3.1 Multispan Statically Determinate Beams 45If loadPD 1 is located at pointBon the suspended beamH 1 BH 2 , then this
force is completely transmitted to the supportBand no part of this force is taken by
the supportH 1 and thus, no force is transmitted to the main beamAH 1. Therefore,
influence lines for shear and moment at sectionshas zero ordinates at pointB.If
unit load is located within theH 1 BH 2 , then the pressure from the secondary beam
on the primary beam at pointH 1 varies proportionally to the distance of the unit
load from pointB.
Similar discussions should be used, when unit load travels along the suspended
beamH 2 H 3.
If load travels along the beamH 3 CD, then no part of this load is transmitted to
the beamAH 1. Therefore, ordinateson influence lines forQsandMsalong the part
H 3 CDare zeros.
If load is located within the parts-B, then bending moment at sectionsis nega-
tive. It means, that the extended fibers at sectionsare located abovethe neutral line.
If any load will be distributed withinBH 3 , then extended fibers at sectionswill be
located below the neutral line.3.1.4 Summary......................................................
For construction of influence lines for multispan statically determinate hinged beam
it is necessary to show interaction diagram, and to show the part of the entire beam,
which contains the support or section under consideration; this part is clamped-free
or simply supported beam with or without overhangs. Next we need to construct
the required influence lines considering the pointed portion of a beam and then
distribute influence line along the all beams which aresuspendedwith respect to
pointed one. Thus construction of influence lines for multispan hinged beams is
based on the influence lines for three types of simple beams and does not requires
any analytical procedures.
Influence lines of reactions and internal forces for Gerber–Semikolenov beams,
as for any statically determinate structure, are linear.
Example 3.1.Load is applied to stringers and transmitted to the Gerber–
Semikolenov beamABHCDby floor beams at pointsm,n,s,andt(Fig.3.7).
Construct the influence lines for reaction atAand for bending moment at sectionk.
Solution.First of all, show the interaction scheme for entire multispan hinged beam.
Influence line forRA:1.Influence line forRAwithout floor beams and stringers is presented by polygon
ahdby dotted line.
2.Draw vertical lines from floor beams’ pointsm,n,s,andtto the intersection
with the influence line.
3.Draw vertical lines from extreme left and right pointsEandFof the stringers
to the intersection with the base line. Corresponding points of intersections have
the notationeandf.