Procedure 4 Large Structures Construction Stage Analysis)
6.9.3 Macros for the Definition of Lanes
As already mentioned, defining a Lane using the above described standard functions is a very tedious and time consuming work because two definitions in the Lane Point Prop- erty Table have to be made for every point on the lane, where related influence lines should be calculated. These are in general every element begin and element end of the main girder elements and maybe also intermediate points.
A set of 4x3 Macros has therefore been provided to generate a part of or the whole Lane Point Property Table with one command and the specification of few data. The Macro creates automatically all Lane Point Property data of the selected Lane for all elements of the deck. This data is stored in the Lane Point Property Table for the calculation. The result of a macro (the data stored in the Lane Point Property Table) can be modified using the above described input functions, but the Macro input data is not available any more. In order to re-create a Lane it is necessary to delete it first and then to run the Macro again.
The provided macros are offered in the Lane Point definition pad where also the basic Lane Point Definition Functions described above are selected. The following macros are available:
• MACRO1X concentric lane on main girder, longitudinal load (braking)
• MACRO1 concentric lane on main girder, vertical load
• MACRO1Z concentric lane on main girder, centrifugal load
• MACRO2X eccentric lane on main girder, longitudinal load (braking)
• MACRO2 eccentric lane on main girder, vertical load
• MACRO2Z eccentric lane on main girder, centrifugal load
• MACRO3X lane on cross beams, longitudinal load (braking)
• MACRO3 lane on cross beams, vertical load
• MACRO3Z lane on cross beams, centrifugal load
• MACRO4X lane on cross beams, longitudinal load (braking)
• MACRO4 lane on cross beams, vertical load
• MACRO4Z lane on cross beams, centrifugal load One of these Macros will be applicable in most practical cases.
Y LANE
X ZL
Y
BEGI END BEGI END BEGI
END
e
Y X
ZL
LANE Y
BEGI END BEGI END BEGI
END
MACRO1:
Elements forming an individual longitudinal deck are defined. The lane is concentric on this element series having only a vertical eccentricity in order to apply the load at the sur- face of the deck.
MACRO1X generates an equivalent lane for forces in the longitudinal direction MACRO1Z generates an equivalent lane for forces in the transverse direction
MACRO2:
Elements forming an individual longitudinal deck are defined. The lane can be eccentric to this element series and can also have a vertical eccentricity in order to apply the load at the surface of the deck.
MACRO2X generates an equivalent lane for forces in the longitudinal direction MACRO2Z generates an equivalent lane for forces in the transverse direction
LANE e
Y X
X ZL
Y
MACRO3:
The deck is defined by two or more series of longitudinal elements being connected by one or more series of transverse elements. The lane can be relative to the transverse elements (cross members) as well as relative to the longitudinal elements. Lanes between two series of longitudinal elements will usually be related to the cross members, lanes outside the longitudinal elements will be relative to these longitudinal elements.
MACRO3X generates an equivalent lane for forces in the longitudinal direction MACRO3Z generates an equivalent lane for forces in the transverse direction
MACRO4:
The loading is related to transverse girders as in Makro3, but the forces are not applied directly on the cross girders but transferred to the longitudinal elements without creating fixed end moments.
The lane points are described by their distance from the element begin of the transverse elements. This distance can be expressed as the percentage of the clear element length [%], or as the distance itself [Length(structure)]. By defining different distances for the first element (x/l-Beg or dx-Beg) and the last element (x/l-End or dx-End) it is possible to define lanes running in a skew direction over the cross girders.
With the additional information ORTHOGONAL TO LANE the primary elements (i.e.
on the longitudinal girder) will be found orthogonal to the lane direction.
301
dx-Beg
eccentric junction
301
dx-Anf.
eccentric junction
101 102 103 104 105 106 107 108
201 202 203 204 205 206 207 208
dx-Beg.
dx-End LANE
101 102 103 104 105 106 107 108
201 202 203 204 205 206 207 208
dx-Beg
dx-End LANE
Input data for the MACROS:
The macro pad contains a table of macro input data. This table is empty after selecting the Macro Definition Function. Data can be entered in this table by using the “Insert before” or
“Insert after” button. Several lines in this tables may be created. As long as the user does not exit the Macro Definition Function he can modify the macro input data by selecting the line to be modified and clicking the “Modify” button.
After exiting the Macro Definition Function the appropriate data of the Lane Point Prop- erty Table will be generated and inserted, and the macro data will not be available any- more, if the Macro Definition function is selected again.
The Macro Input Data Table contains the following data:
• Kw Shows the Position Definition Function to be used in the Lane Point Property Table (e.g. POSEG)
• Elem-from series of elements
• El-to to be considered
• El-step for this lane
• x/l Only for MACRO3, MACRO3X, MACRO3Z: distance of the lane from the begin of the loaded element (cross member) ex- pressed as the ratio between the distance and the element length.
• ey Only for MACRO2, MACRO2X, MACRO2Z and MACRO3, MACRO3X, MACRO3Z: vertical eccentricity of the lane rela- tive to the centre of gravity of the element
• ez Only for MACRO2, MACRO2X, MACRO2Z and MACRO3, MACRO3X, MACRO3Z: horizontal eccentricity of the lane relative to the centre of gravity of the element
• Phi (dynamic) coefficient for this lane; this value is taken as multipli- cation factor (Data7) in the Lane Point Property Table.
• Ndiv Number of subdivisions for each considered element
• Type Only for MACRO1, MACRO1X, MACRO1Z and MACRO2, MACRO2X, MACRO2Z: program internal code for the type of load application
Inserting or modifying these data creates an input pad requiring the following definitions:
For all Macros:
# No ecc. No cross section internal eccentricity is considered
# Ygl The global cross section internal Y eccentricity is considered
# Zgl The global cross section internal Z eccentricity is considered
% El-from elements to be
% El-to considered for
% El-step this lane definition For MACRO3, MACRO3X, MACRO3Z:
% x/l position of the lane inside the element
For MACRO2, MACRO2X, MACRO2Z and MACRO3, MACRO3X, MACRO3Z:
% ey vertical eccentricity of the lane
% ez horizontal eccentricity of the lane For all macros:
% Phi (dynamic) coefficient for this lane, stored as multiplication fac- tor for the lane
% Ndiv Number of subdivisions for each considered element
For MACRO1, MACRO1X, MACRO1Z and MACRO2, MACRO2X, MACRO2Z:
Switch describing where the unit loads should be applied:
# Begin+End of Elements
# Only begin of Element
# Only end of Element
# Begin/End/Begin/End of Element
# End/Begin/End/Begin of Element
The Macros for generating lanes related to main girder elements will create load posi- tions at the begin and/or end of elements (possibly among others defined by Ndiv > 1).
The expression for “x/l” will be 0.0001 for the begin of an element and 0.9999 for the end of an element (column DATA1 in the Lane Point Property Table) in order to get a correct presentation of sudden changes of internal forces at the nodes.
The switch describing whether Lane Points should be created at the begin or the end of the elements is set per default to “Begin+End”, that means the unit loads are applied at the begin and the end of the specified elements. In this case the unit load will be applied at intermediate nodes shortly before and shortly behind the node, giving almost the same influence line twice. It is possible to save computing time by defining Lane points only at the begin or the end of the elements, but internal forces” jumping” at the nodes (e.g. shear forces) will in this case not be maximised or minimised correctly at all ele- ment ends.
The functions Begin/End/Begin/End and End/ Begin/End/Begin allow to set a Lane Point at both sides of every 2nd node, e.g. at the end of the 2nd element and the begin of the 3rd element, at the end of the 4th element and the begin of the 5th element and so on.
LIQV
(Before and after)
Dmin (F1) Dmax (F1) Dstep (F1)
F1 F2
Dmin (F2) Dmax (F2) Dstep (F2)
Dmin (F3) Dmax (F3) Dstep (F3)
F3=0