Van Nostrand's engineering magazine . ll be as desig-nated in Fig. 7. In consequence ofsymmetry, the stresses in correspondingmembers, either side of the center areequal. The equal unknown reactions atthe end supports will be called nF,whence the reaction of the middle sup-port is 2P(l-n). 828 VAN NOSTRANDS ENGINEERING MAGAZINE. Now regarding tension and compres-sion as both plus we have for the inclinedmembers in the compression and theothers in tension, nV l_~h 2 ?n) t,= A=\jfl-*) having one superfluous bar, we can chooseat pleasure the section of any one bar,which involves its stress likewi
Van Nostrand's engineering magazine . ll be as desig-nated in Fig. 7. In consequence ofsymmetry, the stresses in correspondingmembers, either side of the center areequal. The equal unknown reactions atthe end supports will be called nF,whence the reaction of the middle sup-port is 2P(l-n). 828 VAN NOSTRANDS ENGINEERING MAGAZINE. Now regarding tension and compres-sion as both plus we have for the inclinedmembers in the compression and theothers in tension, nV l_~h 2 ?n) t,= A=\jfl-*) having one superfluous bar, we can chooseat pleasure the section of any one bar,which involves its stress likewise, and bythe aid of the 6 statical equations above(two each for J\ and J\) determine thestresses and afterwards the sections ofthe other bars. Thus if we assume thesection wx of the outer inclined member,whence the stress on it is found from theeq., f-^zcew x, we thereby determine thereaction nJ? from the first equationabove; or we may assume nP and com-pute/*, from this equation and thus de-termine all the other stresses from the. 2P(l-ri) These stresses are all plus as assumed,so long as n=\, as we see from the last equation, move particularly; so thatwhen n=^, the system may be made of equal resistance. On dividing each stress by the assumedunit stress s, multiplying by the lengthand adding the results, we obtain forthe total amount of material for the en-tire truss, both spans, ?r Una* + 2a*(1- n) + nl* + l —n?\ This result is independent of n, so thatthe amount of material remains the samehowever we choose n, provided we donot exceed the limits o and ^. Thus wesee that Levys theory is verified forthese two cases of systems with super-fluous bars, as indeed it must be for allcases, as it rests upon a strict mathe-matical basis. In the case of the last truss, Fig. 7, group of equations. So that we areconducted to an interesting property ofthis truss, that if we assume the reactionat pleasure between easily appreciatedlimits, deduce the stresses, and designthe sectio
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectenginee, bookyear1879
