Seismic checks - Braces (Seismic: AISC 341)
Classification
In all cases if the given “width to thickness ratio” is less than or equal to the given limit, then the seismic classification is satisfied.
AISC 341-16 and AISC 341-10
Braces in OCBF – As per Clause F1.5a, braces must satisfy the requirements of clause D1.1b for “moderately ductile” members.
Braces in SCBF – As per Clause F2.5a, braces must satisfy the requirements of clause D1.1b for “highly ductile” members.
See: AISC 341-16 and AISC 341-10 seismic classification - all members
AISC 341-05
Braces in OCBF – As per Clause 14.2, braces must satisfy the requirements of clause 8.2b for 'seismically compact' members.
Braces in SCBF – As per Clause 13.2d, braces must satisfy clause 8.2b for “seismically compact” sections.
Slenderness
AISC 341-16 and AISC 341-10
OCBF
In OCBF for V and A braces only, the design condition is checked for both major and minor axis as per F1.5b,
KL/r ≤ 4 * SQRT[E/Fy]
Where
K = the effective length factor for the relevant axis
L = the system length of the brace
r = the radius of gyration of the brace for the relevant direction
E = modulus of elasticity of steel – 29000 ksi
Fy = minimum yield stress.
SCBF
For all braces in SCBF the design condition for both minor and major axis is checked as per F2.5b (1),
KL/r ≤ 200
Where
K = the effective length factor for the relevant axis
L = the system length of the brace
r = the radius of gyration of the brace for the relevant direction.
For built-up braces i.e. double angles the requirements for interconnection are checked as per F2.5b (2). The minimum number of connectors required by this clause is two and thus the maximum interconnection slenderness of the individual angles is based on a buckling length of one third of the system length, (which is conservative).
Thus,
a/ri ≤ 0.4 * MAX[KL/r]
Where
a = the sub-length of the member between interconnections = taken as L/3
ri = the minimum radius of gyration of the individual angle, taken as rz
AISC 341-05
OCBF
For V and A braces in OCBF the design condition for both minor and major axis is checked as per 14.2,
KL/r ≤ 4 * SQRT[E/Fy]
Where
K = the effective length factor for the relevant axis
L = the system length of the brace
r = the radius of gyration of the brace for the relevant direction.
SCBF
For all braces in SCBF there is a three stage design condition and both minor and major axis are checked as per 13.2a,
KL/r ≤ 4 * SQRT[E/Fy] PASS
KL/r > 200 FAIL
ELSE WARNING
“Brace slenderness satisfies, 4√(E/Fy) < KL/r ≤ 200. The available strength of the associated column is NOT checked as per 13.2a."
Where all variables are as given above.
For built-up braces i.e. double angles the requirements for interconnection are checked as per 13.2e. The minimum number of connectors required by this clause is two and thus the maximum interconnection slenderness of the individual angles is based on a buckling length of one third of the system length, (this will be conservative). Thus,
a/ri ≤ 0.4 * MAX[KL/r]
Where
a = the sub-length of the member between interconnections = taken as L/3
ri = the minimum radius of gyration of the individual angle, taken as rz
Brace strength
AISC 341-16 and AISC 341-10
OCBF
No additional requirements.
SCBF
Where the effective net area is less than the gross area the provisions of F2.5b (3) apply. This is more aimed at gusset plate connections where the cross section of the brace is reduced. The effective net area is specified by the user as a percentage or actual area.
The design condition should be (!),
ɸt * Fu * Ae ≥ Ry * Fy * Ag LRFD
Fu * Ae / Ωt ≥ Ry * Fy * Ag / 1.5 ASD
Where,
ɸt = resistance factor for tension
Ωt = safety factor for tension
Fu = specified minimum tensile strength of steel
Fy = specified minimum yields stress of steel
Ae = effective area of brace (user input)
Ag = gross area of brace
Ry = the overstrength factor – see Section.
Note that for 50 ksi steel this will always fail but providing there is no reduction in area the brace is expected to yield. The Commentary in AISC 341 Comm. F2.5b indicates:
“Where there is no reduction in the section, or where the section is reinforced so that the effective net section is at least as great as the brace gross section, this requirement does not apply. The purpose of the requirement is to prevent net section fracture prior to significant ductility; having no reduction in the section is deemed sufficient to ensure this behavior.”
Consequently the design condition in Tekla Structural Designer is presented as follows, and considers the effective net area provided, Ae.prov, and the effective net area required, Ae.reqd, to satisfy F2.5b (3),
Ae.reqd = MAX[Ag, (Ry * Fy * Ag/(Fu * ɸt)] LRFD
Ae.reqd = MAX[Ag, (Ry * Fy Ag * Ωt/(Fu * 1.5)] ASD
The design condition then becomes,
Ae.reqd ≤ Ae.prov
AISC 341-05
OCBF
No additional requirements.
SCBF
The calculations for this check are exactly the same as those for the AISC 341-10 check.