Pocketbook of Useful Formulæ and Memoranda
for Civil and Mechanical Engineers

180 Molesworth’s pocket-book V = Versed sine of arch. x = Abscissa measured horizontally from crown centre line to any point P. w — Weight of arch and load supposed to be con- centrated at any point P. W — Sum of weights between crown and any point P. = w + 4- &c. J m = Momenta at each point P = w x. M = Sum of moments between crown and P = m + ml + &c. J7 = Horizontal distance of centre of gravity (of portion ot arch between crown and P) M 7 measured from crown = =— . . W y = Ditto ditto measured from P = x — g. H ~ Horizontal thrust of arch = —~~ for symme- , . , , , Wy + Nf'y' „ tncal loads ; = --------■—----for unsymme- trical loads ; Mien Wy and Wy' are for the loaded and unloaded halves respectively. k = Ordinate from tangent to line of equilibrium. The tangent will be horizontal for symme- trical loads and inclined for unsymmetrical loads. Obliquity determined by the for- i Wy , mula -g?. = H '