Oil Canning Problems in Creep

  • Jan Hult
Conference paper
Part of the IUTAM Symposia book series (IUTAM)

Abstract

The stability of some transversely loaded nearly flat structures on hinged supports is studied, assuming the material to be subject to creep. It is shown that a sudden jump in the equilibrium configuration will occur after a certain time, due to simultaneous compression and bending of the structure.

Keywords

Verse 

Nomenclature

A

cross sectional area

E

modulus of elasticity

I

moment of inertia of cross section

k

creep rate parameter

K

dimensionless load parameter = Q L/4 π ϱ S 2 (two-bar system), = Q L/ 4 π ϱ P 2 (curved beam)

L

length of beam

M

bending moment

P, S

compressive axial force

P2, S2

elastic buckling force

q

distributed lateral load

Q

concentrated lateral load

s

dimensionless force parameter = P/P 2, S/S 2

t

time

w

deflection of beam

x

axial coordinate

z

dimensionless deflection parameter = (L ϑ/2 π ϱ)2 (two-bar system), = (δ 1/ϱ)2 (curved beam)

δ

midspan deflection of beam

δ1, δ2

amplitudes of first and second harmonics in beam deflection

ε

compressive strain

ϑ

angle

ϱ

radius of inertia of cross section = √I/A

σ

compressive stress

τ

dimensionless time parameter = E k t

ζ

dimensionless deflection parameter = (δ/ϱ)2/2 (two-bar system), = (2 δ 2/ϱ)2 (curved beam)

Subscript j

refers to jump condition

Superscript 00

refers to the initial state prior to application of load

Superscript 0

refers to the initial state immediately after application of load

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References

  1. [1]
    Pian, T. H. H.: Creep Buckling of Curved Beaim Under Lateral Loading. 3rd US Congr. Appl. Mech. Proc. (1958) pp. 649–654.Google Scholar
  2. [2]
    Marguerre, K.: Neuere Festigkeitsprobleme des Ingenieurs. Berlin/Göttingen/ Heidelberg: Springer 1950, Ch. V.MATHGoogle Scholar
  3. [3]
    Hoff, N. J., and V. G. Bruce: Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches. VIII Int. Congr. Theor. Appl. Mech. Istanbul. J. Math. Phys. XXXII, 276–288 (1952).Google Scholar
  4. [4]
    Hoff, N. J.: Buckling and Stability. J. Roy. Aer. Soc. 58, 1–52 (1954).Google Scholar
  5. [5]
    Hult, J.: Creep Buckling of Plane Frameworks. Durand Centennial Conferen ce, Stanford University, Proc. (1960) pp. 227–246.Google Scholar

Copyright information

© Springer-Verlag OHG., Berlin/Göttingen/Heidelberg 1962

Authors and Affiliations

  • Jan Hult
    • 1
  1. 1.Royal Institute of TechnologyStockholmSweden

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