Advanced Methods of Structural Analysis

574 Appendix

Beams with equal spans. Settlements of supports

Bending moments at supports areMDk.EI=l^2 /,whereis a vertical settlement

of support directed downward. Coefficientkis presented in TableA.18.

Ta b l e A. 1 8 Bending moments due to the settlements of supports (factorEI=l^2 )

Design diagram of the beam

Supports

moments

Settlement of support

ABCDE

ACB

MB 1:500 3.000 1:500 ––

ABC D

MB 1:600 3.600 2:400 0.400 –

MC 0.400 2:400 3.600 1:600 –

ll

ACB

l

D

l

E MB 1:6072 3.6429 2:5714 0.6429 0:1072

MC 0.4286 2:5714 4.2857 2:5714 0.4286

MD 0:1072 0.6429 2:5714 3.6429 1:6072

Example.Three-span uniform beamABCDwith equal spans has settlementB.#/

of supportB. Calculate the bending moment at all supports.

Solution.

1.Bending moment at supportBisMBD3:6.EI=l^2 /(extended fibers below of
the neutral line).
2.Bending moment at supportCisMCD2:4.EI=l^2 /(extended fibers above
of the neutral line).