Masonry Magazine August 1975 Page. 16
The maximum compressive stress in a jack arch
The maximum compressive stress in a jack arch may be computed directly from the following formulae:
For uniform loading over full span,
f = 3WS / 4bd
For triangular loading,
f = WS / bd
Formulae 8, 9 and 10 include a factor which allows for non-axial loading. In formulae 6 through 10, inclusive:
H = horizontal thrust in pounds,
W = total load in pounds,
S = clear span in inches,
d = depth of arch in inches and
b = breadth of arch in inches.
THRUST RESISTANCE
Resistance to horizontal thrust, developed by the arch, is provided by the adjacent mass of masonry. In areas where limited masonry is available, i.e. corners, openings, etc., it may be necessary to check the resistance of the wall to the horizontal thrusts. Figure 4 illustrates how such resistance may be calculated.
H₁ = vnxt (11)
By using the principle given in formula (11), the minimum distance from a corner or opening at which an arch may be located is easily determined. This can be done by writing formula (11) to solve for x, substituting actual arch thrust for resisting thrust:
x = H / vnt (11a)
In these formulae:
H₁ = resisting thrust in pounds,
v = allowable shearing stress in the masonry wall in pounds per square inch,
n = the number of resisting shear planes,
x = the distance from the center of the skew-back to the end of the wall in inches and
t = wall thickness in inches.
The tendency for arch thrust to overturn a section of masonry, rather than slide it or rack it, must also be investigated. In general, such overturning forces are found to govern only at arches near the top of a wall, since that portion of masonry which tends to overturn must first become separated from the body of the wall.
ALLOWABLE STRESSES
Recommended allowable compressive stresses for use in the design of brick arches are given in Table 1. Recommended allowable shearing stresses in unreinforced walls for use in the design of abutments are given in Table 2. These are based on the requirements of Recommended Building Code Requirements for Engineered Brick Masonry, SCPI, May 1966.
TABLE 1
Allowable Compressive Stresses for Brick Masonry, psi
Mortar Type and Mix (parts by volume)
Compressive Strength of Units, psi
| | Type M 1PC:1/4L:3-5 | Type S 1PC:1/2L:4-1/2 | Type N 1PC:1:6 |
| :------ | :------------------- | :------------------- | :------------- |
| 14,000 plus | 1150 | 975 | 800 |
| 12,000 | 1000 | 850 | 700 |
| 10,000 | 850 | 725 | 600 |
| 8,000 | 700 | 600 | 500 |
| 6,000 | 550 | 475 | 400 |
| 4,000 | 400 | 350 | 300 |
| 2,000 | 250 | 225 | 200 |
Based on Recommended Building Code Requirements for Engineered Brick Masonry, SCPI, May 1966. Linear interpolation is permissible.
It is assumed that the thrust of the arch attempts to move a volume of masonry enclosed by the boundary lines ABCD. For calculating purposes the area CDEF is equivalent in resistance. It can be seen that the thrust is acting against two planes of resistance, CF and DE. The resistance to arch thrust is determined by the following formula:
TABLE 2
Recommended Allowable Shearing Stresses in Unreinforced Brick Masonry Walls
| Mortar Type | Allowable Shearing Stress |
| :---------- | :------------------------ |
| M or S | 50 |
| N | 40 |
MAJOR ARCH LOADING
The principal forces acting upon arches in buildings are the result of vertical dead and live loads and wind loads. Many masonry arches are integral with surrounding masonry. In such instances, loads transmitted to the arch through the masonry are indeterminate, due to arching action of adjacent masonry.