Vol. 12, No. 2 (1956)
1956-01-20
目录
CONTENT
1956, 12 (2): 139-151.
doi: 10.7498/aps.12.139
Abstract +
The non-linear theory of elastic thin-walled bars of open cross-sections proposed by the auther is applied to the study of large torsion of such bars. The fundamental equations are simplified for the case of bisymmetrical ane central symmetrical cross-sections. For non-symmetrical cross-sections, it is generally impossible to obtain pure torsion without bending in the non-linear theory. The problem is solved by a perturbation method. Two specific examples are considered.
1956, 12 (2): 152-169.
doi: 10.7498/aps.12.152
Abstract +
In this paper the non-linear theory of thin
一
walled beams of open cross sections Proposed by
the author [1] recently is applied to the investigation of the stability of such beams.
Fundamental
equations of the previous paper [ 1 ] are firstly linearized and simplified for the determination of
the critieal load and the mode of buckling.In the ease of eccentrie compression, the fundamental equations of this paper differ from those in the theory of V.Z.Vlasov in the following
two points : l) A new generalized displacement P is in troduced.2 ) The initial bent state of the beam is taken in to account.
A numerieal exaple (an angle of unequal legs ) shows that in the case of central uniform compression, P has little in fluence on the magnitude of the critical load, The re fore P is then neglected in this paper.In the ease of beams loaded by pure bending momments , two numerical examples are carried out (a cross beam and an I-beam , see Figs.4 and 6 ).
Critieal moments are ploted against a d imensionless parameter a as shown in Figs.5 and 7(curves I), where a is the ratio of width to depth of the cross section of the beam·Our critical moments are greater than those given by V.Z. Vlasov (curves II in Figs.5 and 7).This is because in this paper the initial bent state of the beam is taken into : account.
It is interest
to point out that according to our theory, beams may lose lateral stability under pure bending
moment only when the ratio of width to depth of the cross section is less than a certain critical value.
This fact is in agreement with common exprience .
