Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

P
e
x
p16.26 A steel [E = 200 GPa] pipe with an outside diameter of
170 mm and a wall thickness of 7 mm supports an axial load P,
which is applied at an eccentricity of e = 150 mm from the pipe
centerline (Figure P16.25/26). The column is fixed at its base and
free at its upper end, and its length is L = 4.0 m. The maximum
compressive stress in the column must be limited to σ max =
80 MPa.
L
(a) Use a trial-and-error approach or an iterative numerical
solution to determine the allowable eccentric load P that can
be applied.
(b) Determine the lateral deflection at the upper end of the
column for the allowable load P.
y
z
FIGURE p16.25/26
16.5 Empirical column Formulas—centric Loading
The Euler buckling formulas for the critical buckling load [Equation (16.16)] and critical
buckling stress [Equation (16.17)] were derived for ideal columns. In considering ideal
columns, it was assumed that the column was perfectly straight, that the compression
load was applied exactly at the centroid of the cross section, and that the column material
remained below its proportional limit during buckling. Practical columns, however,
rarely satisfy all of the conditions assumed for ideal columns. Although the Euler equations
give reasonable predictions for the strength of long, slender columns, early researchers
soon found that the strength of short and intermediate-length columns were not
well predicted by these formulas. A representative graph of the results from numerous
column load tests plotted as a function of slenderness ratio is shown in Figure 16.11. The
FIGURE 16.11 Representative
column test data for a range of
slenderness ratios.
σ
σ
cr
Y
cr
σcr= =
π
696