Civil Engineering Reference
In-Depth Information
tion is correct, the moments will vary linearly in the members, and points of inflection
will be located fairly close to member midpoints.
No consideration is given in the portal method to the elastic properties of the mem-
bers. These omissions can be very serious in unsymmetrical frames and in very tall build-
ings. To illustrate the seriousness of the matter, the changes in member sizes are
considered in a very tall building. In such a building, there will probably not be a great
deal of change in beam sizes from the top floor to the bottom floor. For the same loadings
and spans, the changed sizes would be due to the large wind moments in the lower floors.
The change, however, in column sizes from top to bottom would be tremendous. The re-
sult is that the relative sizes of columns and beams on the top floors are entirely different
from the relative sizes on the lower floors. When this fact is not considered, it causes large
errors in the analysis.
In the portal method, the entire wind loads are assumed to be resisted by the building
frames, with no stiffening assistance from the floors, walls, and partitions. Changes in the
lengths of girders and columns are assumed to be negligible. They are not negligible,
however, in tall slender buildings, the height of which is five or more times the least hori-
zontal dimension.
If the height of a building is roughly five or more times its least lateral dimension, it
is generally felt that a more precise method of analysis should be used. There are several
approximate methods that make use of the elastic properties of structures and give values
closely approaching the results of the “exact” methods. These include the factor method,
7
the Witmer method of
K
percentages, and the Spurr method.
8
The building frame shown in Figure 14.30 is analyzed by the portal method, as de-
scribed in the following paragraphs.
At least three assumptions must be made for each individual portal or for each girder.
In the portal method, the frame is theoretically divided into independent portals (Figure
14.31), and the following three assumptions are made:
1.
The columns bend in such a manner that there is a point of inflection at middepth.
2.
The girders bend in such a manner that there is a point of inflection at their
centerlines.
3.
The horizontal shears on each level are arbitrarily distributed between the
columns. One commonly used distribution (and the one illustrated here) is to as-
sume that the shear divides among the columns in the ratio of one part to exterior
columns and two parts to interior columns.
The reason for the ratio in assumption 3 can be seen in Figure 14.31. Each of the interior
columns is serving two bents, whereas the exterior columns are serving only one. Another
common distribution is to assume that the shear
V
taken by each column is in proportion
to the floor area it supports. The shear distribution by the two procedures would be the
same for a building with equal bays, but for one with unequal bays the results would dif-
fer, with the floor area method probably giving more realistic results.
7
Norris, C. H., Wilbur, J. B., and Utku, S., 1976,
Elementary Structural Analysis
, 3rd ed. (New York: McGraw-
Hill), pp. 207-212.
8
“Wind Bracing in Steel Buildings,” pp. 1723-1727.
