A treatise on concrete, plain and reinforced : materials, construction, and design of concrete and reinforced concrete; 2nd ed. . (14) 2 mMe + 2 Hcl y ~ 2 Mr - I Mi, = 0 (15 ) Combining (13) and (15), _ mlMRy + ml MLy--^: Mr ly - I Mj,! y ^^ z[mly^-(lyyi ^^> , ^ I Ml X -1 Mr x From (14) Vc = ^^^^^^ (17) ^^ f ^ ,^ lMR+lML-:^Hc2y From (15) Me = ^ (18) M = moment. He = crown thrust. Vc = crown shear. m — number divisions of halfaxis. X, y — coordinates of a point. 554 A TREATISE ON CONCRETE These are fundamental equations in arch analysis. The method ofapplication is illustrated in the example
A treatise on concrete, plain and reinforced : materials, construction, and design of concrete and reinforced concrete; 2nd ed. . (14) 2 mMe + 2 Hcl y ~ 2 Mr - I Mi, = 0 (15 ) Combining (13) and (15), _ mlMRy + ml MLy--^: Mr ly - I Mj,! y ^^ z[mly^-(lyyi ^^> , ^ I Ml X -1 Mr x From (14) Vc = ^^^^^^ (17) ^^ f ^ ,^ lMR+lML-:^Hc2y From (15) Me = ^ (18) M = moment. He = crown thrust. Vc = crown shear. m — number divisions of halfaxis. X, y — coordinates of a point. 554 A TREATISE ON CONCRETE These are fundamental equations in arch analysis. The method ofapplication is illustrated in the example, page 574. All I signs denote summations for one-half of the arch axis. All numerical values of M^, M^, x, y, are positive. A positive value of V^ indicates that the line of pressure at the crownslopes upward toward the left; a negative value, upward towards the right. A positive value of M^ indicates a positive moment at the crown; a nega-tive value, a negative moment. The moment at any point between B and C is M = M, - V,x + Hj - Mj,while at any point between A and C M =.]/, + \\x+H,y -M^ (19) (20) ^^^^^^^^^^iillHT^. Fig. 164.—Diagram for finding Constant . {See p. 554)
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