Youngs Modulus can be set to 1 if beam displacements are not required.

Click the compile button; this transfers the data to the next form. If the data looks OK, click the run button. The results will appear below the data.

Point Load = 1 KN

Length = 50mm

Second Moment Of Area I = 20000 mm4

Maximum distance From the Neutral Axis to the surface of the beam Ybar = 50mm

Therefore Stress at Support = 125 N/mm2

Element 1 Element 2

Nodes 1 2 3

0.001mm

49.99mm

1000 N

Constraints

MBD0000B1E0.docFE Model

Enter Data in the Data Modeller Sheet

Enter number of elements

Node and element numbers are in column F . The left hand side of this column is node properties and the right hand side is element properties. (Note the number of nodes = number of elements + 1)

Enter distance along the beam, the first node is 0, the next node is 0.001 and the third node 50. (Note the maximum stress will be a node 1, therefore to evaluate the stress at this point element one must be small.)

Enter a one in the constraints column for Displacement and a one in the column for rotation for node 1. (Note 1 denotes a constraint, a blank cell no constraint.)

Enter 1000 N force, in force column for node 3

Enter Youngs modulus E, Second Moment of area Ybar, and I, for element 2 only.

Note; Any element property cell left blank will assume the value of the next cell below that contains data. Values can be changed for each element if required, but no account is taken of the stress concentration effect caused by discontinuities in the beam.

Youngs Modulus can be set to 1 if beam displacements are not required.

Click the compile button; this transfers the data to the next form. If the data looks OK, click the run button.

Uniformly Distribute Loads

The program will apply a UDL to the whole Beam. However the UDL on half of each element adjoining a constraint is ignored. Therefore for optimum accuracy small elements are recommended on either side of constraints.

Tools Sheet

Some useful tools for taper sections and varying UDLs. All the data has to be manually copied from this sheet into the Beam Modeller.

Element 1 Element 2

Nodes 1 2 3

0.001mm

49.99mm

1000 N

Constraints