Masonry Magazine August 1975 Page. 20
TABLE 7
Values of M, N, and Q, at Increments of x 0.1L
| x (fr) | 0.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 |
|---|---|---|---|---|---|---|
| Vertical Complementary Parabolic Loading: | | | | | | |
| M | -1528.3 | +534.9 | +706.0 | +60.2 | -634.5 | -917.3 |
| N | 31907 | 1737.5 | 919.0 | 586.0 | 566.2 | 615.8 |
| Q | +662.2 | +210.9 | -111.4 | -278.7 | -243,3 | 0.0 |
| Vertical Uniform Loading: | | | | | | |
| N | 19,300 | 16,100 | 13,000 | 10,300 | 8200 | 7430 |
Note: The above moments are in fast-pounds. Shears and axial thrusts are in pounds.
In this example, moments, shears and axial thrusts are determined at increments of 0.1L (each 2 ft of span). Tabular computations are suggested for ease in evaluating these equations. The results of such tabular computations are shown in Table 7.
The stresses in the arch may be determined from the following equations:
f = N6M,
td td
V= Q
td
In the above equations, f denotes maximum and minimum fiber stresses and v, denotes shearing stresses. All quantities in the equations must be in units of inches and pounds. Table 8 shows stresses in the arch.
Plus signs indicate compression and minus signs tension, for values of f. These signs have only directional significance for values of v. No tensile stresses should be permitted in unreinforced masonry arches under static loading conditions. The reader is referred to Technical Notes, No. 31 for a discussion of mortars in arch construction. See Table 1 for allowable compressive stresses in brick masonry.
TABLE 8
Stresses in the Arch at Increments of x 0.1L
| x (fr) | 0.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 |
|---|---|---|---|---|---|---|
| Max f | +152.8 | +105.5 | +89.0 | +57.9 | +60.5 | +63.3 |
| Min f | +81.2 | +80.5 | +56.0 | +55.1 | +30.9 | +20.3 |
| V | +3.45 | +1.10 | -0.58 | -1.45 | -1.27 | 0.00 |
Note: The above stresses are in pounds per square inch.
Interpretation of Results. Table 8 indicates that the compressive stresses are, in all instances, less than the allowable 300 psi. No tensile stresses exist. The shearing stresses are insignificant. The arch is adequate. The moments and shears are caused by other than uniform loads. For this arch, and perhaps for most arches, the predominant load is uniformly distributed. As a result the moments and shears are relatively small and the arch is predominantly in compression.
Copies of Leontovich's "Frames and Arches" may be ordered on a 10-day free examination basis from the publisher, McGraw Hill Book Co., Inc., 330 West 42nd Street, New York, New York 10006. Price-$20.00.
R10M-6-75
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