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ACCURATE CALCULATION OF ELASTIC BUCKLING LOADS FOR SPACE FRAMES BUILT UP OF UNIFORM BEAMS WITH OPEN THIN‐WALLED CROSS‐SECTION
Author(s) -
SÄLLSTRÖM J. H.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960715)39:13<2319::aid-nme960>3.0.co;2-p
Subject(s) - buckling , stiffness matrix , image warping , stress resultants , bending stiffness , discretization , space frame , beam (structure) , torsion (gastropod) , structural engineering , differential equation , finite element method , mathematics , timoshenko beam theory , direct stiffness method , mathematical analysis , geometry , engineering , computer science , medicine , surgery , artificial intelligence
A so‐called exact static stiffness matrix for a uniform beam element with open thin‐walled cross‐section carrying an axial compressive load is derived. This stiffness matrix is useful in an accurate calculation of bifurcation loads and corresponding buckling modes of space frames built up of such beam elements. One may also calculate displacements and sectional forces caused by external joint loads taking into account the second‐order effect of the axial beam loads. The exact stiffness matrix is derived by use of the general solution to a set of three coupled differential equations. This means that no preselected shape functions need be introduced and that discretization errors are avoided. The differential equations model coupled Euler–Bernoulli bending in the two principal planes and Saint‐Venant/Vlasov torsion and warping with respect to the shear centre axis. No cross‐sectional symmetries are assumed. Numerical examples are given. One application will be to loaded pallet racks. The ‘effective length’ for a rack column is calculated.