Van Nostrand's engineering magazine . posed for double track railways; but thesystem is faulty in having superfluouslines. Thus for the number of divisions shown,we lhave ?i=9 and ra = 16 v 16>18—3= 15, and we have one superfluous to compute the strains arisingfrom any given loading we must writethat at each joint the sum of the hori-zontal components of the forces, includ-ing the stresses, are zero, and that thesum of the vertical components are gives 18 equations or 15 indepen-dent ones. The additional equation isfound by considering any one of the righttriangles,
Van Nostrand's engineering magazine . posed for double track railways; but thesystem is faulty in having superfluouslines. Thus for the number of divisions shown,we lhave ?i=9 and ra = 16 v 16>18—3= 15, and we have one superfluous to compute the strains arisingfrom any given loading we must writethat at each joint the sum of the hori-zontal components of the forces, includ-ing the stresses, are zero, and that thesum of the vertical components are gives 18 equations or 15 indepen-dent ones. The additional equation isfound by considering any one of the righttriangles, whose hypothenuse has a lengthav and the other sides the lengths aa anda8 respectively, so that we have the rela-tion, whence, as previously explained, we de-rive, and, ew. ,/, ejo„ + a, eaw„ This last equation added to the othersfurnished by statics gives 16 equations todetermine the stresses in the 16 bars. The next figure (16) has the main com-pression members in the shape of an in-»verted W, and suffers even more than the. previous truss from superfluous of the diagonals are supposed outof action from the side pressure; but,even then, we have, wi = 17 and n=9, sothat we have, m— (2w — 3) = 17 —15=2superfluous bars. Consequently to the 15 independentequations of statics we must add twoequations resulting from the geometricalrelations between the sides. Thus con-sider one of the triangles above, whosesides have the lengths, al9 «a, a,, respect-ively ; the acute angle formed by thesides a% and as being desigated by 6, wehave the well known relation, F=axa—a22 — a8a + On giving the sides the increments inlength a,, a2, a3, and subtracting the firstequation from the second, neglecting dif-ferences of the second order, we obtain, ^A- (ai — ascosd)a2— (as — «2cos#)«3 = 0. On substituting the values for a=*— we obtain one of the required the other is obtained by con-sidering one of the other triangles, s
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectenginee, bookyear1879
