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.
Straight Elements
Each straight element has its own local coordinate system.
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a-axis (local x-axis): Always points from the From Node to the To Node
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b-axis (local y-axis): b = a ´ Y (global vertical axis)
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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).
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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 a-axis 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.
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.
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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.
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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.
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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 out-plane bending term.
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.
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a-axis (local x-axis): Always points from the From Node to the To Node. This is the torsion term.
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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.
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c-axis (local z-axis): c = a ´ b. Where defined by the piping code, this is the out-plane bending term.