Essentials in the theory of framed structures . be the angle. which the tangent through A makes with the tangent throughB; then, since <^ = o, the area of the M-diagram between Aand B is zero; therefore Ml + M3 ,, ,M3 + M2 , ,,, . ^ kl + (l — k)l = O (?}) 2 2 -^ The line AB is tangent to the elastic curve at B, and the Sec. I RESTRAINED AND CONTINUOUS BEAMS 245 tangential deviation a,t A is h = o; therefore the area-momentof the M-diagram about TU is zero, hence , MaCi -k)l2 kl + -ii-k)l\= o (4) A third elastic equation may be written by equating to zerothe area-moment of the M-diagram abou

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Essentials in the theory of framed structures . be the angle. which the tangent through A makes with the tangent throughB; then, since <^ = o, the area of the M-diagram between Aand B is zero; therefore Ml + M3 ,, ,M3 + M2 , ,,, . ^ kl + (l — k)l = O (?}) 2 2 -^ The line AB is tangent to the elastic curve at B, and the Sec. I RESTRAINED AND CONTINUOUS BEAMS 245 tangential deviation a,t A is h = o; therefore the area-momentof the M-diagram about TU is zero, hence , MaCi -k)l2 kl + -ii-k)l\= o (4) A third elastic equation may be written by equating to zerothe area-moment of the M-diagram about QP; but obviouslythis equation would not be independent of Eqs. (3) and (4).Eqs. (3) and (4) may be reduced to kMi + (i - k)Mi + Ms = o isa)k^Mi + {2 - k- P)M2 + (i + k)M3 = o (40)Solving Eqs. (i), (2), (30) and (4a) Ri= (i- 3k + 2k)PR^ = {2,k^ - 2¥)P Ml = -k{i - kypi M2= - k\i- k)Pl M3 = 2k\i - kypi Since the limits of k are o and i, it is clear that Mi and M2are negative bending moments and M3 is a positive bendingmoment. The M-diagram in Fig. 151c

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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922