863_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Problem 11.3-12
A long slender column ABC is pinned at ends A and
C and compressed by an axial force P (see figure). At the midpoint B ,
lateral support is provided to prevent deflection in the plane of the
figure. The column is a steel wide-flange section with
E = 200 GPa. The distance between lateral supports is L = 5.5 m.
Calculate the allowable load P using a factor of safety n = 2.4, taking
into account the possibility of Euler buckling about either principal
centroidal axis (i.e., axis 1-1 or axis 2-2).
( W 250 * 67)
SECTION 11.3 Critical Loads of Columns with Pinned Supports
857
Solution 11.3-12
B
UCKLING ABOUT AXIS
1-1
P
cr1
p
2
EI
1
(2 L )
2
P
cr1
1680 kN
I
2
22.2 * 10
6
mm
4
n 2.4
L 5.5 m I
1
103 * 10
6
mm
4
W 250 * 67 E 200 GPa
B
UCKLING ABOUT AXIS
2-2
axis 2-2 governs
A
LLOWABLE
L
OAD
; P
allow
P
cr
n
P
allow
604 kN
P
cr
P
cr 2
P
cr 2
p
2
EI
2
( L )
2
P
cr 2
1449 kN
Problem 11.3-13