Design of Braces for Compression per AISC 360-16
The design of steel braces subject to axial compression is explained in detail under this title according to AISC 360-16.
Symbols
A_{g} : Gross cross-sectional area of member
A_{e} : Effective area
c_{1}, c_{2} : Effective width imperfection adjustment factor determined from Table E7.1
F_{cr} : Critical stress
F_{e} : Elastic buckling stress
F_{y} : Specified minimum yield stress of the type of steel being used
K : Effective length factor
L: Laterally unbraced length of the member
L_{c} : Effective length of the member, (= KL)
r: Radius of gyration
λ: Width-to-thickness ratio for the element part
λ_{r} : Limiting width-to-thickness parameter for noncompact element
C_{w} : Warping constant, in.^{6} (mm^{6})
E: Structural steel modulus of elasticity
G: shear modulus of elasticity of steel = 11,200 ksi (77 200 MPa)
J: Torsional constant, in.^{4} (mm^{4})
L_{cz} : Effective length of the member around the z-axis (= KL)
I_{x} , I_{y} : Moment of inertia about the principal axes, in.^{4} (mm^{4})
F_{ey} : Elastic buckling stress in buckling limit state with bending around y-axis
F_{ez} : Elastic buckling stress in torsional buckling limit state z-axis
H: Flexural constant
Flexural Buckling Limit State
The buckling deformations all lie in one of the principal planes of the column cross-section. No twisting of the cross-section occurs for flexural buckling.
The limit state of flexural buckling is applicable for axially loaded columns with doubly symmetric sections, such as bars, HSS, round HSS, and I-shapes, and singly symmetric sections, such as T- and U-shapes. Flexural buckling is the simplest type of buckling.
Flexural Buckling Design with AISC 360-16
The compressive strength of the elements is determined according to the axial force acting from the section center of gravity. According to the regulation, the flexural buckling limit state is considered in all compression elements, regardless of cross-section properties.
First of all, local buckling control should be done. The calculation is made to determine whether the elements are compact or noncompact.
Flexural Buckling Members without Slender Elements
The nominal compressive strength, P_{n}, is determined based on the limit state of flexural buckling:
The critical stress, F_{cr}, is determined as follows:
When
When
Flexural Buckling Members with Slender Elements
The nominal compressive strength, P_{n}, is determined based on the limit states of flexural buckling, torsional buckling, and flexural-torsional buckling in interaction with local buckling.
Effective areas of the cross-section, A_{e}, based on reduced effective widths, b_{e}, d_{e} or h_{e}.
Critical stress, F_{cr}, is determined by limit states of Flexural Buckling or Torsional and Flexural-Torsional Buckling.
When
When
TABLE E7.1 | |||
---|---|---|---|
Case | Slender Element | c_{1} | c_{2} |
(a) | Stiffened elements except for walls of square and rectangular HSS | 0.18 | 1.31 |
(b) | Walls of square and rectangular HSS | 0.20 | 1.38 |
(c) | All other elements | 0.22 | 1.49 |
Torsional Buckling Limit State
Buckling occurs when the element rotates around its longitudinal axis. The limit state of torsional buckling applies to axially loaded columns with doubly symmetric open sections with very slender cross-sectional elements consisting of 4 corners placed back to back.
Design with AISC 360-16
The compressive strength of the elements is determined according to the axial force acting from the section center of gravity.
In the torsional buckling boundary case where buckling occurs by the rotation of the element around its longitudinal axis (+ shaped cross-section or open cross-section elements consisting of 4 corners placed back to back), the elastic buckling stress F_{e} is calculated for doubly symmetric members by equation E4.2.
The nominal compressive strength, P_{n}, is determined based on the limit states of torsional and flexural-torsional buckling:
The critical stress, F_{cr}, is determined as follows:
When
When
The torsional or flexural-torsional elastic buckling stress, F_{e}, for doubly symmetric members twisting about the shear center is determined as follows:
Flexural Torsional Buckling Limit State
The buckling deformations consist of a combination of twisting and bending about two flexural axes of the member.
The symmetry axis is the y-axis, where the buckling around the y-axis is caused by the tilting and rotation of the element around its longitudinal axis. The limit state of flexural-torsional buckling applies to columns with singly symmetric shapes, such as double angle, T- and U-shapes, and asymmetric cross-sections.
Flexural-Torsional Buckling Design with AISC 360-16
The compressive strength of the elements is determined according to the axial force acting from the section center of gravity.
With the symmetry axis being the y-axis, the elastic buckling stress F_{e} in the flexural-torsional buckling limit state where buckling around the y-axis occurs by tilting and rotating around the longitudinal axis, F_{e} equation E4-3 is calculated.
The torsional or flexural-torsional elastic buckling stress, F_{e}, for singly symmetric members twisting about the shear center where y is the axis of symmetry is determined as follows: