ake the flex out of a roof beam

huangyhg

take the flex out of a roof beam
i have double-pitch roof beams spanning 24 m,
the rise from support to apex being 0.5 m.
each beam is designed for ultimate moments due
to wind loads and factored dead loads, and a
permissible service load deflection of l/250.
the owner has attached a suspended ceiling to
the roof purlins. as a result, the ceiling moves
with the purlins, i.e. it can lift up to 95 mm
off the mezzanine office partitions.
the problem with the ceiling can be fixed by
supporting it on the partitions instead of
hanging it from a flexible roof. however, the
owner also wishes to reduce the flex, and i
have investigated three alternatives:
1. install columns at or near midspan. this is
   highly effective and not expensive, but so
   impractical as to be unacceptable.
2. stiffen the beams with inverted t-sections
   welded to the bottom flange. this is very
   costly and may not reduce the flex by much.
3. prestress the beam with a cross tie. this is
   experimental for me, and is the reason for
   posting in the hope that you will check my
   reasoning as follows:
under permanent dead load, the mid-span moment
is 115 knm. at the given rise of 0.5 m, a tie
load of 230 kn would conteract that moment.
the serviceability wind load moments are 318 knm
upward and 191 knm downward.
i reason that ...
(i) the downward moment would increase the load in
    the tie (to what?) but would not cause much flex
    at the apex; and
(ii) the upward moment would first absorb the prestress
    in the tie, then the permanent dead load, and then
    deflect commensurate with the remaining moment, i.e
    318-115-115 = 88 knm.
would someone please agree with my reasoning or tell me
where it is flawed?
thank you, helmut
in my experience, tie-rods or post-tensioning only serves to reduce the deflection or stresses due to permanent or dead loading. the live load deflectiions are still totally dependent on the ei of the beam. if the tie rods are harped far enough below the beam so that it acts as a truss, you can increase the i of the system enough to effect deflections. in my experience, this has been inpractical because the cross-sectional area of the cables or rods is too small in relation to the area of the beam. also the anchorages at the ends tend to get pretty big since they should develope the strength of the cable or a safety factor x the expected max cable force.