Page 215 - Aircraft Stuctures for Engineering Student

Problems 199

tv I vo

Fig. P.6.4
P.6.5 The uniform pin-ended column shown in Fig. P.6.5 is bent at the centre so
that its eccentricity there is 6. If the two halves of the column are otherwise straight
and have a flexural stiffness EI, find the value of the maximum bending moment
when the column carries a compression load P.

Fig. P.6.5

P.6.6 A straight uniform column of length I and bending stiffness EI is subjected
to uniform lateral loading w/unit length. The end attachments do not restrict rotation
of the column ends. The longitudinal compressive force P has eccentricity e from the
centroids of the end sections and is placed so as to oppose the bending effect of the
lateral loading, as shown in Fig. P.6.6. The eccentricity e can be varied and is to be
adjusted to the value which, for given values of P and w, will result in the least
maximum bending moment on the column. Show that
e = (w/Pp2) tan2 p1/4
where
p2 = PIE1
Deduce the end moment which will give the optimum condition when P tends to
zero.
Ans. w12/16.
w/unit length
1 2illli ill1 1
.-
P e e P
Z

Fig. P.6.6