bf

52

52

= 6.0 < 8.7 =

=

2t f

36ksi

Fy

(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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