Masonry Magazine June 1988 Page. 18
α = Tan [(S1-S2)/2t]
Where:
α 1/2 the angle AOB, in degrees
S₁ Length of each side of the polygon forming the exterior face of the wall, in inches (length of the unit plus the width of one mortar joint)
S2 Length of each side of the polygon forming the interior face of the wall, in inches (length of the unit plus the width of one mortar joint)
t Actual unit thickness, in inches
n = 180/α
Where:
n Number of units (number of sides to the polygon). For circular walls, n should be a whole number. For semi-circular walls and where walls intersecting at 90° are connected by a radial wall, the number of units should be an even whole number.
r = S1/(2 Tan a)
Where:
Radius to the exterior face of the wall, measured to the midpoint of a unit, in inches
EQN 1
EQN 2
EQN 3
Example
Nominal 8"x8" x 16" concrete masonry units are being considered for use in a circular wall. The actual length of a unit is 15 5/8 inches, width 7 5/8 inches and the exterior mortar joint is to be 3/8 inch. The width of the interior mortar joint is to be 1/8 inch. What is the smallest radius to which the circular wall can be constructed without cutting the units?
Step 1: Determine the angle required for 1/2 the unit length by the use of equation 1.
Tan¹[(S1-S2)/21]
Given: S₁= 155/8" + 3/8" 16"
S2 15 5/8" + 1/8" 15 3/4"
t = 7 5/8"
α = Tan (16-15.75)/ (2×7.625)]
= Tan (0.0164)
= 0.939 Degrees
Step 2: Determine the number of units required by the use of Equation 2.
n = 180/α
180/0.939
191.7 units
Step 3: Adjusting n to be equal to a whole number, determine the required angle.
n = 180/α
180/α
192
α = 180/192
= 0.9375 Degrees
Step 4: Determine the minimum radius for the wall by the use of equation 3
r = S₁/(2 Tan a)
= 16/(2 Tan 0.9375)
= 16/.0327
489.3 inches
= 40 ft.-9 in.
Although the equations remain the same, there are several practical methods which may be employed to vary the minimum radii of curved or circular concrete masonry walls:
1. Reduce the length of the units. Changing from a 16" nominal unit to an 8 nominal unit will reduce the radius by 1/2, while the number of units required remains the same.
2. Vary the width of the mortar joints. An increase in the width of the mortar joints at the exterior face of the wall, with or without a decrease in the width of the mortar joint at the interior face of the wall, reduces the length of the radius while also reducing the number of units required. Although it is generally recommended that the width of the mortar joint at the face not be decreased to less than 1/8 inch, this may be acceptable under certain circumstances.
3. Shorten the length of the units at the interior face. Cutting of the units is practical if stretcher units having flanged ends are used. This may be difficult, if not impractical, if the units are double corner units having plain ends (Figure 3).
Stretcher Unit-Flanged Ends
Double Corner Unit-Plain Ends
Figure 3. Cuts for Concrete Masonry Units