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GEO5

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Coordinate Systems

Global coordinate system

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is right-handed

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the positive X axis is directed from the left to the right

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the positive Z axis is directed from the bottom to the top

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the positive Y axis drills in to the XZ plane

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the rotation about the Y axis is positive when measured clockwise

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The GCS is used for coordinates

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in general, the positive surcharge is assumed to act in the opposite direction to the positive axis and the positive rotation follows the positive sense of the global rotation

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particular definitions of the positive direction must be carefully examined for all cases

Surcharge

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is always assumed to act along the horizontal line (or at a point)

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the origin (point) and the length are the required input data

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the positive surcharge at zero angle is assumed to act in the opposite direction to the positive direction of the Z axis

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the zero angle corresponds to vertical surcharge

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the angle increases clockwise

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the angle ranges from -180º to 180º

Anchors

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an anchor can also be specified by the origin and an angle

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the zero angle corresponds to the direction of the X axis

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the angle increases clockwise

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the angle ranges from -180º to 180º

Prescribed displacements and rotation of supports

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prescribed displacements are positive in the directions of the X, Z axes and about the Y axis

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displacements are positive when developed in the opposite direction to the positive directions of the coordinate axes

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the positive rotation is measured clockwise

Load of beams

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the local coordinate system is right-handed

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the positive XL axis of the beam is assumed in direction from the starting to the end point

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the positive ZL axis is perpendicular and rotated counterclockwise by 90º from the beam axis

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load can be applied three directions:

- global Z

- global X

- local normal (Z)

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the positive load in the global direction acts in the opposite direction to the positive direction of the corresponding axis

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the positive load in the normal direction acts in the opposite direction to the positive direction of the local ZL axis

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the positive load angle α is measured clockwise

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the moment is positive when acting clockwise

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definition of load along the XL axis

- coordinates, coordinates of the origin

- load span

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types of load (always in above mentioned directions)

- concentrated force

- concentrated moment

- distributed uniform over the whole beam

- distributed trapezoidal over the whole beam

- distributed uniform over a segment of the beam

- distributed trapezoidal over a segment of the beam

Stresses and strains

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positive normal stress Sigma corresponds to compression, negative to tension

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positive normal strain Epsilon corresponds to compression, negative to tension

Internal forces along beams

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positive normal force corresponds to tension, negative to compression

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positive normal strain Epsilon corresponds to compression, negative to tension