A thin-walled compressive member with an arbitrary open section is shown in Figure 1, where point O is the centroid of the section and point C([y.sub.c], [z.sub.c]) is the shear center. Oxyz is the centroidal principal axis.
where u, v, and w are the displacements of shear center in x, y, and z directions.
Location of shear center of each cross section is not constant in this case.
Thus, the arising additional loading (Figure 3) at the middle surface of the plate and the loading along the centroid axis (coinciding with the shear center axis), of each beam, can be summarized as follows.
(vi) A distributed twisting moment [m.sup.i.sub.bxj] = [q.sup.i.sub.bxj][e.sup.i.sub.yj] - [q.sup.i.sub.yj][e.sup.i.sub.zj] along [C.sup.i][x.sup.i] local beam shear center axis due to the eccentricities [e.sup.i.sub.zj] and [e.sup.i.sub.yj] of the components [q.sup.i.sub.yj] - and [q.sup.i.sub.zj] from the beam shear center axis, respectively.
Examples are the problem of shear center
for thin-walled sections, and the allied problem of torsion.
Commonly analyzed properties include stiffness, neutral axes, center of gravity, mass, principal inertial axes, shear correction factors, and shear center
. Analysis also covers 3-D displacement and strain and stress fields.
Commonly analyzed properties include stiffnesses--such as axial, bending, torsional, and shear--neutral axes, center of gravity, mass, principal inertial axes, shear correction factors, and shear center
. Analysis also covers 3-D displacement, and strain and stress fields.
These section properties include area, moment of inertia, section modulus, center of gravity, shear center
, and torsional constants.
Additionally, the presence of open sections points to another parameter that is an important factor in the optimization of these structures: the shear center location for the principal structural members.
In the second case, location of the shear center turned out to be a key issue.