sm11 50

________________________________________________________________________
PROBLEM (11.50) A 50-mm-diameter steel pinned-end column is loaded as shown in Fig.
P11.48. For a factor of safety of ns with respect to yielding, use Fig. 11.16a to determine
allowable load Pall , for eccentricities of:
(a) e = 5 mm.
(b) e = 3 mm.
Given: E = 200 GPa, σy = 275 MPa, ns = 3
SOLUTION
43
(25) 306.8 10
44
I
mm
π
==× , 4 50 4 12.5rd mm
=
==
22
(25) 1963.5Am π == m
(a) e=5 mm
22
525 0.8
(12.5)
ec
r
×
==
From Fig. 11.16a: 133 .
y
PA So, MPa=
66
133 10 (1963.5 10 )
y
P− =× × 261 kN
=
261 87
3
y
all s
P
Pk
n
== = N
(b) e=3 mm
22
325 0.48
(12.5)
ec
r
×
==
Figure 11.16a:
163 .
y
PA MPa= Thus,
36
320 kN163 10 (1963.5 10 )
y
P− =× ×
=
320 106.7
3
all
Pk== N
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