Proceedings of the Royal Society of Queensland . e, and much moneyspent in experiment to determine formulae and principlesgoverning the design of such members. The failure of the Quebec Bridge in 1907, when manylives were lost, and hundreds of thousands of pounds fellinto the river, showed that our knowledge of column designwas not complete. The author, in a series of papers collected and publishedunder the title of Column Analysis and Design,* hasmade a comparison of the various formulae proposed,and has deduced sets of curves for the purpose ofanalysing experimental results and for use in th
Proceedings of the Royal Society of Queensland . e, and much moneyspent in experiment to determine formulae and principlesgoverning the design of such members. The failure of the Quebec Bridge in 1907, when manylives were lost, and hundreds of thousands of pounds fellinto the river, showed that our knowledge of column designwas not complete. The author, in a series of papers collected and publishedunder the title of Column Analysis and Design,* hasmade a comparison of the various formulae proposed,and has deduced sets of curves for the purpose ofanalysing experimental results and for use in the design•of columns. The deductions made in the paper mentioned werebased on interpretations of previous work, and on newmethods of analysis, which it is the purpose of this paperto explain and discuss. ?Published by the University of Queensland and the SydneyUniversity Engineering Society. BY R. W. H. HAWKEX. 95 The basic result is that of Euler (1707-1783), whichwill be here stated in the notation to be adopted ;See Fig. 1).. Fig. i. Xiet 0 be the centre of coordinates I - be the length of a column fixed at one end and2 free at the other (equivalent to a columnlength I pin ended). y be the ordinate of the deflection curveI x- the abscissa measured from 0 2 E be the Modulus of Elasticity of the materialI be the Moment of Inertia of the cross section?Q be the Load centrally applied. 96 THE STRUT PROBLEM. The differential equation of equilibrium d*yis EI =-Qy (1> dx2 The solution of this equation is a cosine curve y=a cos x- (2) 2 and it has been proved that Q can have only one value, viz. 7Z2EI Q= •-. (3) Z2 which will be called the Euler Value or Q of thecolumn (3a) The results (2) and (3) were deduced a century anda-half ago by Euler ; the derivation of the Euler resultsappears in almost any book on infinitesimal calculus, oron the theory of structures, yet it is with their meaning andinterpretation that this paper deals, because the authorthinks tha
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