Pocketbook of Useful Formulæ and Memoranda
for Civil and Mechanical Engineers

182 MOLESWORTHS POCKET-BUUK Iron Arches. (Strains due to expansion.) I Hmensions to be all in inches. V = Versed sine. _ R R — Radius of arch = ----~—i. 2 V g a = Angle of half arch; = Sin. a — —— . b = Angle of P with centre line. 2 ® d = Effective depth of arched rib from centre to centre of top and bottom booms of rib. E = Modulus of elasticity = 11,000 tons for iron. = 12,800 tons for steel. K — Constant for rib, say Ed2 ~2~ * t = Range of temperature in degrees Fahr. e = Extension of half arch due to t. = -00000(367 A Bf. A — Circular measure of arc =’0174533, a° = 00029, a'. h — Thrust force per square inch due to ex- tension at abutment. H = Stress per sq. in. due to bending moment. M = Bending moment at any point P. /esin.«\ h = K ____________ (± > R3 x A (■ 5 sin?a+1 • 5 cos.2 a) — J • 5 sin. a cob, << M H = — ; M = h V (cos. b — cos. a).