A Treatise On Statics: With Application to Physics 1

Cover A Treatise On Statics: With Application to Physics 1
A Treatise On Statics: With Application to Physics 1
George Minchin Minchin
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Suppose that the props are fixed in the ground at D 9 E, and F (Fig- 309), and their extremities were originally a, b, c, which are in a horizontal line ; but that when the «.
shrinking has taken place, their extremities, A, B, C, lie in a line slightly inclined to the horizon.
446 ANALYSIS OP STRAINS AND STRESSES. [393.
Let their original lengths be p, q } r, so that A a = bp, Bbszbq, Ce = br; let the pressures on them at A, B, and C be P f Q, and B ; let G be the centre of gravity of the bar
...and W its weight Then we have P+Q+B=W, and P.GA+Q.QB-R.GC = 0, (1) the second being obtained by moments about G.
Now if the areas of the normal sections of the props are a, /3, y, we have (Art. 387) a p' /3 y y r' w supposing that Young's modulus is the same for all.
Again, we must express the fact that ABC ia a right line. Drawing through C a parallel to at*, we have 6j>— br AC tq-br** BC .-. BC .bp-AC .bq+AB .6> = 0, (3) ..urn. *Je,-t£ 9+ :J'M-* The three equations (1) and (4) determine P, Q, B.


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