MDX Software - FAQ #8<BR><BR>

How is the stiffness of a cross frame determined for use in system analysis?<BR>
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<UL>
The classical approach is used by releasing one side from the connections
    (but retaining the connection plate as a member of the truss), placing the
    released side on a roller, and applying a unit moment as a force couple
    with equal and opposite forces at the top and bottom nodes of the
    released side.  Horizontal displacements of the top and bottom end nodes
    are determined by analysis, and converted to an angular displacement of a
    line connecting those two nodes.  The stiffness of an equivalent prismatic
    brace, for use in system analysis, then is determined using inversion to
    find that moment which causes a unit rotation of the released end of the
    brace.

       Since the moment at the pinned end of a prismatic beam which is
       fixed at the opposite end is

                M = (4 E I / L) x theta

       where theta is the rotation of the pinned end, for a unit moment

                (4 E I / L) theta = 1.0

       and I of an equivalent prismatic beam  =  L / (4 E theta).

    Torsional stiffness is simply the sum of the torsional stiffnesses of
    the members in the cross frame.
</UL>