Procedure 4 Large Structures Construction Stage Analysis)
5.4.3 Definition of the Constraint Points
The following parameters are required for the definition of the position of constraint points:
# Space point The definition of the position is done via global coordinates
# Structure element The definition is done relative to a structural element 5.4.3.1 Parameters for global definition
The definition of the position of constraint point via global coordinates in space is nut very often used, because usually the geometry is given in relation to the structural sys- tem. This option is provided in RM2000 only for special cases.
Besides the below described Constraint Point Type the global coordinates in space of every constraint point describing it’s position are entered in this case. Additionally, the direction of the tangent of the tendon geometry must be entered for all points. In this input mode it is not possible to set free the tangent direction of some constraint points, i.e. using this input mode is only allowed if the tangent direction in all constraint points is known.
% x, y, z Coordinates of the Constraint Point in Space
% dx, dy, dz Vector for describing the tangent direction
5.4.3.2 Parameters for element related definition
The input field ‘Ref. Elem’ contains the number of the reference element. This element number describes the position of the point in the structural system together with the value x/l describing the position between element start and element end.
The position of the tendon point within the cross-section defined by the element number and x/l may be defined in local or global directions and either
• in terms relative to the centroid,
• in terms relative to the nodal point (often on top of the cross-section) or
• in terms relative to a specified cross-section reference point.
(see figure below).
The specification of the position related to the longitudinal direction of the element is performed via the clear length related coordinate x/l. The eccentricities in y- and z-
The direction of the tangent in the constraint point can be prescribed as a compulsory condition additionally to the position. This direction is specified by the angles Alpha1 (“vertical angle”) and Apha2 (“horizontal angle”), being the angles in the vertical plane and in the horizontal plane respectively. These angles may be related – similar to the position – to 3 different axes: the element axis, the system line or the line connecting the specified reference points (selection switch „Elem“, „Node“ and „CS pnt“ below the input fields Alpha1 and Alpha2).
Alpha1 Vertical angle of the tendon at the current position. Switch ‘Free’ (no direc- tion constraint) or ‘Value’ for a user defined constraint value.
Alpha2 Horizontal angle of the tendon at the current position. Switch ‘Free’ (no direction constraint) or ‘Value’ for a user defined constraint value.
Attention: The meaning of “vertical angle” (resp. elevation plane) and
“horizontal angle” (resp. horizontal plane) is in this context not exactly the same than in the structural element definition part.
See description below.
The vertical angle is the angle between the reference line (element axis, system line, connection line of reference points) and the normal projection of the tangent to the “ele- vation plane“ (from the reference line to the projection of the tangent anticlockwise positive). The „elevation plane“ is in this case built by using the reference line for cre- ating a new local coordinate system in accordance with the general rules, and consider- ing a possibly for the structural element prescribed angle Beta. The yL-axis of this new local coordinate system forms the elevation plane together with the reference line.
The horizontal angle is the angle between the reference line (element axis, system line, connection line of reference points) and the normal projection of the tangent to the
“plan“ (from the reference line to the projection of the tangent anticlockwise positive).
eY/eZ rel. to the node YL
ZL
eY/eZ rel. to the element
eY/eZ rel. to a CS Pnt
The „plan“ is in this case built by using the reference line for creating a new local co- ordinate system in accordance with the general rules, and considering a possibly for the structural element prescribed angle Beta. The zL-axis of this new local coordinate sys- tem forms the “plan” plane together with the reference line.
There is also the possibility to prescribe a straight part between 2 constraint points.
This is done by setting the switch „Straight part“ at the constraint point, where the straight section begins. The straight section the extends to the next constraint point. Pre- scribed direction constraints at the begin and the end of the straight section are ignored, the tangent direction on both sides is equivalent with the direction of the straight part of the tendon. A fold in the tendon geometry curve is generally not allowed.
5.4.3.3 Summary of input parameters
% Type Type of the considered tendon segment (see chap. 5.4.4)
% Ref.Elem No. of the assigned structural element
% CS pnt Name des reference point in the cross-section
Note: Every defined cross-section reference point may be used for defining the reference line for the specification of the tendon constraint point. But the specified point is only used, if also the switch ($ CS Pnt) is set, defining that the geometry is related to the connection line of reference points rather than to the element axis or system line.
ZG K YG
XG
I
xL zL
yL
QSPnt.
QSPnt.
Alfa1 (rel. to the CS Pnt.) Alfa1 (rel. to the element)
# Global The entered eccentricities are defined in global axis directions
# Local The entered eccentricities are defined in local axis directions Attention: The switch “local” always means the local coordinate system of
the considered element - built by using the element axis (centroid line) and not by using the reference line if $$$$Node or $$$$CS Pnt has been selected.
% x/l Position in longitudinal direction (related distance from the ele- ment start)
% ey Eccentricity in (global or local) y-direction
% ez Eccentricity in (global or local) z-direction
# Elem Reference line is the element axis (centroid)
# Node Reference line is the system line (straight connection between the start node and end node of the element)
# CS pnt Reference line is the connection line of a reference point in the start and end cross-section
% Alpha1 „Vertical angel“ of the tendon tangent
% Alpha2 „Horizontal angle“ of the tendon tangent
Attention: For the exact meaning of the terms „Vertical angle“ and „Hori- zontal angle“ see chap. 5.4.3.2.
# Value „Vertical angle“ and „Horizontal angle“ respectively are pre- scribed (the above defined value is prescribed as constraint con- dition)
# Free Alpha1 and Alpha2 respectively are free (not prescribed)
# Elem Reference axis for Alpha1 or Alpha2 resp. is the element axis
# Node Reference axis for Alpha1 or Alpha2 resp. is the system line
# CS Pnt Reference axis for Alpha1 or Alpha2 resp. is the connection line between reference points
! Extern The straight section is outside the cross-section
% Number Element number (new structural element) of the external tendon segement
% Radius Radius of the curved segment
Note: A new free structural element no. has to be assigned to external tendon segments.