bf
52
52
= 6.0 < 8.7 =
=
O.K.
2t f
36ksi
Fy
Choose W14X26 (W355.6mm X 0.38KN/m), Z = 40.2-in3 (658.8X103 mm3), φ Vn = 69-kip (306.9KN),
v
I = 245-in4 (102X106 mm4)
(5) Columns. Columns are sized based on the strong column /weak beam requirements of the AISC
Seismic Provisions for Structural Steel Buildings (dated April 15, 1997) herein referred to as the AISC
seismic provisions.
Using ASTM A572 Grade 50;
∑M
*
pc
≥ 1.0
(EQ. 9-3 AISC Seismic Provisions)
∑M
*
pb
∑M
∑ (1.1R
*
=
+ Mv)
yMp
pb
where; Ry
= 1.5
= Plastic Moment = ZFy = 40.2-in3(36ksi)
Mp
= 1,447in- kips (163.5KN-m)
Mv
= Additional moment due to offset of the plastic
hinge from the column centerline (this is equal to the plastic
shear ` p' times the offset distance). Mp is determined using
V
the following free body diagram;
Note; The offset from the column centerline is determined by choosing the column depth approximately
equal to the beam depth, the haunch length to be 3/4 of the beam depth, and as recommended in FEMA
267, by noting that the plastic hinge will occur another 1/3 of the beam depth beyond the toe of the haunch.
d c 3d b d b
+
+
≈1.6d b
Therefore;
Offset distance ` '
x
=
2
4
3
= 1.6(13.91")
= 22.25" or 1.85' (0.56m)
2(1,447in- kips )
2M p
= 9.17 k (40.8KN)
Vp =
=
(L - 2x) (30'- 2(1.85' ))(12"/1' )
∴ M v = Vp (1.85' ) = 9.17 k (22.25" ) = 204in- kips (23.1KN-m)
∑M
= 1.1(1.5)1,447in- kips + 204in- kips = 2,591in- kips (292.8KN-m)
*
Therefore;
pb
∑M
∑ Z (F
*
=
- Puc / A g )
and;
pc
c
yc
where; Puc ≈1.2(20psf)20' 15' (1k/1000lb) = 7.2k (32.0KN)
( )
Ag ≈10-in (6.45X103 mm2) (assumed)
2
∴ Puc/Ag ≈0.7ksi (4.83MPa)
∑M
*
= Z req'd (50ksi - 0.7ksi) = 49.3Z req'd
Therefore;
pc
H4-6
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