Asymmetrical Tower Enlargement Solution
The tower dimension controls the location of the façade wall and cross vault in the geometric algorithm of the concept design, as well as the size of the façade wall and room width, folio 106:01.
Therefore, increasing the tower octagon size means making some fundamental changes to key structural components.
The tower enlargemen approach has to be very careful to be a minor and nearly insignificant change in the plant design. Key measures defined in the concept design have to be preserved unaltered. These include the width dimension of the footing, the façade wall, and the room.
The tower octagon will always have a center point that falls on the major diagonals of the base octagon, which are the base octagon corner direction lines, folio 106:01.
The next question is the reference point for increasing the tower octagon. Keeping the center of the octagon fixed and increasing the tower octagon uniformly in all radial directions causes the inner corner A to move toward the center of the plant and the outer corner E away from the center of the plant.
This is not a promising approach, because the façade wall is attached to the inner corners of the tower and footing octagons. A movement of the corner A toward the center of the plant brings the façade wall closer to the cross vault center, thus reducing the room width.
In addition, the move of corners E, which are the anchor points for the minor diagonals, away from the center of the plant results in a move of the cross vault (the intersection of the minor diagonals) toward the façade wall, further reducing the room width.
A promising approach is to increase the tower octagon asymmetrically, keeping the inner corner of the tower octagon A fixed and letting the outer corner E slide out along the corner direction as the tower octagon is enlarged, folio 106:01.
This causes only the minor diagonals to move, thus minimizing the secondary issues that need to be dealt with.
Converging toward a final solution, it is also noted that the minor diagonals drawn from the footing octagon outer corner EE have the potential of providing a geometric solution to the structural requirements of minor diagonals as lateral thrust lines, folio 106:02.
The minor diagonals anchored to the outer footing octagon corners EE pass through corners BB and HH, which are candidates as critical points with some modification to the outdoor face of the façade wall, folio 106:02.
These lines have the feature of keeping the resolution of the lateral thrusts within the absolute footprint of the concept design, now including the base octagon drawn at the footing corners EE (footing base octagon).
In this approach, the tower is enlarged in geometric proportions on the outer side of corner A, which remains fixed from the concept design. The tower octagon is enlarged up to the point where the outer corner E reaches the position of the footing tower octagon EE from the concept design, folio 106:02.
The separation between the minor diagonals anchored at the tower octagon outer corner E and the minor diagonals anchored at the footing octagon outer corner EE is very small, folio 106:03.