Design of Compression Members (Columns) Prepared by Prof. Marcia C. Belcher, PE

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1 Design of Compression Members (Columns) Prepared by Prof. Marcia C. Belcher, PE

2 Most Common Shapes for Columns Hollow Steel Section Steel Tube HSS12x6x0.5 TS12x6x0.5 Either nomenclature is acceptable; however, HSS is more common Pipe Pipe 4 STD Pipe Wide Flange W12x36 Flange surfaces are parallel; flange thickness is not necessarily equal to the web thickness.

3 Design of Steel Columns For ease of construction, if W shapes are used they should be 10 inches or deeper. W shapes less than 10 inches deep will pose potential fit-up problems for connecting elements. (See illustration below)

4 Design of Steel Columns Tubes and pipes are often favored by engineers due to equal bending properties in x-x and y-y directions. W shapes are much stronger bending about the x-x axis than the y-y axis. This causes column placement & orientation challenges.

5 Examples: Orientation of Columns Which column type would you pick for this steel frame and why?

6 Column Modes of Failure Column stability is almost ALWAYS a function of slenderness There are three categories for failure in columns: a. Short stubby columns will yield = deform by shortening under compressive load i. However, such columns are rarely found. ii. A typical steel column is likely to be long and slender. b. Intermediate columns will buckle laterally with permanent deformation = inelastic buckling c. Long slender columns will buckle in the elastic range = elastic buckling Inelastic Buckling Elastic Buckling

7 Column Failure Failure load of a steel column is associated with the load that causes initial buckling This is directly related to the column slenderness. In general, a column of practical proportions will fail in a buckling mode before crushing of steel occurs. As the axial load in a column is increased, a value is reached at which the column buckles and deforms perpendicular to its axis. The value of load is called the buckling load. When a column has reached its buckling load it has effectively failed as a structural element and is incapable of sustaining the load. The aim of column design is to predict the load at which a column will collapse and to ensure that there is an adequate factor of safety compared with the applied load.

8 Physical Properties of Columns: Radius of Gyration The buckling resistance for a steel section is largely dependent on a physical property call the radius of gyration. By definition: r = (I/A) (Steel tables provide r values) y Non-symmetric sections will have r x r y x x Symmetric section r x = r y x y x y y

9 Pin-Pin Fixed-Fixed End Constraints The end constraints of a column will substantially influence the buckling behavior. 1 2 The columns 1 &2 shown at the left are both W12 x 22 and are of equivalent length. Which column can sustain the larger axial load?

10 Pin-Pin Effective Length When designing columns, we use a length multiplier called K to adjust the effective length due to end constraint conditions. The deflected shape is one complete arc. The effective length = KL =1 x L K=1 for a pin/pin combination

11 Pin-Free to Translate Effective Length Now, let s look at a column with pin/free to translate combination: Deflected shape is ½ of a complete arc. Effective Length = KL = 2L So, to achieve FULL arc, length must be multiplies by 2. K = 2 for pin/free to translate combination

12 Conventional Value of K **Columns with end that are free to rotate and/or translate have a greater potential for buckling than fixed end columns.

13 Slenderness Ratio Slenderness Ratio: KL/r Used to evaluate the buckling potential of columns. In practice, members with KL/r > 200 should not be used as compression members.

14 Safe Axial Loads for Steel Columns Pu ØPn = ØF c A ; where Ø =.85 for compression F c = critical stress from AISC Table 10.1 A = area of column cross-section NOTE: Table 10.1 may be used to calculate BOTH strong axis and weak axis buckling loads.

15 Example: Checking Column Strength