. The action of materials under stress; . -Line Formula for Columns.—Rankines formula P-^S=/^(i-hrt —^), when plotted for various values of P -^ S = j, and I ^ r — x, gives a rather flatreversed curve, as shown in Fig. 62. The first part of thecurve is not of practical value, as columns v^^hich have small I50 STRUCTURAL MECHANICS. F\g 62 values of / — r can be determined with sufficient accuracy byP = fS. The largest values of / ^ r also are of no service,as the curve yields too small values of/for use, and ap-proaches the quantity P — S= 4-^Er^ — /^ The equationof a straight line which shalln
. The action of materials under stress; . -Line Formula for Columns.—Rankines formula P-^S=/^(i-hrt —^), when plotted for various values of P -^ S = j, and I ^ r — x, gives a rather flatreversed curve, as shown in Fig. 62. The first part of thecurve is not of practical value, as columns v^^hich have small I50 STRUCTURAL MECHANICS. F\g 62 values of / — r can be determined with sufficient accuracy byP = fS. The largest values of / ^ r also are of no service,as the curve yields too small values of/for use, and ap-proaches the quantity P — S= 4-^Er^ — /^ The equationof a straight line which shallnearly coincide with the flattestportion of the curve, on eitherside of the point of contra-flexure, may be substituted forRankines formula for conven-ience, and the same values ofmean stress will be practically obtained within working limitsof / -^ r. Rankines formula, upon the substitution of the symbolsX and J as above, may be written j = f ^ (^i -|- ax^), and theco-ordinates x and j/ of the points of contraflexure found by. puttmg dydx dx O. Thus 2afx d^y — 2(^{x — Vs ) = t/— tA/3^ • ^- If/ = t6,ooo, E = 29,000,000 and a =? f — 4-^E,P -^- S ^=1 j ?=. 18,000 — 39 - for fixed ends, and / = 18,000 78 — for hinged (?) COLUMNS. 151 The curve of Fig. 62 is plotted for these values of/ andE, and the tangent at the point of contraflexure is showa fora column with fixed ends. If y = 14,000, and E and a are as before, there result twocorresponding values of the mean stress, for fixed and forhinged ends. / = — 32 — and 15,750 — 64-. (2.) ; r If it is desired to use a straight line formula for moder-ately short col
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectstrengt, bookyear1897
