Statically indeterminate stresses in stiff framed structures . span, a similar procedure gives M1L1t2M2(L1+L2)tM3L2 s -i^Lf -iWgL§ (17). G Equations similar to the ones which have been written forthe two spans shown in fig. 25, may be written for the other spansof a beam extending over any number of supports. This will giveas many equations as there are unknowns. 86. 15. CONTINUOUS BEj\M OYER THREE SUPPORTS. EFFECT OF SET-TLEMENT OF SUPPORT. Fig. 26 shows a beam similar to the one shownin Fig. 25, except that the left hand support has settled an am-ount equal to D. The equations for this beam
Statically indeterminate stresses in stiff framed structures . span, a similar procedure gives M1L1t2M2(L1+L2)tM3L2 s -i^Lf -iWgL§ (17). G Equations similar to the ones which have been written forthe two spans shown in fig. 25, may be written for the other spansof a beam extending over any number of supports. This will giveas many equations as there are unknowns. 86. 15. CONTINUOUS BEj\M OYER THREE SUPPORTS. EFFECT OF SET-TLEMENT OF SUPPORT. Fig. 26 shows a beam similar to the one shownin Fig. 25, except that the left hand support has settled an am-ount equal to D. The equations for this beam are UjJ^ = 2EI(201-^ 92- £0/1^) -(P1a1(L1-a1)2/L1).M2L1 s-2EI(2©£+ ©x- 3DAi) -(P^lx-a^af/l,-^.M2L2 as 2EI(202+ ©3) - (Pgfigdg-ag) &A2) •M3L2 s-2El(2©3+ 92) -(P2(L2-a2)ag/L2).Combining these equations to eliminate values of 9, gives M iV^B tLl+L2> +%L2 « eEI^^fl-g) -P^fe!^). . 11 2 2 2 . . • • • .(13). The deflection is negative and therefore the value of Dt when sub-stituted in the equation, must have a negative sign before 27 B. FRAMES UNDER VERTICAL LOADING. FRAMESAND LOADING SYMMETRICAL ABOUT A VERTICAL CENTER LINE. 16. GENERAL. Fig. 27 represents any frame symmetricalabout a vertical center line. If the l08ds are symmetrical, thehorizontal deflections of the points A and B are equal to zero, andthe slopes of the tangent to the elastic curve at A and B are equal,but opposite in sign* Therefore , equations 1 and 3 of Table Iwhen applied to the member AB take the form shown in equations 19and 20 of Table II; ^ : applied to the member AD, take the form shown in equations 21 and 22 of Table II, with the loadingsdesignated* TABLE II. Special Forms of the Fundamental Equations. Member l/a/i/e5 of &z a /£ //o fx. ferna/ lead. 0fl*-0B DO A/A- 2£/T0* - A/b f/9j. G 1 * 1 O* Symmefr/tra/ load. Ma= 2£/f&# -f = Sl3 {2a ) ( T 77777T. y D ft a fx tamo/ load. =-2tf0 (21). D/stance -to -the c ( y ,0 flo fjtfernal load. -3K0*£- {22). 17. THL THREE SIDED FRAME W
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Keywords: ., bookcentury1900, bookdecade1910, booksubjecttheses, bookyear1915
