Engineering Transactions,

**9**, 4, pp. 745-756, 1961### Wpływ Sztywności Giętnej Przepon na Stateczność Pręta Cienkościennego

The problem is solved on the basis of the theory of thin-walled beams and the theory of plates. In Chapter 1 the formula (1.4) is derived giving the bimoment constituting the only inter- action between the diaphragm and the beam, since the interaction forces must constitute a self- balanced system.

In Chapter 2 the torsional buckling of n I-beam is considered. In the case where the end diaphragms are the only two, the differential equation (2.4) and the boundary conditions (2.6) result in the transcendental equation (2.8). The critical values of axial strain are collated in Table 1 in terms of the thickness g of the diaphragm. In the case of many diaphragms with small spacing, an approximate solution is obtained, the continuous distribution of interactions being assumed; the results are shown in Table 2 in terms of the number m of diaphragms. Next, solution by means of Fourier series is described; the series does not fulfil the boundary conditions; therefore it must be completed with an additional function (2.15), thus obtaining an infinite set of homogeneous equations. The first approximation gives the simple formula (2.22). In practical cases (i, e. if g is small the error involved does not exceed a fraction per cent. The second approximation gives a quadratic equation (2.24); the results obtained are satisfactory for any value of g, including the beam with clamped ends i.e. g=w.

In Chapter 3 the flexural-torsional buckling of a channel is considered, the solution by Fourier series being presented, of which the practical efficiency has been proved for the I-beam, The numerical results obtained lead to the conclusion, that the influence of the diaphragms is usually insignificant and may be disregarded in statical analysis. The intermediate diaphragms are much less efficient than the end ones.

In Chapter 2 the torsional buckling of n I-beam is considered. In the case where the end diaphragms are the only two, the differential equation (2.4) and the boundary conditions (2.6) result in the transcendental equation (2.8). The critical values of axial strain are collated in Table 1 in terms of the thickness g of the diaphragm. In the case of many diaphragms with small spacing, an approximate solution is obtained, the continuous distribution of interactions being assumed; the results are shown in Table 2 in terms of the number m of diaphragms. Next, solution by means of Fourier series is described; the series does not fulfil the boundary conditions; therefore it must be completed with an additional function (2.15), thus obtaining an infinite set of homogeneous equations. The first approximation gives the simple formula (2.22). In practical cases (i, e. if g is small the error involved does not exceed a fraction per cent. The second approximation gives a quadratic equation (2.24); the results obtained are satisfactory for any value of g, including the beam with clamped ends i.e. g=w.

In Chapter 3 the flexural-torsional buckling of a channel is considered, the solution by Fourier series being presented, of which the practical efficiency has been proved for the I-beam, The numerical results obtained lead to the conclusion, that the influence of the diaphragms is usually insignificant and may be disregarded in statical analysis. The intermediate diaphragms are much less efficient than the end ones.

**Full Text:**PDF

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

#### References

[in Russian]

J. RUTECKI. Wytrzymałość konstrukcji cienkościennych, Warszawa 1957.PWN.

A. CHUDZIKIEWICZ, Ogólna teoria stateczności prętów cienkościennych z uwzględnieniem odkształcalności przekroju poprzecznego, Rozpr. Inzyn., 4, 8 (1960).