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Southwell and lundquist plots for struts suffering subbuckling cyclic excursions

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Abstract

An experimental investigation into the effects of subbuckling low-frequency cyclic hysteresis upon a range of imperfection-sensitive circular hollow section struts has involved a novel application of the Southwell and Lundquist semi-empirical plot procedures. A static strut testing procedure was modified to provide for the inclusion of cyclic action phases, these cyclic excursions possessing amplitudes that constrained behavior to the subbuckling compression regime throughout. Cyclic action was introduced at some prescribed static axial compression, buckling being statically induced upon completion of the cyclic action phase. For each strut test, appropriate semi-empirical plots were determined, where possible, for both pre- and post-cyclic action phase static data sets, each successful plot thereby consisting of a respective pair of linear loci. It is deemed that such bilinear loci be parallel, indicating no change in boundary conditions or effective length, but offset, indicating cyclic hysteresis amplification of any initial strut imperfection. This bilinear technique is shown to be particularly useful in assessing quality of experimentation and in providing imperfection data applicable to the analysis of nominally static struts suffering subbuckling cyclic action. Design implications are briefly identified for completeness. Serviceability considerations are shown to be the dominant issue.

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Abbreviations

A :

cross-sectional area

a o1,a os :

Lundquist and Southwell estimates ofw oc

E :

direct (Young's) modulus

f :

frequency (1/16 Hz)

I :

second moment of area

n c :

number of cycles employed (1000 cycles)

P :

axial loading

P b :

buckling load (fully static)

P bc :

post-cyclic action phase static buckling load

P c :

Euler or critical load

P c1,P cs :

Lundquist and Southwell estimates ofP c

P mn :

axial load at which cyclic action phase initiated/ECCS load

P′, w′ :

Lundquist pivot coordinates

r :

radius of gyration

u :

axial displacement

u a :

half amplitude

u mn :

mean axial displacement during cyclic action phase

w c :

central transverse displacement of a pin-ended strut under axial loadP

w oc :

initial transverse displacement of a pinended strut under axial loadP=0

w c ′:

cyclic step

ℓ:

effective length

ℓ1,ℓ s :

Lundquist and Southwell estimates of ℓ

Δa os , Δa o1 :

difference between respective pre- and post-cyclic Southwell and Lundquist imperfection parameter estimates

λ m :

modified slenderness ratio

σ y :

yield stress

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Authors and Affiliations

  1. Department of Civil Engineering, Sheffield City Polytechnic, Pond Street, S1 1WB, Sheffield, UK

    N. Taylor (Principal Lecturer)

  2. Department of Civil Engineering, Leeds University, LS2 9JT, Leeds, UK

    P. Hirst (Research Fellow)

Authors
  1. N. Taylor
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  2. P. Hirst
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Taylor, N., Hirst, P. Southwell and lundquist plots for struts suffering subbuckling cyclic excursions. Experimental Mechanics 29, 392–398 (1989). https://doi.org/10.1007/BF02323856

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  • DOI: https://doi.org/10.1007/BF02323856

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