A continuous beam ABC is shown in the figure. End supports are simple (i.e., A and C) and span AB = span BC = L. There is a concentrated load ‘W’ at the centre of the span AB while no load over the span BC. EI is the same for both spans. What is the moment at the continuous support B?
Calculation:
Fixed end moments:
M_{fAB} = - M_{fBA} = \(-\frac{WL}{8}\)
M_{fBC} = - M_{fCB} = 0
Distribution factor calculation:
Joint |
Members |
Stiffness |
Total Stiffness |
Distribution factor |
B |
BA |
\(\frac{3EI}{L}\) |
\(\frac{6EI}{L}\) |
\(\frac{1}{2}\) |
BC |
\(\frac{3EI}{L}\) |
\(\frac{1}{2}\) |
Using moment distribution method:
Sign convention: (+ → clockwise, - → anticlockwise)
The following figure shows the BMD of the beam -
Hence, Hogging moment at support B = \(\frac{3WL}{32}\)