Engineering Transactions, 6, 2, pp. 233-252, 1958

### Drgania Swobodne i Wyboczenie Płyty Trójkątnej Wzmocnionej Żebrami

Z. Reipert
Politechnika Warszawska
Poland

In the first part of this paper, an isotropic triangular plate is considered. The plate is simply supported on the edges and rests on an elastic foundation. The stiffening rib is parallel to one of the sides adjacent to the right angle. The plate is loaded by longitudinal forces uniformly distributed along the edges. The stiffening bar is loaded by a concentrated force S Fig. 1a. The interaction between the plate and the rib is replaced by a continuous load p(x). The load p (x, y) of the plate due to the action of the rib, is expressed by a double trigonometric series using the expression for a triangular plate loaded by the unit force. Starting from the differential equation for plates, the amplitude surface w (x, y) is determined for a compressed plate loaded additionally by p(x, y), Eq. (1.3). The amplitude curve for the rib v (zc), Eq. (1.4)), is determined from the differential equation for the rib subjected to longitudinal compression, and the additional load p(zc) expressed by means of a simple trigonometric series. From the compatibility condition between the plate and the rib, Eq. (1.5), the Eq. (1.7) is obtained. Finally, the determinant of a system of equations is obtained in which the unknown quantity is o the frequency of free vibration of the system (plate and rib). Setting =0, the critical compressive force Scr for the rib or the critical load Ncr may be found. In the second part, certain particular cases are examined. These concern a triangular plate with one or more ribs loaded by concentrated forces.

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

#### References

S. Timoshenko, Theory of Plates and Shells, 1940.

Z. Kączkowski, Drgania swobodne i wyboczenia płyty trójkątnej, Arch. Mech. Stos. 1 (1956).

W. Nowacki, Stateczność płyt prostokątnych wzmocnionych zebrami, Arch. Mech. Stos. 2 (1954).

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