. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . \-7-r lOO Fiff. 52. 200 The ratio I ^ r for steel columns of practice rarely exceeds 150,and is usually less than 100. Ficr. 53 is a combination of Figrs. 49, 50, 51 and 52, andrepresents graphically a comparison of the Rankine, straight-line,Euler, parabola-Euler, and broken straight-line formulas for flat-ended mild-steel columns. It well illustrates the fact that ourknowledge of the strength of columns is not so e
. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . \-7-r lOO Fiff. 52. 200 The ratio I ^ r for steel columns of practice rarely exceeds 150,and is usually less than 100. Ficr. 53 is a combination of Figrs. 49, 50, 51 and 52, andrepresents graphically a comparison of the Rankine, straight-line,Euler, parabola-Euler, and broken straight-line formulas for flat-ended mild-steel columns. It well illustrates the fact that ourknowledge of the strength of columns is not so exact as that, forexample, of the strength of beams. P-^A 5CX)00^. lOO 200 300 Fi^. 53. 89. Design of Columns. All the preceding examples relat-ing to columns were on either (1) computing the factor of safety STREXGTH OF MATERIALS 105 of a given loaded column, or (2) computing the safe load for agiven column. A more important problem is to design a columnto sustain a given load under given conditions. A complete dis-cussion of this problem is given in a later paper on design. AVeshow here merely how to compute the dhnensions of the cross-section of the column after the form of the cross-section has beendecided u])on. In only a few cases can the dimensions be compui;ed directly(see example 1 following), but usually, when a column formula isapplied to a certain case, there will be two unknown quantities init, A and r or d. Such cases can best be solved by trial (seeexamples 2 and 3 below). EQmn2)le. 1. What is the proper size of white pine columnto sustain a load of 80,000 pounds with a factor of safety of 5,when the length of the column is 22 feet i W
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