A Beginner's Guide to the Steel Construction Manual, 13th ed. (old) Chapter 6 - Buckling Concepts © 2006, 2008 T. Bartlett Quimby |
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Section 6.4 Example Problem 6.1 Grid 3 Columns Last Revised: 11/04/2014
The figure given here shows the support conditions for this column. We will start from the top and work our way down for computing the effective lengths. Third Floor Column Segment Weak Direction: At this level and direction, there are no beams fixed to the column to create joint rotational restraint and the column is part of a frame that inhibits sidesway (i.e. it is braced) as stated on the drawings. For these conditions, K = 1.00. This gives an effective length, (KL)Y,33 = 1.0*12' = 12 ft. The subscript used denotes the weak direction, "Y", on grid "3" on the third floor, "3". Strong Direction: At this level, the support conditions are:
Entering the sidesway uninhibited nomograph on SCM page 16.1-242 with these two values and I get something close to 1.79. It is difficult to get a precise value from the nomographs so your value may be slightly different. The effective length, then, for the 3rd floor column segment is: (KL)X,33 = (1.79)(12 ft) = 21.48 ft Second Floor Column Segment Weak Direction: At this level and direction, there are no beams fixed to the column to create rotational restraint and the column is part of a frame that inhibits sidesway (i.e. it is braced) as stated on the drawings. For these conditions, K = 1.00. This gives an effective length, (KL)Y,32 = 1.0*10' = 10 ft. Strong Direction: At this level, the support conditions are:
Entering the sidesway inhibited nomograph on SCM page 16.1-241 with these two values and I get something close to 0.86. It is difficult to get a precise value from the nomographs so your value may be slightly different. The effective length, then, for the 2nd floor column segment is: (KL)X,32 = (0.86)(10 ft) = 7.60 ft First Floor Column Segment Weak Direction: At this level and direction, there are no beams fixed to the column to create rotational restraint and the column is part of a frame that inhibits sidesway (i.e. it is braced) as stated on the drawings. Also, the column at this level, and in this direction, is braced at mid-height, as stated on the drawing. For these conditions, K = 1.00. This gives an effective length, (KL)Y,31 = 1.0*5.50' = 5.50 ft. Strong Direction: At this level, the support conditions are:
Entering the sidesway uninhibited nomograph on SCM page 16.1-242 with these two values and I get something close to 1.88. It is difficult to get a precise value from the nomographs so your value may be slightly different. The effective length, then, for the 1st floor column segment is: (KL)X,31 = (1.88)(11 ft) = 20.68 ft Column Line Summary To summarize the results, the effective lengths for the column segments on grid 3 are:
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