F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

288 Eccentrically loaded columns and slender columns
(a)
For Mxlh' ~ Mylb':
h'
M~ = Mx + {Jb,MY
(b) For Mxlh' < Mylb':
M; =My+ {J~:Mx
State the meanings of the symbols and briefly explain the technical
background to these equations.
Ans.
See Section 7.3(b): Biaxial bending-the technical background.
7.5 Work out fully the solution to part (d) of Example 7.1-3.
7.6 A pin-ended elastic, homogeneous column of uniform flexural
stiffness EI has an initial crookedness defined by e 0 = e 1 sin Tlzll.
r
Problem7.6
When a load N is applied the transverse deflection is increased, by an
amount eadd, to eo + eadd. Show that
aE
eadd = 1 - aE
where aE =NINE and NE(= 1'l 2 EI/l 2 ) is the Euler load of the column. (If
necessary, read Section 9.3 of Reference 6.)
Comments
Note that the eccentricity magnification factor is
7.7 Problem 7.6 appears at first sight to be rather restricted because it