How to Draw a Three-Centered Arch in Revit
A three-centered arch is defined by an arch whose width and height can be freely specified. However, the arch must exhibit the following key characteristics:
The primary function of an arch as a load-bearing structure is to transfer internal stresses caused by applied loads along the tangent direction at every point on the arch, directing these stresses toward the arch supports (or wall foundations). Importantly, the radial stress (whether tensile or compressive) at any point on the arch is zero. Theoretically, this means that the tangent at any point along each of the three arcs forming the arch must be perpendicular to the radius of the arc at that same point. This includes the tangent points where the three arcs of different radii meet—the tangent here must be perpendicular to the line connecting the centers of these arcs. Without this property, the shape cannot be considered a standard arch. Both the semicircular arch and the curved arch satisfy this condition and can be seen as special cases of the three-centered arch.
The center of the top, larger arc lies on the arch’s axis of symmetry, while the centers of the smaller arcs on both sides are connected by a line that is perpendicular to this axis of symmetry.
Furthermore, the dimensions of the arch must fit precisely within the arcs. The tangent line at any tangent point must be perpendicular to the line connecting the centers of the overlapping arcs.
Calculation: Refer to the diagram below for clarification:
When drawing these three-centered arches in Revit, the first step is to calculate point M. This can be accomplished using Revit’s EQ function, which helps determine the center points accurately.
The values shown in the diagram can be adjusted as needed, but the method remains the same.
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