THE COLUMN SHOWN BELOW IS FIXED AT THE BASE AND FREE AT THE TOP.

THE COLUMN IS SUBJECTED TO A COMPRESSIVE FORCE P ACTING AT AN

ECCENTRICITY E FROM THE AXIS OF THE COLUMN.

a$)$ DERIVE THE DIFFERENTIAL EQUATION

b$)$ FIND THE EQUATION OF THE DEFLECTED SHAPE

c$)$ FIND THE MAXIMUM MOMENT IN THE COLUMN

d$)$ VERTICAL STEEL PIPE $d_0=3$ INCHES, $d_i=2\mathrm{.}5$ INCHES, $IN=9FT,e=\mathrm{.}25$ INCHES,

AND E $=30000$ KSI. DETERMINE THE VALUE OF THE CRITICAL LOAD P SO

THAT THERE IS NO TENSILE STRESS AT THE BASE OF THE PIPE.

e$)$ FIND THE CORRESPONDING COMPRESSIVE STRESS

f$)$ COMPARE THE VALUE OF PART d TO THE VALUE OBTAINED FOR AN

AXIALLY LOADED COLUMN.