Statically indeterminate stresses in stiff framed structures . and (h), gives MAZo+ MBZ2 f Mc(2Z2f3Z3) + Md(2Z0+3Z3) = 0 (k), Adding equations (d) and (g); two times equations (e) and (f); andsubtracting equations (a) and (b), gives - MAZ0 + MB(2Z2+Zi) f MC(2Z2+Z3) - MdZo = - £f^£l . (1) L L This gives the four equations, (i), (j), (k), and (1), containingthe four unknown moments. Let n=Zo/Z]_t PsZ3/Zi, SsZg/Z^, and,kaa/L#When these values are substituted in equations (i), (j), (k)t and(1), they take the form shown in Table IVf on the next page. ======^ - 47. TABLE IV. Equations for the Rectan
Statically indeterminate stresses in stiff framed structures . and (h), gives MAZo+ MBZ2 f Mc(2Z2f3Z3) + Md(2Z0+3Z3) = 0 (k), Adding equations (d) and (g); two times equations (e) and (f); andsubtracting equations (a) and (b), gives - MAZ0 + MB(2Z2+Zi) f MC(2Z2+Z3) - MdZo = - £f^£l . (1) L L This gives the four equations, (i), (j), (k), and (1), containingthe four unknown moments. Let n=Zo/Z]_t PsZ3/Zi, SsZg/Z^, and,kaa/L#When these values are substituted in equations (i), (j), (k)t and(1), they take the form shown in Table IVf on the next page. ======^ - 47. TABLE IV. Equations for the Rectangular Framewith Concentrated Load ©t any Point on Top. Equation Mc % Known Term. j n + 1 1 + 8 8 + p p + n - Pab/L. k n 8 2s + 3p 2n + 3p C 1 - n 1 + 2s 2s + p - n - Pebk/L. i - 1 + 1 - 1 + 1 0 In the above table, the quantities in each column are thecoefficients of the moment indicated at the head of the column, andthe quantities in the last column are the right hand members of theequations. Solving these equations simultaneously for the moments,gives. (34c), tr/iere A - -[22(spn -hsp+sn+np) +2(spz+5p+npi-ph + s\s+n3+n)+6(sn^-s*n+p+p)l 48. If l£ e Iqi so that the frame is symmetrical about the vert-ical center line, s = n, and equations 34, 34a, 34b, and 34c become (35) v £ -a- f^b). and fi= (on + / -hp. (b). Load at Middle. Frame symmetrical about the verticalcenter line. With the load at the middle, ks-§-,and (£ ? 0« Equations 35, 35a, 35b, and 35c then become M*=A/0= §Y- (36). tfc*Af/>* _n_) (36a) From equations 29 and 29a of paragraph 24, f-lO±3&). (29). (29a) The last two equations are essentially the same as equations 36 and36a. 49. (c). Uniformly Distributed Load. Frame Symmetrical aboutthe Vertical Center Line. The uniform load is equal to W/L poundsper lineal foot. In this case F/L equals WL/12, and equations 29end 29a become £(- &OL±3£.J (37). (37e) (d). Two Point Loading. Frame and Loads Symmetrical aboutthe Vertical Center Line. See Fig. 4
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