Page 221 - Aircraft Stuctures for Engineering Student

Problems 205

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Fig. P.6.18

P.6.18 Figure P.6.18 shows the doubly symmetrical cross-section of a thin-walled
column with rigidly fixed ends. Find an expression, in terms of the section dimensions
and Poisson’s ratio, for the column length for which the purely flexural and the purely
torsional modes of instability would occur at the same axial load.
In which mode would failure occur if the length were less than the value found? The
possibility of local instability is to be ignored.

Am. I = (27rb2/t)dm. Torsion.

P.6.19 A column of length 21 with the doubly symmetric cross-section shown in
Fig. P.6.19 is compressed between the parallel platens of a testing machine which
fully prevents twisting and warping of the ends.
Using the data given below, determine the average compressive stress at which the
column first buckles in torsion
I = 500 mm; b = 25.0 mm, t = 2.5 mm, E = 70 000 N/mm2, EIG = 2.6

AYE. OCR = 282 N/m2.

Fig. P.6.19