Buckling of Steel Columns
Source: Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
In the design of civil works, it is important to deliver structures that are not only safe under unexpected loads, but also provide excellent performance under everyday loads at a reasonable economic cost. The latter is often tied to minimum use of materials, ease of fabrication, and rapid construction in the field. Structures made of steel members can be very economical because of the great strength of the material and the extensive prefabrication of their members and connections, which help maximize the speed of construction on site. Generally, the skeleton of a steel structure will be very slender as compared to a reinforced concrete one. While its behavior in tension is governed primarily by the strength of the material, steel in compression is governed by another failure mode common to all materials- buckling. This behavior is easily demonstrated by pressing down on a slender wooden ruler, which under a compressive load will suddenly move sideways and lose load carrying capacity. This phenomenon will occur in any slender member of a structure. In this lab, we will measure the buckling capacity of a series of slender aluminum columns to illustrate this failure mode, which over time has led to many catastrophic failures including that of the Quebec River Bridge, which was erected in 1918.
- Obtain several long pieces of a 1in. by ¼ in. aluminum bar (6061 or similar), and cut them to lengths of 72, 60, 48, 36, 24, 12 and 8 in., respectively. Round both ends of the bars to a circumference of 1/8 in.
- Measure the dimensions of the bar (length, width and thickness) to the nearest 0.02 in.
- Machine two small block of steel (2 in. x 2 in. x 2 in.) to have a very smooth ½ in. circular penetration along one of its sides to serve as the column end support. Provide an insert on the opposite side, so that
Plot the results from the table as buckling stresses vs. slenderness (kL/r), along with the curve given by Eq. 9. Compare your results with the predicted values. The experimental results shows two distinct regions. When the columns are relatively long, the critical load is given by multiplying Eq. 9 by the area of the column. As the columns begin to get shorter, the critical load begins to approach the strength of the material. At this point the behavior shifts from a purely elastic one
This experiment demonstrated the validity of the Euler approach for calculating local buckling loads for simple columns. Although the problem becomes far more complicated if either the boundary conditions are not well known, the member is not prismatic, or if the material does not exhibit a bi-linear stress-strain curve, the solution of the problem follows the same general process. In many practical cases, it will not be possible to solve the resulting differential equations exactly, but there are many numerical techniqu
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