STRENGTH OF WOOD. 137 



varies inversely as the length, directly as the breadth, and 

 directly as the square of the depth, so that, in the example given 

 above, the longer beam will only require to be 17 inches deep in 

 order to be as strong as the shorter. If the beams are equal in 

 breadth, but of different length, and are required to be equal 

 in stiffness, their breadths must be as the cubes of the lengths. 

 In two beams 24 and 12 feet long, for example, the breadths 

 must be in the ratio of 24 3 to 12 3 , i.e. 13,824 to 1728, or as 8 is 

 to 1. In other words, the long beam would have to be eight 

 times as broad as the shorter one to be equally rigid, whereas it 

 only requires to be twice as broad to be equally strong. So, too, 

 in cylinders, the strength varies as the cube, the stiffness as the 

 fourth power of the diameter. 



The constants or values of deflection were deduced by Barlow 



/ 3 x W 

 from the formula D = , ~, where / = length in feet, W = the 



greatest weight in pounds which the beam can bear without losing 

 its elasticity or acquiring a permanent set, b = breadth in inches, 

 d = depth in inches, and 8 = deflection in inches. From this 

 it obviously follows that 



~ 



It is found in practical engineering that the deflection of timber 

 beams (8) should not exceed ^l^th f their length. 



Bauschinger employed, for testing tensile strength, rods 1 8 inches 

 long and 1 or 2J inches square for 5 \ inches at each end, reducing to 

 \ or If inch in the middle. He does not, however, consider these, 

 or his experiments on bending (in which the individual variation 

 of the large beams employed, as to knots, etc., produces wide 

 differences in the results) so instructive as to the relative values 

 of timbers as are crushing experiments. For such experiments he 

 used blocks 6 inches high and 3| inches square, protected at the 

 ends with metal plates. 



Results will be affected by so many circumstances that it is 

 most important that the history of logs experimented with should 

 be known. The nature of the locality in which^ilie timber is 



THE 



UNIVFDQITV 



