sm11 83

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PROBLEM (*11.83) A load of P = 10 kips is applied with an eccentricity of e = 1 ½ in. to
a timber post (Fig. P11.83). Let E = 1.7 x 106 psi , ( σall )b = 1.2 ksi for compression parallel
to the grain, and Le = 5 ft. Employing the interaction method, determine smallest allowable
diameter d of the post.
*SOLUTION
, 0.7 0.7(5 12) 42 .
e
LL==×=in 2dc
=
Assume 50
e
Ld and use Eq. (11.32) : ≤
632
2
0.3(1.7 10 )
( ) 1.156 10
(42 2 )
all c c
c
σ
×
==
×
Then,
1
()()
all c all b
PA McI
σσ
+≤
32 3 4
32 3
10 10 1.5 10 10 ( 4) 1
1.156 10 1.2 10
ccc
c
ππ ×××
+≤
××
; 43
2.754 15.92 1
cc
+
≤
Solving by trial and error : 2.56 .cin
=
5.12 .di=n
Check :
42 5.12 8.2 50
e
Ld==< O.K.
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