. Proceedings of the annual convention . -e„=(l-v)qM3L^j Equations : e^ = [vqMBL-(l-u)pM^L]^ (A)eB = [upMAL-(|-v)qMBL]^ (B) Solving Equations (A) and (B) . ^ _ EI [-(i-v)eA-veB] p L(l-u-v) Ei[-ueA-(i-u)eBl q L(l-u-v) (I) (2) AB 2p(|-U-V) C ond C 2p (l-u-Ol-u BA 2q (l-u-v) C 2q (l-u-v) Ref : See Anoly »ii ofRigid Frames,by Amirikion , FIGURE A2 40 Iron and Steel Structures FORMULAS FOR p, q, u, v CUBIC VARIATION OF I A —• B ^1 1 d-^ dxbL-x - X T3 E bL ri-bM Az Area = |^—^J. i (^)] m[,.»{^)] rl» (m +1) I [-(^)T ^^ = ^* L [iT^bn] Ml [x Area under -^ Diogram in Length bLIx MaA=—^
. Proceedings of the annual convention . -e„=(l-v)qM3L^j Equations : e^ = [vqMBL-(l-u)pM^L]^ (A)eB = [upMAL-(|-v)qMBL]^ (B) Solving Equations (A) and (B) . ^ _ EI [-(i-v)eA-veB] p L(l-u-v) Ei[-ueA-(i-u)eBl q L(l-u-v) (I) (2) AB 2p(|-U-V) C ond C 2p (l-u-Ol-u BA 2q (l-u-v) C 2q (l-u-v) Ref : See Anoly »ii ofRigid Frames,by Amirikion , FIGURE A2 40 Iron and Steel Structures FORMULAS FOR p, q, u, v CUBIC VARIATION OF I A —• B ^1 1 d-^ dxbL-x - X T3 E bL ri-bM Az Area = |^—^J. i (^)] m[,.»{^)] rl» (m +1) I [-(^)T ^^ = ^* L [iT^bn] Ml [x Area under -^ Diogram in Length bLIx MaA=—^ L xdx [..(-^)] = 2(m + l) (2o)» Centroid of Areo under .511 Oiogrom in Length bL :Ix Ma x^dx L r. / bL- X xT0 [+n^( bL ^J ^b- ^ _ ,, 2(m + l) r. „ f„ * n x m liLzlil (■^„\*- bL — Logg(m + l)+m — (oai See Mondbooli of Frome Cons fonts, p. 30, Published by Portlond Cement Associotion,Chicogo, Illinois, 1947, for prior publication. FIGURE A3 Equivalent Joi nt Method of Rigid Frame Analysis 41 FORMULAS FOR p,q,u,v. CUBIC VARIATION OF I. A2=Areo=MBL^-^
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