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American Steel Design
Section 2
2-36
2
6
50 10 1.75 8.6564 0.28389 11.46
0.772 9.87
33.38789 120 8.6564 120
cz
F
××
⎛⎞ ⎛⎞
=
+=
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
64375.03 psi
From this, calculated FCZ = 64.37.As this is larger than 0.55xF
Y
FCZ = 0.55xF
Y
= 19.8 ksi
Axial Compression:
Critical (kL/r)
y
= 1.0 x 120/1.5038 = 79.7978
22
2 2 *29000
126.099
36
c
y
E
C
F
ππ
== =
As (kL/r)
y <
C
c
, the allowable axial stress in compression
()
()
2
2
22
79.79 36
36
1 1 13.58
. . 4 2.12 4 29000
yy
a
FKLrF
F
FS E
ππ
⎡⎤
⎡⎤
⎢⎥
=− =− =
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎣⎦
ksi
Shear:
Allowable shear stress as per gross section, F
v
= 0.33xF
Y
= 11.8
ksi
Actual Stress Calculation:
Actual stress (f
a
) = 25/7.65 = 3.26 ksi.
Actual bending stress = 56.5 x12/33.4 = 1.691616 x 12 = 20.29932
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.