Question 16.4: Determine the member end moments for the continuous beam sho...
Determine the member end moments for the continuous beam shown in Fig. 16.10(a) by using the moment-distribution method.
This beam was previously analyzed in Example 15.4 by the slope-deflection method.
Distribution Factors. Since the cantilever portion CD does not contribute to the rotational sti¤ness of joint C, we can treat joint C as a simple end support and use the reduced relative bending sti¤ness of member BC in the analysis:
K_{B A}=\frac{I}{6} \quad \text { and } \quad K_{B C}=\frac{3}{4}\left(\frac{I}{9}\right)=\frac{I}{12}At joint B,
DF _{B A}=\frac{I / 6}{(I / 6)+(I / 12)}=\frac{2}{3}DF _{B C}=\frac{I / 12}{(I / 6)+(I / 12)}=\frac{1}{3}
At joint C,
DF _{C B}=1Fixed-End Moments. Using the fixed-end moment expressions and Fig. 16.10(b), we obtain
FEM _{A B}= FEM _{B A}=0FEM _{B C}=+67.5 kN \cdot m \quad FEM _{C B}=-67.5 kN \cdot m
FEM _{C D}=+30(4)=+120 kN \cdot m
Moment Distribution. The moment distribution is carried out as shown on the moment-distribution table in Fig. 16.10(c). Final Moments. See the moment-distribution table and Fig. 16.10(d).
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