scholarly journals BUCKLING STRENGTH OF FIXED END COLUMNS BRACED CONTINUOUSLY WITH VARYING AXIAL FORCE

2014 ◽  
Vol 79 (698) ◽  
pp. 525-532
Author(s):  
Masae KIDO ◽  
Keigo TSUDA
Keyword(s):  
Axial Force ◽  
Buckling Strength ◽  
Fixed End

A Discussion on How Internal Pressure is Treated in Offshore Pipeline Design

2004 ◽  
Author(s):  
Nelson Szilard Galgoul ◽  
Andre´ Luiz Lupinacci Massa ◽  
Cla´udia Albergaria Claro
Keyword(s):  
Internal Pressure ◽  
Axial Force ◽  
Research Work ◽  
Lateral Force ◽  
Poisson Effect ◽  
Cross Sectional ◽  
Starting Point ◽  
Global Buckling ◽  
Temperature And Pressure ◽  
Fixed End

The design of rigid submarine pipelines has been the object of extensive research work over the last few years, where the most relevant issues include upheaval and lateral buckling problems. Both of these problems systematically associate temperature and pressure loads, where the treatment of the first is obvious, while the latter have always been a matter of discussion. In 1974 Palmer and Baldry [1] presented a theoretical-experimental contribution, in which they have set a pattern that has been followed ever since. Another similar and well known paper was published by Sparks in 1983 [7], who only present a physical interpretation of this same theory. Most of the present day industry codes define an effective axial force, according to which, fixed end pipelines will be under compression due to internal pressure. The starting point of the discussion presented in [1] was that internal pressure produces a lateral force, which is numerically equal to the pressure times internal cross-sectional area times the pipeline curvature: q=p.Ai.d2y/dx2(1) This equation is demonstrated further ahead in this paper. Palmer and Baldry then based their arguments on the traditional equation of the pinned column buckling problem, studied by Euler [2]: EId4y/dx4+Pd2y/dx2=0(2) for which the well known solution is: P=π2EI/L2(3) and on the associated problem studied by Timoshenko [3], which adds a distributed lateral load q to the same problem: EId4y/dx4+Pd2y/dx2=q(4) Replacing q with the lateral pressure given above, they were able to have their own problem fall back onto the Euler solution: EId4y/dx4+Pd2y/dx2=p.Ai.d2y/dx2P-pAi=π2EI/L2(5) After correcting for the Poisson effect they were able to determine the new critical axial force caused by the pressure. Unfortunately, however, the arguments set forth in [1] have been misunderstood. The fact that both axial force and lateral force multiply curvature does not make them forces of the same nature. Being able to add them has solved a mathematical equation, but still hasn’t converted the lateral force to axial. The authors wish to prove that [1] presents no more than a tool, which can be used in the analysis of global buckling problems of pipelines subject to both temperature and pressure. It will be shown, however, that this pressure will not produce an axial force, as now-a-days prescribed conservatively in many pipeline codes, which is even used for stress checking.

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