42 3 Multispan Beams and Trusses
BDCAEH 1 H 2 H 3PPFig. 3.5 Interaction diagram of Gerber–Semikolenov beam
so entire system is statically determinate and geometrically unchangeable structure.
On the other hand, in general case of loads there are six reactions of supports arise
in the structure; they are five vertical reactions at supports and one horizontal reac-
tion at supportA. For their calculation we can use three equilibrium equations and
three additional conditions, i.e., the bending moment at each hinge is equal to zero.
Therefore, the structure is statically determinate one.
The beamH 2 H 3 is both main forH 3 Ebeam and suspended forH 1 CH 2 one.
Therefore, the loadP, which is applied to the beamH 2 H 3 is transmitted only to
beams located below and does not transmitted to the beams located above this one.
It is not difficult to form the rules of distribution of hinges which transforms the
continuous beam with one (or two) clamped ends into Gerber–Semikolenov beam.
3.1.3 Influence Lines for Multispan Hinged Beams
For construction of influence lines of reactions and internal forces for statically de-
terminate multispan beams the following steps are recommended:
Step 1.The entire multispan hinged beam should be presented in the interaction
diagram form. This helps to classify eachelement of the structure as primary
or secondary beams, and visualize the load path from the secondary beam
on the primary one.
Step 2.Consider structural element of a multispan beam, which contains a support
or section for which the required influence line should be constructed. This
element is the primary or secondary simply supported beam with/without
overhangs or cantilevered beam. Then we need to construct an influence
line for the required function for this beam only.
Step 3.Take into account the influence of moving load which is located on theadja-
cent suspendedbeam and distribute the influence line which is constructed
in step 2 along this secondary beam. For this it is necessary to connect an
ordinate of influence line at the end point (hinge) with a zero ordinate at the