Displacement Participation Factor
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Based on a lateral load case, displacement participation by each element for each force component (Axial, Torsional, Moment-y, Moment-z, Shear-y & Shear-z) can be checked in Contour and Value. In order to check the displacement participation factor, a unit load needs to be input in the direction of the lateral load at the location of the maximum displacement. | ||||||||||||||
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From the Main Menu select Results > Displacement Participation Factor.
Select Results > Displacement Participation Factor in the Menu tab of the Tree Menu. | ||||||||||||||
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Let us take an example of a simply supported beam, which exhibits a deflection of ツ under the external load L (Fig. 1a). We then apply a unit load at the location of ツ (Fig. 1b) in the same direction of ツ
Fig. 1 Unit load method
The external virtual work ( ) in Fig. 1b is expressed as
The deflection ツ due to the external load L in Fig. 1a can be expanded into axial deformation , flexural deformation , shear deformation and torsional deformation . And the internal force in the simple beam due to the unit load is consisted of . The internal virtual work done by the unit load to cause the deformation ツ becomes
If the above beam behaves linearly, and we define the internal forces caused by the external load L as , the deformation of the beam element becomes
We then apply the principle of virtual work, ( ), to derive the equation of the unit-load method.
where, : shape factor for shear
Expanding the concept of the unit load method to a building subject to a wind load as shown in Fig. 2b, we apply a unit load at the top of the building as Fig. 2a to find the maximum lateral displacement. If we consider the maximum displacement due to the wind as a virtual displacement is the sum of displacements contributed by the individual elements.
where, m : Number of elements
is said to be the displacement participation of each element, which is expressed as
Displacement participation in a lateral resisting system can be quantified and as such it can be optimized.
Fig. 2 Unit load application for lateral displacement calculation
Components
Select a component for displacement participation by elements and section properties.
Total: Sum of displacement participation for all the components
Axial: Displacement participation for axial component in the x-axis direction of the Element Coordinate System
Torsional: Displacement participation for torsional moment component about the x-axis of the Element Coordinate System
Moment-y: Displacement participation for bending moment component about the y-axis of the Element Coordinate System
Moment-z: Displacement participation for bending moment component about the z-axis of the Element Coordinate System
Shear-y: Displacement participation for shear force component in the y-axis of the Element Coordinate System
Shear-z: Displacement participation for shear force component in the z-axis of the Element Coordinate System
Type of Display
Define the type of display as follows:
Type of Display
Click the Displ. Participation Factor button to prompt a dialog box, which shows the prediction of lateral displacement and the change of weights based on changing sections.
Section for Design dialog box
: Used to change sections selected in the list
: Used to revert sections selected in the list to the sections of the original model
: Used to revert all the changed sections to the sections of the original model
Calculated Displacement: Lateral displacement
Displacement Decrease: Change (reduction) of displacement
Weight Increase steel: Increase in weight of structural steel
concrete: Increase in weight of concrete
: Incorporate the changed sections into the model.
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