Revisited the Critical Load Assessment of Huang et al. on Willems Tested Beck Column

Abstract

Dynamic stability of elastic structures is a fascinating topic. Many researchers have examined the problem theoretically considering a cantilever column under a tip-concentrated tangential load, the so-called Beck column. Experimental verification is demanded since the critical load of Beck column is found to be approximately eight times to that of the classical Euler column. Different types of testing procedures are being adopted to create the follower force. Among them, notable Willems experimentation provides the critical load close to that of Beck column. Investigations made by other researchers indicate the controversy associated with modeling and testing of Willems on Beck column. Such an intriguing problem of structures loaded by non-conservative forces is revisited here through a simple mathematical formulation. This paper confirms the adequacy of Willems approach on Beck column and the wrong critical load assessment of others. It indicates the possibility on the practical realization of follower forces

Reinvestigation on Assessing the Stability of Mullagulov Tested Steel Rods under Follower Forces

“…Though the configuration has a critical load close to Beck's problem, theoretical analysis of Huang et al (1967) and discussion of Augusti et al (1967) have concluded that Willems test results are not representing the Beck column. Praveen et al (2021) have revisited the critical load assessment of Huang et al (1967) and corrected the error in the computed values and confirmed the adequacy of Willems's (1966) approach on the Beck column. Xiong et al (1989) have considered a centripetally loaded model and simulated Beck's column showing equivalence of the first and second modes individually, whereas Praveen et al (2020) have demonstrated the equivalence of the first and second modes directly from the dynamic characteristics of the Beck column.…”