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<br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />EM 1110-2-2902 <br />3 Mar 1969 <br /> <br />C ~ C.. + C', + C'2 (where Co' = 0.85f',Db) <br /> <br />d" = Co' <D/2 - d') . C. (d - d')(moments about tens. reinf.) <br />C <br /> <br />x. = D/2 - d' - d" ~ to plastic centroid-see fig. 3) <br />Taking moments about the plastic centroid, <br />Td" + C,(D/2 + x. - a/2) + C.(D/2 + x. - d') - P,e, = 0 <br />Solve this equation for "e,". If it is found to be less than He", the ultimate capacity is contro!led by <br />tension. <br /> <br />p. <br /> <br />b b <br /> eb= A~/Pb d" d' <br />I - ;-Xo <br />~I I <br />~ I <br /> r;;jJ <br /> Ob I <br /> I <br /> I Plostic <br /> centroid <br /> <br />c <br /> <br />Fig. 3. Typical Stres8 Diau,oam-Ultimate Strength Design, Balanced Condition <br /> <br />C, = N" + T - C. = 0.85f',ab <br /> <br />No + T - C. (' f N ) <br />a = 0.85f',b In terms 0 0 - - - - - - - - - - - <br /> <br />10 = e - 0.5D + 0.5a (distance C, to No in tenns of a) <br /> <br />Taking moments about C" <br />Nul' - C. (0.5a - d') - T (d - 0.5a) = 0 <br /> <br />N" = C.(O.s: ~ ~.~; :~~5: O.5a) _______________________________(24) <br /> <br />. _ __._ _ _ _ ._._ _ ____ _ _ _ __. _ _ _ _ _ _ _ (23) <br /> <br />Assume value of "a" and solve for No. Insert this value in equation for "a" above as a check <br />upon assumed value of "a". Nu represents an "ideal" value before applying the capacity reduction <br />factor, <p. <br /> <br />FS = <p No/N (use <p = 0.70 for most designs) _________________._________________(25) <br /> <br />The factor of safety should be close to 1.8 for economy. <br /> <br />c. Joints and Colmrs. Spacing of contraction joints generally should be limited to a maxi- <br /> <br />9 <br />