B.6 Determine cm and cr
The braces must be designed before the center of rigidity is determined.
Each braced bay must resist a total shear of 11.65 kips. It is assumed that the compressive and tension
braces resist of the load to each braced frame and that the braces do not resist gravity loads. Therefore,
the unfactored load to each brace is :
(1/2)(11.65 kips) = 5.83 kips / brace. (25.9 KN)
Note: Section 14.5 of the AISC Seismic Provisions exempt low rise buildings designed to Load
Combinations 4-1 and 4-2 from the special requirements of Sec. 14.2. 14.4. However, some of the
provisions will be followed as they are considered good design practice.
1.2D + 0.5L + 0.2S + Ω 0QE
(AISC Seismic Provisions Eq. 4-1)
0.9D Ω 0QE
(AISC Seismic Provisions Eq. 4-2)
Note: The live load factor of 1.0 is required for use in Eq. 4-1 for garages, areas occupied as places of
public assembly and all areas where the live load is greater than 100 psf. This structure is considered to be
a garage.
1.2D + 1.0L + 0.2S + Ω 0QE
(AISC Seismic Provisions Eq. 4-1)
Required bracing strength based on Eq. 4-1:
Ω 0QE = 2.0 ( 5.83 kips ) = 11.7 kips (52.0 KN)
The braces are at a 45 degree angle, axial force = 1.414 x hor. shear = (1.414)(11.7 k) = 16.5 k (73.4 KN)
AISC Seismic Provisions require that braces in V-Type or Chevron-Type configurations have a design
strength of at least 1.5 times the required strength using LRFD Specification Load Combinations A4-5 and
A4-6.
1.2D 1.0E + 0.5L +0.2S
(AISC LRFD Eq. A4-5)
0.9D (1.3W or 1.0E)
(AISC LRFD Eq. A4-6)
1.5 x factored force = (1.5)(5.83 kips) = 8.7 kips (38.7 KN) (AISC 14.4.a). This provision is exempt as
noted above but is included here for illustrative purposes.
The braces are at a 45 degree angle, axial force = 1.414 x hor. shear = (1.414)(8.7 k) = 12.4 K (55.2 KN)
The axial force from equation 4-1 governs. Use 16.5 kips (73.4KN) for design.
The required compressive strength of a bracing member in axial compression shall not exceed 0.8 times
φPn. (AISC Seismic Provisions 14.2.b)
c
Try 3" standard pipe brace, A = 2.23 in2, L = 14.1 ft., r = 1.16in., A36, K =1 per AISC LRFD Sec. C2.1
KL Fy
(1)(14.1)(12)
36
λ=
=
= 1.64
(AISC LRFD ' 3 Eq. E2-4)
9
π
π(1.16)
r E
29000
0.866
(AISC LRFD ' 3 Eq. E2-2)
9
Fcr = 2 Fy = 11.65ksi
λ
φ n = (0.85)(11.65ksi)(2.23in2 ) = 22.1kips
P
0.8φ n = (0.8)(22.1 kips) = 17.68 (78.6 KN) kips > 16.5 kips (73.4 KN), OK
P
Use 3" Standard pipe braces
H1-30
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