# Design with Axial Compressive Force

**SYMBOLS**

**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 as defined in Section B4.1

**λ _{r} : **Limiting the width-to-thickness ratio as defined in Table B4.1a

**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 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 (deflections) 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 and round HSS, and I-shapes and singly symmetric sections, such as T- and U-shapes. Flexural buckling is the simplest type of 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 taken into account in all compression elements, regardless of cross-section properties. The equations used for this are given below in order.

First of all, local buckling control should be done. The calculation is performed to determine whether the elements are compact or non-compact.

#### Flexural Buckling Members without Slender Elements

#### Flexural Buckling Members with Slender Elements

## Torsional Buckling Limit State

Buckling occurs when the element rotates around its longitudinal axis. The limit state of torsional buckling is applicable 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.

## 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 is applicable to columns with singly symmetric shapes, such as double angle, T- and U-shapes and asymmetric cross-sections.

### 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.

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