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Section 2
2-41
I
YC
= tb
3
/12 = 0.53 x 8.0
3
/12 = 22.61in
4
J = (2 x 8.0x0.53
3
+ (13.66 – 2x0.53)x0.305
3
)/3 = 0.913 in
4
2
6
50 10 1.75 22.61 0.917 12.6
0.772 9.87
62.7 132 22.61 132
cz
F
××
⎛⎞ ⎛⎞
=
+=
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
83
187.61 psi
Since FCZ is larger than 0.55xF
Y,
FCZ = 0.55xF
Y
= 19.8 ksi
Axial Compression:
Critical (KL/r)
y
= 1.0 x 11x12/1.894 = 69.69
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
69.69 36
36
1 1 14.387
. . 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
) = 25.5 / 12.6 = 2.024 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 = 112.17 x12/62.7 = 1.789 x 12 = 21.467 ksi
(KL/r)
z =
1x132/5.828 = 22.649