End Fixture Design to Enhance Column Buckling Lesson

Column buckling is an important topic in strength of materials courses. This topic has been emphasized with a compression/buckling experiment using a Satec uni-axial testing machine to compressively load 1/2 inch diameter Polyvinyl Chloride (PVC) pipe columns to failure due to buckling. Several lengths of pipe have typically been used to demonstrate failures due to both normal compressive stresses and column buckling for a variety of slenderness ratios and end fixity conditions. In the past, the butt ends of the PVC pipes were placed against the moving loading platform and the stationary stage of the Satec machine to approximate an end fixity condition similar to that of a “fixed-end”; however, often buckling would occur in two stages, especially for taller PVC columns. First, the PVC columns would behave as if they were fixed at both bearing surfaces. Minor lateral deflection prior to the critical buckling load lead to eccentric loading conditions at the bearing surfaces as the neutral axis shifted. This eccentric load caused local deformation in the portion of the PVC loaded highest in compression at the surface, which accelerated the asymmetry and caused the opposite portion of the pipe to experience lower and lower compressive loads. At a critical point, the end fixity transitioned from an approximately cantilevered connection to something more closely related to a pinned connection when the butt end dramatically pivoted about a corner of the PVC tube resulting in a single point of contact remaining between the tube and the surface. Although this transition was interesting and provided an opportunity to discuss in more detail why the demonstration progressed the way that it had, the ambiguity of end fixity made it difficult for students to correlate the resulting load-deflection curves to those predicted by theory. To better simulate loading conditions discussed in lecture, two sets of fixtures were designed and fabricated. One set (top and bottom) was rotationally fixed and provided support for the pipe ends to simulate a cantilevered/fixed end condition. The second set was designed to hold the pipe end securely but allowed rotation about one axis to better approximate a “pinned” joint. Both sets of fixtures worked very well in practice. The effective length factor calculated by the students as a result of using these fixtures was very comparable to predicted values.