122. The size and thickness of stone flagging required for sidewalks, when the distance between supports is given, can be calculated by the following formula:

Let b = width of stone in inches; d = thickness of stone in inches; l = distance between bearings in inches; A = constant from table; W = breaking load at center of span; W = breaking load uniformly distributed over span.

Then,

W=Abd2

W'= 2Abd2

In words this formula may be expressed as follows: Multiply together the width in inches, the square of the thickness expressed in inches, and the proper constant from the table, and divide by the span in inches; the quotient will be the breaking load at the center; and the quotient multiplied by 2 will be the breaking load if uniformly distributed. The allowable load should not exceed 1/10 of the breaking load.

The following table gives the value of A in the above formula, in tons of 2,000 pounds, according to the different materials used.

 Bluestone Flagging........................ .744 Quincy Granite............... .624 Little Falls Freestone.......... .576 Belleville, N. J., Freestone..... .480 Connecticut Freestone................... .312 Dorchester Freestone.......... .264 Aubigny Freestone.................. .216 Caen Freestone................. .144 Glass.................... 1.000 Slate................. 1.200 to 1.700

For example, a block of Quincy granite 80 inches wide, and 6 inches thick, resting on supports 36 inches in the clear, would break under a load, resting midway between supports of W = 36 = 49.92 tons; dividing this by 10, to get the safe weight, we have 49.92 ÷10 = 4.99, or say 5 tons. When the load is equally distributed over the flagging, it will carry 2x5 = 10 tons.