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Section 2
2-39
As (KL/r)
y <
C
c
, the allowable axial stress in compression
()
()
2
2
22
39.92 36
36
1 1 16.13
. . 4 2.12 4 29000
yy
a
FKLrF
F
FS E
ππ
⎡⎤
⎡⎤
⎢⎥
=− =− =
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎣⎦
Shear:
Allowable shear stress as per gross section, F
v
= 0.33xF
Y
= 11.8
ksi
Actual Stress Calculation:
Axial stress (f
a
) = 8.71 / 7.65 = 1.138 ksi.
The critical moment occurs at the end node of the beam. So we use
the AASHTO equation 10.42 in section 10-36 to calculate the
design ratio.
Actual bending stress = 56.5 x12/33.4 = 1.691 x 12 = 20.299 ksi
(KL/r)
z =
1x60/5.16 = 11.618 11.628
() ()
22
22
*29000
998.524
. . 2.12 11.618
ez
E
F
FS KLr
ππ
== =
From table 10-36A, C
mz
= 0.85
So the design ratio is
Equation 10-42
1.138 0.85* 20.299
0 0.942
1.138
16.13
1- 19.8
1
1
1000.22
'
'
my by
amxbz
a
a
a
bz
by
ez
ey
Cf
fCf
F
f
f
F
F
F
F
++ =+ +=
⎛⎞⎛⎞ ⎛ ⎞
−
⎜⎟
−
⎜⎟⎜⎟
⎜⎟
⎝⎠
⎝⎠
⎝⎠