This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

In Fig. 23 the pressures in the two supports are unequal. The supports are also unequal in length. The length of the supports, however, does not alter the amount of pressure from the concentrated load supported; but generally long timbers are not so capable of resistance as shorter ones. For, not being so stiff, they bend more readily, and, since the compression is in proportion to the length, they therefore shorten more. To ascertain the pressures in Fig. 23, let the weight suspended from b d be equal to two and three quarter tons (2.75 tons). The line b d measures five and a half tenths of an inch (0.55 inch), and the line b e half an inch (0.5 inch). Therefore, the proportion

b d: W:: b e: P becomes 0.55: 2.75:: 0.5: P,

and

2.75 x0.5/ 0.55 = P.

2.75 0.5

0-55(1.375)2.5 =P.

1 10

275

275

The strain upon the timber A. is, therefore, equal to two and a half tons.

Again, the line e d measures four tenths of an inch (0.4 inch); therefore, the proportion

b d: W:: e d: Q becomes 0.55: 2.75:: 0.4: Q,

and

2.75 x0.4/0.55:Q,

The strain upon the timber B is, therefore, equal to two tons.

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