Lecture 15 – Page 1 of 12Lecture 15 – Columns (cont.) In the previous lecture, we talked about columns having small eccentricity (i.e., small applied moment) . While this may be the case fo r interior columns with offsetting moments, the majority of concrete columns do experience applied moments. Concrete framed buildings typically have columns that are poured monolithically with beams and slabs, thus creating a statically-indetermin ate frame such as the one shown below: The analysis of such a frame is usually quite complex and requires computersoftwar e such as STAAD or approximate analysis methods such as the Portal Method and others discussed in Structural Theory.
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In the previous lecture, we talked about columns having small eccentricity (i.e.,small applied moment). While this may be the case for interior columns withoffsetting moments, the majority of concrete columns do experience appliedmoments.
Concrete framed buildings typically have columns that are poured monolithicallywith beams and slabs, thus creating a statically-indeterminate frame such as the
one shown below:
The analysis of such a frame is usually quite complex and requires computer software such as STAAD or approximate analysis methods such as the PortalMethod and others discussed in Structural Theory.
The compression capacity of a reinforced column is reduced by the bendingstresses on the column and vice-versa. A graph of the axial load capacity of a
column vs. the moment capacity of a typical column is shown below (fromLecture 14):
Determining points along the curve is quite laborious and typically not done usinghand calculations. Instead, computer programs or design guides are used toperform column analysis and design.
Below are some “Column Interaction Diagrams” that are used for column
ExampleGIVEN: A 20” x 20” square interior tied column is shown below. Use concrete f’c
= 4000 PSI and 8 - #8 grade 60 vertical bars and #3 ties. Concrete cover = 1½”. All loads are factored and includes beam weight. Assume the beams are “fixed”to the columns.
REQUIRED:
1) Determine the applied factored axial load, Pu on the middle column. Besure to add column weight. Assume the loads from the roof above are75% of the floor load.
2) Determine the slenderness ratiominr
KLusing K = 0.7 and determine if
column qualifies as “short.”3) Determine total factored moments Mtotal applied to the column.
4) Determine if the column is acceptable based on “Column InteractionDiagram.”