Page 216 - Aircraft Stuctures for Engineering Student

200 Structural instability

P.6.7 The relation between stress u and strain E in compression for a certain
material is
10.5 x 106~ = a+ 21 000 -
(49:OO) l6
Assuming the tangent modulus equation to be valid for a uniform strut of this
material, plot the graph of ab against l/r where fsb is the flexural buckling stress, 1
the equivalent pin-ended length and r the least radius of gyration of the cross-section.
Estimate the flexural buckling load for a tubular strut of this material, of 1.5 units
outside diameter and 0.08 units wall thickness with effective length 20 units.
Ans. 14 454 force units.
P.6.8 A rectangular portal frame ABCD is rigidly fixed to a foundation at A and
D and is subjected to a compression load P applied at each end of the horizontal
member BC (see Fig. P.6.8). If the members all have the same bending stiffness EI
show that the buckling loads for modes which are symmetrical about the vertical
centre line are given by the transcendental equation
- = -? 1 (I;) tan ($)
Xa
a
2
where

X2 = P/EI

Fig. P.6.8
P.6.9 A compression member (Fig. P.6.9) is made of circular section tube,
diameter d, thickness t. The member is not perfectly straight when unloaded,
having a slightly bowed shape which may be represented by the expression
v = Ssin (7)

Show that when the load P is applied, the maximum stress in the member can be
expressed as