5/11/23, 5:51 PM
Hexagon Documentation Site Export
CAESAR II Users Guide
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
1/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Hexagon Documentation
Generated 05/11/2023
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
2/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Coordinate Systems
Many analytical models in engineering are based upon being able to define a real physical object mathematically. This is
accomplished by mapping the dimensions of the physical object into a similar mathematical space. Mathematical space is
usually assumed to be either two-dimensional or three-dimensional. For piping analysis, the three-dimensional space is
necessary, because almost all piping systems are three dimensional in nature.
Two typical three-dimensional mathematical systems are shown in the following illustration. Both of these systems are
Cartesian coordinate systems. Each axis in these systems is perpendicular to all other axes.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
3/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Each axis can be thought of as a number line, where the zero point is the point where all of the axes intersect. While only
the positive side of each axis is shown in the illustration, each axis has a negative side as well.
The direction of the arrow heads indicates the positive direction of each axis.
The X-axis has one arrowhead, the Y-axis has two arrowheads, and the Z-axis has three arrowheads. The circular arcs
labeled RX, RY, and RZ define the direction of positive rotation about each axis.
Any point in space can be mapped to these coordinate systems by using the point's position along the number lines. For
example, a point 5 units down the X-axis has a coordinate of (5.0, 0.0, 0.0). A point 5 units down the X-axis and 6 units
down the Y-axis has a coordinate of (5.0, 6.0, 0.0).
If the system on the right side of the illustration is rotated 90-degrees about the X-axis, the result is the system on the left
side.
In addition, for these Cartesian coordinate systems the right hand rule defines positive rotation about each axis and the
relationship, or ordering, between the axes.
The coordinate system on the left side is the default CAESAR II global coordinate system. In this system, the X-axis and Z-axis
define the horizontal plane, and the Y-axis is vertical.
The coordinate system on the right side can be obtained in CAESAR II by selecting Z-axis Vertical.
Other Global Coordinate Systems
There are other types of coordinate systems that can be used to mathematically map a physical object.
A Polar coordinate system maps points in a two-dimensional space using a radius and a rotation angle (r, theta).
A Cylindrical coordinate system maps points using a radius, a rotation angle, and an elevation (r, theta, z). The origin in
this system could be considered the center of the bottom of a cylinder. Cylindrical coordinates are convenient to use when
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
4/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
there is an axis of symmetry in the model.
A Spherical coordinate system maps points using a radius and two rotation angles (r, theta, phi). The origin in this system
could be considered the center of a sphere. Spherical coordinates are convenient to use when there is a point which is the
center of symmetry in the model.
Typically, none of these coordinate systems are easily used to map piping systems. Most piping software deals exclusively with
the Cartesian coordinate system.
The Right Hand Rule
In the Cartesian coordinate system, each axis has a positive and a negative side, as previously mentioned. Translations,
straight-line movement, can be defined as movement along these axes. Rotation can also occur around these axes, as shown
in the following illustration.
A standard rule must be applied in order to define the direction of positive rotation about these axes. The right-hand rule is used
as the standard. Put the thumb of your right hand along the axis, in the positive direction of the axis. The direction your fingers
curl is positive rotation about that axis:
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
5/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
The right-hand rule can also be used to describe the relationship between the three axes. Mathematically, the relationship
between the axes can be defined as:
X cross Y = Z (EQ 1)
Y cross Z = X (EQ 2)
Z cross X = Y (EQ 3)
where cross indicates the vector cross-product.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
6/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
The left and center illustrations correspond to vector equation 3 (EQ 3). The right illustration corresponds to vector equation 2
(EQ 2).
Straight-line movement along any axis can be therefore described as positive or negative, depending on the direction of motion.
This straight-line movement accounts for three of the six degrees of freedom associated with a given node point in a model.
Analysis of a model requires the discretization of the model into a set of nodes and elements. Depending on the
analysis and the element used, the associated nodes have certain degrees of freedom. For pipe stress analysis, using 3D beam
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
7/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
elements, each node in the model has six degrees of freedom.
The other three degrees of freedom are the rotations about each of the axes.
When modeling a system mathematically, there are two coordinate systems to deal with, a global or model coordinate system
and a local (or elemental) coordinate system. The global or model coordinate system is fixed, and can be considered a constant
characteristic of the analysis at hand. The local coordinate system is defined on an elemental basis. Each element defines its
own local coordinate system. The orientation of these local systems varies with the orientation of the elements.
An important concept here is the fact that local coordinate systems are defined by, and therefore associated with,
elements. Local coordinate systems are not defined for, or associated with, nodes.
Pipe Stress Analysis Coordinate Systems
As noted previously, most pipe stress analysis computer programs use the 3D beam element. This element can be described as
an infinitely thin stick, spanning between two nodes. Each of these nodes has six degrees of freedom three translations and
three rotations. Piping systems models are constructed by defining a series of elements, connected by nodes. These pipe
elements are typically defined as vectors, in terms of delta dimensions referenced to a global coordinate system.
For most pipe stress applications, there are two dominant global coordinate systems to choose from, either Y-axis or Z-axis up.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
8/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
The global coordinate system is fixed, and all nodal coordinates and element delta dimensions are referenced to this global
coordinate system. In the example that follows, the pipe element spanning from node 10 to node 20 is defined with a DX (delta
X) dimension of 5 ft. Node 20 also has a global X coordinate 5 ft. greater that the global X coordinate of node 10. Similarly, the
other two elements align with the global Y and global Z axes.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
9/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
In CAESAR II, you can choose between the two global coordinate systems. The default global coordinate system puts the
global Y-axis vertical. You can use two different methods to change the global coordinate system to global vertical Z-axis.
The first method modifies the configuration file in the current data directory. This can be accomplished by selecting Home >
Setup > Configuration Editor on the main window ribbon. In the Configuration Editor, select Geometry Directives and select
True for New Job Z-axis Vertical.
This configuration affects all new jobs created in this data directory. Existing jobs with the Y-axis vertical are not affected by this
configuration change.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
10/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
The second method switches coordinate systems from within the input for the specific job at hand. This can be accomplished
from the Special Execution Parameters dialog box of Classic Piping Input.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
11/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Select Z Axis Vertical to change the orientation of the global coordinate system axis, with corresponding updates to the
element delta dimensions. The relative positions and lengths of the elements are not affected by the vertical axis change.
Defining a Model
Use the CAESAR II default coordinate system (Y-axis vertical) with the following example to define element definitions.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
12/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
For this model, most of the element definitions are very simple:
The first element, 10-20, is defined as 5 ft. in the positive global X direction. This element starts at the model origin.
The second element, 20-30, is defined as 5 ft. in the positive global Y direction. This element begins at the end of the first
element, because both elements share node 20.
The third element, 30-40, is defined as 5 ft. in the negative global Z direction. Note in Figure 8 that the delta dimension for
this element is a negative number. This is necessary to define the element in a negative direction.
The fourth element, 40-50, runs in both the positive global X and negative global Y directions. This element slopes to the
right and down, and is defined with delta dimensions in both the DX and DY fields. These delta dimensions are equal in
magnitude; therefore, this element slopes at 45 degrees.
Continuing the model, from node 50, along the same 45-degree slope can be rather tedious, because most often only the
overall element length is known, not its components in the global directions. This can be accomplished with the Edit Deltas
dialog box by clicking the Browse button next to the DX field. Using this dialog box, you can enter the element length, and the
software determines the appropriate components in the global directions, based on the current direction cosines, which default
to those of the preceding element.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
13/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
CAESAR II provides an additional coding tool, for longer runs of pipe with uniform node spacing. Element Break enables you to
break an element into equal length segments, given a node number increment.
In the example, the model is defined solely using delta dimensions. By constructing the model in this fashion, it is assumed that
the world coordinates of node 10 the first node in the model are at (0., 0., 0.). This assumption is acceptable in all but one
instance, when environmental loads are applied to the model. In this instance, the elevation of the model is critical to the
determination of the environmental loads, and therefore must be specified. You can specify the starting node of the model using
View/Set Coordinates
, and all nodal coordinates display as absolute coordinates. The relative geometry of the model does
not change based on specification of the global coordinates of the starting node.
After a model has been defined, there are a number of operations that can be performed on the entire system, or on any section
of the system. These operations include:
Translating the model by specifying the global coordinates of the starting node of the model. If the model consists of
disconnected segments, CAESAR II requests the coordinates of the starting node of each segment.
Rotating the model by using the List processor or by clicking List Input
grid.
. The List processor presents the model in a
Options in this processor allow you to rotate the model about any of the three global axes, or a specified amount. For
example, if the model is rotated a negative -90 degrees about the global Y-axis, the result is as shown in the following
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
14/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
illustration.
Duplicating the model by using the List processor. The entire model, or any sub-section of the model, can be duplicated.
Using Local Coordinates
When analyzing a piping system, there are a number of items that must be checked and verified. These items include:
Operating loads on restraints & terminal points
Hanger design results
Equipment evaluations
Expansion joint evaluation
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
15/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Maximum operating displacements
Code stresses for code cases
Vessel nozzle evaluation
Restraint loads and displacements are checked in the global coordinate system. This is necessary because restraint loads and
displacements are nodal quantities. Element loads and stresses are most often evaluated in their local coordinate system. A
good example illustrating the use of a local (element) coordinate system is the free body diagram, of forces and moments. The
forces and moments in this free body diagram remain the same, regardless of the position of the element in the global
coordinate system. Note however, that each element has its own local coordinate system. Furthermore, the local coordinate
system of one element may be different from the local coordinate system of a different element.
While the global coordinate system is typically referred to using the capital letters X, Y, and Z, local coordinate systems use a
variety of nomenclature. In almost all cases, local coordinate systems use lower case letters. Typical local coordinate system
axes are: xyz, abc, and uvw. CAESAR II uses xyz to denote the local element coordinate system.
The local coordinate system for an element is related to the global coordinate system through a rule. There may be a number of
such rules, depending on the type of element. In CAESAR II, the following rules are used to define the local coordinate systems
of the piping elements in a model.
CAESAR II Local Coordinate Definitions
CAESAR II shows global coordinates in upper case (global force in X displays as FX) and local coordinates in lower case (local
force in x displays as fx). For the following examples the local terms a, b, c are used in place of x, y, z. In other words, global
coordinates are referenced by X, Y, Z and local coordinates are referenced by a, b, c.
The example model contains straight elements and bend elements.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
16/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Straight Elements
Each straight element has its own local coordinate system.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
17/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
a-axis (local x-axis): Always points from the From Node to the To Node
b-axis (local y-axis): b = a ´ Y (global vertical axis)
This is a cross-product operation, except when the element is vertical (local a is vertical). Then b (local y-axis) is defined
as X (global X-axis).
c-axis (local z-axis): c = a ´ b
The positive direction of the a-axis for each element is defined according to the From - To Node direction. For example, the aaxis of element 10-20 aligns with the positive global X-axis. The a-axis of element 30-40 aligns with the negative global Z-axis.
The local axes of skewed element 40-50 have the coordinates shown.
Bend Elements
Each bend element has a local coordinate system at its end points.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
18/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Think of the bend as a centerline arc bounded by a near and a far node. The near node is the tangent point joining the bend
with the straight pipe entering the bend. The far node is the tangent point joining the bend with the straight pipe exiting the
bend.The software does not require a near node, but creates one by default. Any additional nodes along the bend arc reference
the orientation of the tangent line at the node. This tangent is a vector pointing toward the far end of the arc.
a-axis (local x-axis): Defined by the tangent vector, where positive is toward the far end of the bend. This is considered
the torsion term.
b-axis (local y-axis): b is perpendicular to the plane formed by the straight pipes entering and exiting the bend. Where
defined by the piping code, this is the in-plane bending term.
c-axis (local z-axis): c points to the center of the bend arc (c = a ´ b). Where defined by the piping code, this is the outplane bending term.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
19/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Tee Elements and Stress Intensification Factors (SIFs)
Local coordinates are also significant for the three straight pipes that join at a tee or for any other straight pipe end where a
stress intensification factor (SIF) is defined, such as when tees are added to the example model.
Each tee element and the run elements in a branch connections have their own local coordinate system.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
20/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
a-axis (local x-axis): Always points from the From Node to the To Node. This is the torsion term.
b-axis (local y-axis): b is perpendicular to the plane that contains the three elements that form the tee. b = a(branch) ´
a(run).
The b-axis is the same for all three elements forming the tee.
Where no plane is evident (such as a SIF specified at a node where no run or branch exists), b is defined for straight pipe.
In those cases where the two run elements have opposite a-axes, CAESAR II uses the orientation of the first run pipe
entered to set a run in the definition of b. Where defined by the piping code, this is the in-plane bending term.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
21/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
c-axis (local z-axis): c = a ´ b. Where defined by the piping code, this is the out-plane bending term.
In-Plane and Out-Plane SIFs After FEA Translation
For Home > FEA Tools > FEA Translation
, the translator might change in-plane and out-plane SIFs in the translated
CAESAR II model based on the orientation of elements forming the tee.
In order to properly apply FEA-calculated flexibilities, the translator creates a beam model and breaks the tee component into a
series of straight pipes and rigids with corresponding connections (restraints with CNodes).The definition of intersections, as
defined by the CAESAR II local coordinates, is lost. The translator must determine the correct way of implementing the SIFs of
the branch connection of the CAESAR II model from the FEA Tools beam model. At the run and branch C-Node connections,
the in-plane orientation is indeterminate because only two collinear beam elements exist.
The translator sets the intersection type to blank to complete import into CAESAR II. The elements created with a C-node at the
branch connection are no longer associated with a 3D fitting. Because the two elements are now collinear, the software uses
the default straight element orientation for in-plane and out-plane SIFs. The default in-plane and out-plane orientations might
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
22/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
not match the actual 3D fitting’s orientation. The FEA translation correctly places the in-plane and out-plane SIFs based on the
original tee orientation.
Applications Using Global and Local Coordinates
Global coordinates are used most often when dealing with piping models. Global coordinates are used to define the model and
review nodal results. Even though element stresses are defined in terms of axial and bending directions, which are local
coordinate system terms, local coordinates are rarely used. A typical piping analysis scenario is:
A decision is made as to how the global coordinate system for the piping model will align with the plant coordinate system.
Usually, one of the two horizontal axes is selected to correspond to the North direction. However, if this results in a
majority of the system being skewed with respect to the global axes, you should consider realigning the model. It is best to
have most of the system aligned with one of the global coordinate axes.
The piping system is then assigned node points at locations where: there is a change in direction, a support, a terminal
point, a point of cross section change, a point of load application, or any other point of interest.
After you assign the nodes, define the piping model using the delta dimensions as dictated by the orientation of the global
coordinate system. Use Break, List, Rotate, Duplicate, and the Direction Cosines to construct the model.
After verifying the input, confirming the load cases, and analyzing the model, output review commences.
Output review involves checking various output reports to ensure the system responds within certain limits. These checks
include:
Checking that operating displacements make sense and are within any operational limits to avoid ponding.
Displacements, being nodal quantities, are reviewed in the global coordinate system. There is no local coordinate system
associated with nodes. For the model defined in Figures 7 and 8, the operating displacements are shown in Figure 15
below.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
23/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Figure 15 - Operating Displacements
This report shows the movements of all of the nodes in the model, in each of the six degrees of freedom, in the global
coordinate system.
Checking that the restraint loads for the structural load cases are reasonable. This includes ensuring that the restraints
can be designed to carry the computed load. Restraints being nodal quantities are reviewed in the global coordinate
system. There is no local coordinate system associated with restraints. For the model defined in Figures 7 and 8, the
operating / sustained restraint summary is shown in Figure 16 below.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
24/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Figure 16 - Operating / Sustained Restraint Summary
This report shows the loads on the anchor at 10 and the nozzle at 50, for all six degrees of freedom, for the two selected
structural load cases, in the global coordinate system.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
25/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Checking the code cases for codes stress compliance. Typically, the code stress is compared to the allowable stress for
each node on each element. Occasionally, when there is an overstress condition, a review of axial, bending, and torsion
stresses are necessary. These stresses axial, bending, and torsion are local coordinate system terms, and therefore relate
to the element’s local coordinate system. For the model defined in Figures 7 and 8, a portion of the sustained stress report
is shown in Figure 17 below.
Figure 17 - Sustained Stress Report
These reports provide sufficient information to evaluate the pipe elements in the model, to ensure proper behavior and code
compliance. However, the analyst’s job is not complete, loads and stress must still be evaluated at terminal points, where the
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
26/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
piping system connects to equipment or vessel nozzles. Depending on the type of equipment or nozzle, various procedures and
codes are applied. These include API-610 for pumps and WRC-107 for vessel nozzles, as well as others. In the case of API-610
and WRC-107, a local coordinate system specific to these codes is employed. These local coordinate systems are defined in
terms of the pump or nozzle/vessel geometry.
When the equipment coordinate system aligns with the global coordinate system of the piping model, the nozzle loads from the
restraint report (node 50 in Figure 14) can be used in the nozzle evaluation. However, when the equipment nozzle is skewed as
it is in the case of node 50 in Figure 14, the application of the loads is more difficult. In this case, it is best to use the loads from
the element’s force/moment report, in local coordinates. The only thing to remember here is to flip the signs on all of the forces
and moments, because the element force/moment report shows the loads on the pipe element, not on the nozzle. For the
element FROM node 40 to node 50, the local element force/moment report is shown in Figure 18 below.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
27/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Figure 18 - Local Element Force/Moment Report
Because the correlation between the pipe model’s coordinate systems and those of equipment codes API and WRC are often
times tedious and error prone, CAESAR II provides an option in its equipment modules to acquire the loads on the nozzle
directly from the static output. Select the node and the load case; CAESAR II acquires the loads and rotates them into the
proper coordinate system as defined by the applicable equipment code. You really do not have to be concerned with the
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
28/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
transformation from global to local coordinates, even for skewed components. This is illustrated below, in Figure 19. In this
figure, the API-610 nozzle loads at node 50 have been acquired by clicking Select Loads by Job/Load Case.
Notice that the loads shown in Figure 19 are in the CAESAR II global coordinate system. This can be easily verified by
comparing these values to those in the restraint summary for the operating load case as shown previously in Figure 16.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
29/35
5/11/23, 5:51 PM
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
Hexagon Documentation Site Export
30/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Figure 19 - API-610 Nozzle Load Acquisition
In the corresponding output report for this API-610 analysis, both the global and API local loads are reported. This is shown
below in Figure 20.
Figure 20 - API-610 Nozzle Output Report Segments
Notice in Figure 20, that each report segment indicates which values are related to the global coordinate system and which are
related to the local API coordinate system.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
31/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Restraint Data in Local Element Coordinates
A new report Local Restraint Loads, is available to assist in dealing with restraint loads on skewed nozzles. This report uses the
local coordinate system of the "defining" element (because restraints do not have a local coordinate system). If the restraint is
defined on the straight element to which the restraint is attached, then the proper orientation of local loads is reported in the
Local Restraint Loads report. However, if the restraint was defined on some other element, or on the mid-side node of a bend,
then the loads reported in the Local Restraint Loads report are associated with the local coordinate system of that defining
element.
Transforming from Global to Local
Converting or transforming values from the CAESAR II Global Coordinate System to a local coordinate system involves
applying a number of rotation matrices to the global values. Matrix mathematics is not a trivial task, and you must exercise the
utmost care to arrive at the correct result. To complete this task, visit the CAESAR II Downloads page at
http://www.intergraph.com/products/ppm/caesarii/downloads.aspx and click CAESAR II "Global to Local" to download the
GlbtoLocal utility, glbtoLoca. zip. For more information, see the July 2001 issue of our Mechanical Engineering News. For an
example on how to use the GlbtoLocal utility using the nozzle at node 50 see below.
The element 40-50 is defined with the delta coordinates of:
DX = 3 ft. (6.426 in)
DY = -3 ft. (6.426 in)
DZ = 0.0
The global restraint forces at node 50, in global coordinates, for the operating case are:
FX = 323 MX = -953
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
32/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
FY = 4 MY = -9
FZ = -271 MZ = -548
Using this data as input to GlbtoLocal, the utility yields the forces on the restraint in the element’s local coordinate system. This
is shown in Figure 21 below.
Example Global to Local Transformation
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
33/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
Compare the set of values labeled Rotated Displacements / Load Vector with the Local Element Force / Moment report, as
shown above. A change in sign is necessary because the Restraint report shows loads acting on the restraint, while the
Element report shows loads acting on the element.
Frequently Asked Questions
What are global coordinates?
Global coordinates define the mapping of a physical system into a mathematical system. For a given model, the global
coordinate system is fixed for the entire model. In CAESAR II, there are two alternative global coordinate systems that you can
apply to a model. Both coordinate systems follow the Right Hand Rule and use X, Y, and Z as mutually perpendicular axes.
The first uses the Y-axis vertical, while the second uses the Z-axis as vertical.
What are local coordinates?
Local coordinates represent the mapping for a single element. Use Local coordinate systems to define positive and negative
directions and loads on elements. Typically, Local Coordinate systems are aligned with the elements, therefore vary
throughout the model.
What coordinates are used to plot and view the model?
Use the global coordinate system of the model to generate plots of the model. This is necessary because each element has its
own local coordinate system, and these local systems vary from element to element. Local coordinate systems are an element
property, not a system property.
How do you obtain nodal displacements in local coordinates?
In general, you do not. Displacements are a nodal property. Nodes do not have local coordinate systems, elements do. For
more information, see Restraint Data in Local Element Coordinates.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
34/35
5/11/23, 5:51 PM
Hexagon Documentation Site Export
What do you do with local coordinates?
In most instances, nothing. The local coordinates are only useful in CAESAR II is when dealing with a skewed nozzle. This
coordinate system is used in the Local Restraint Report.
Copyright
Copyright© Hexagon AB and/or its subsidiaries and affiliates. All rights reserved.
https://docs.hexagonppm.com/internal/api/webapp/print/df9a44b4-2e15-496c-b26d-55a37385cd82
35/35