An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
Chimneys carried above the roof
Gather the flues of the fireplaces into the walls and carry them up through the roof, high enough to throw off the smoke, finishing each stack with a cap.
A stack is built where the fireplaces are: in the walls the fireplaces stand against, the flues of the floors one above another gathered into it, each with its own pot once pots came into use late in the eighteenth century.
Related rules
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
In a row of arches the thrusts of neighbouring arches cancel over each intermediate pier, which may therefore be slender; at the ends of the row nothing balances them, so the outermost piers must be made wider or buttressed.
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
Carry the front wall up as a parapet in front of the roof instead of eaves of timber (1707); set the window frames back four inches behind the face of the brick (1709), and later hide the sash boxes wholly in the reveals (1774).
Set urns or statues on the pedestals of a balustrade crowning a front, over the piers and the angles, so that the skyline is broken at regular intervals.
Cite this page Chris Paton, “Chimneys carried above the roof”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/palladio-chimneys. Text, drawings and models licensed under CC BY-NC 4.0.