Seismic checks - Braces (Seismic: AISC 341)

Tekla Structural Designer
2021
Tekla Structural Designer

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.

See: AISC 341-05 seismic classification - all members

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

Note: While checking the minimum slenderness of individual elements in built-up members to F2.5b (2), It is assumed the minimum number of shear connectors is provided i.e. two. The shear strength of the connectors is NOT checked against the tensile strength of each element.
Note: The brace net area is NOT checked against the brace gross area as per F2.5b (3) and where this might be an issue suitable reinforcement is assumed to be provided.

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

Note: While checking the minimum slenderness of individual elements in built-up members to 13.2e, it is assumed the minimum number of shear connectors is provided i.e. two. The shear strength of the connectors is NOT checked against the tensile strength of each element.
Note: The brace net area is NOT checked against the brace gross area and where this might be an issue suitable reinforcement is assumed to be provided.

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.

Note: The brace required strength to 13.2b is NOT limited to the "maximum load effect" as per 13.2b (b).
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