Strength of Projecting Veranda

STRENGTH OF PROJECTING VERANDA. To the craftsman who is desirous of adding a little theory to his practical knowledge, there is nothing, perhaps, so repellant as the apparently difficult arithmetical formulas with which he is confronted in the pages of many of his trade books. The writer's success in making some of these formulas clear to a couple of his crafts men friends, led to a continuation of the lessons, and he begs to offer an account of the next step taken in helping his two friends past some more little difficulties.

It is a well-known maxim in all teaching, that we "must proceed from the known to the unknown," and it seems that the consideration of the strength of a wooden cantilever beam, just discussed, leads naturally to the question of the method of calculating the strength of verandas and similar structures, which are sup ported by a number of projecting beams or cantilevers.

The method given by which the strength of the projecting beam used for hoisting goods to an upper story is ascertained, can be easily applied to a series of such beams, and their combined strength readily ascertained.

The first step, then, was to look about for a suitable example of such a structure, the strength of which could be calculated for pur poses of the lesson. A very short excursion round the neighborhood led to the discovery of a veranda or balcony which suited the purpose admirably; and our two craftsmen pupils soon measured the structure and jotted down the necessary particulars, which were as follows: The veranda, Fig. 164, projected from the second story of a dwelling-house some 3 feet, the house itself being 24 feet in width, with the veranda right across the face. It was carried on 11 spruce beams, each 4 by 6 inches, projecting through the face of the wall, giving 10 bays of flooring. There was a sloping roof to the ve randa; but, as this was carried on some beams projecting from the floor above, its weight had not to be taken into account. A light balustrade about 2 feet 6 inches high completed the structure.

The first proceeding was to calculate the strength of one beam, or cantilever, of the size used in the veranda. Going back to the first lesson, we proceeded to find the strength of such a piece, supposing it to be a simple beam loaded in the middle and supported at each end, the calculation being as shown in Fig. 165, the steps being as follows: Put down the figure for spruce (see table) cwts. Put down the breadth 4 inches, then the depth 6 inches, and, as that was to be "squared," 6 again. Put underneath, the length, 3 feet. This stun gave us 168 cwt. as the breaking weight when the piece was supported at both ends.

But we had already seen that a cantilever loaded at the end is only one-fourth as strong as the same piece is when supported at both ends and loaded in the middle. In the case of the ve randa, however, the load would not be at the end, but would be distributed along the length of the cantilever, thus bringing in another rule, which is: A cantilever loaded evenly throughout will carry twice as much as a similar one loaded at the end only. (A similar rule applies when the beam is supported at each end.) Accordingly, we divided our answer by 2, giving us 168÷2.84 cwts. as the breaking weight for a spruce cantilever, 4 inches by 6 inches, project ing 3 feet from its support, the wall of the house.

As the veranda would have to carry a live load, we divided this again by 8, the factor of safety, and obtained cwts. as the safe load for one cantilever.

The next step was to find what safe load the whole veranda would bear. As there were eleven cantilevers, the first thought of the pupils was to multiply the safe load of one of them by 11. A little consideration, how ever, showed them that it was the number of bays of floor which had to be counted; each bearer having to support half the load of the bays on each side of it. As 11 bearings gave us 10 bays, our sum was cwts. multiplied by 10, giving us 105 cwts. for the whole veranda.

The next consideration was one about which the craftsmen pupils had no definite knowledge —namely, as to the weight of a number of peo ple standing on a floor. As this is a very useful thing to remember, it should be noted that numerous experiments have shown that the weight of a crowd of people does not exceed one cwt. per foot super of floor space. "But, sup pose," said one of the pupils, "that the veranda was filled with people excitedly watching a street procession." ("Or a dog fight," inter posed his mate.) "Would not that make some considerable difference'?" As this was a very proper matter to take into account, it was de cided to count upon a live load of cwts. per super foot. The veranda being 24 feet by 3 feet gave us 24X3=72 feet super, which, at cwts. per foot, gave us 72 cwts. as the greatest possible load which would be likely to be placed on it.

As this came marvelously near to the pre viously calculated strength of the structure, it appeared that the designer of it had been fairly correct, and that it was perfectly safe as long as its members were not weakened by age, rot, or other defects.

NOTE—The curved rib or bracket shown under the cantilever in the drawing, Fig. 164, is almost wholly orna mental and was not considered at all in the calculations.