classification
Steel columns can be divided into solid web columns and lattice columns according to the section form (Figure 1). The solid web column has an overall section (Figure 2a), and the most commonly used is I-shaped section; The section of lattice column is divided into two or more limbs, and each limb is connected by batten strips or batten plates (Figure 2b). When the load is large and the column body is wide, the steel consumption is less. Steel columns can generally be divided into axial compression columns and eccentric compression columns according to the stress conditions. The longitudinal pressure on the axially compressed column coincides with the centroidal axis of the column section. Eccentric compression columns bear both axial pressure and bending moment, also known as compression bending members.
design calculation
The steel column section shall meet the requirements of strength, stability and slenderness ratio, and each component of the section shall also meet the requirements of local stability. The maximum compressive or tensile normal stress of strength column shall not exceed the design strength of steel. For axially compressed columns, the axial pressure causes uniform compressive normal stress in the section; For eccentrically compressed columns, due to the effect of bending moment, uneven normal stress is generated in the section. Generally, the outermost fiber stress on the eccentric side of the section is the maximum compressive stress, and the outermost fiber stress on the other side is the minimum compressive stress. When the bending moment is large, the maximum tensile stress may occur.
Stability of axial compression columns with solid web
When a solid web column is axially compressed, when the pressure increases to a certain value, the column will suddenly bend from the linear equilibrium state to the side with less stiffness, and sometimes sudden torsion, or both bending and torsion may occur; If the pressure is slightly increased, then the bending, torsion or bending torsion deformation will rapidly increase, so that the column will lose its bearing capacity, which is called the overall loss of stability of the column, and according to its instability deformation, it is called bending instability, torsional instability or bending torsion instability (Figure 3). The minimum axial pressure that causes the column to lose stability is called critical force.
The stress obtained by dividing the critical force by the gross section area is called the critical stress. The critical stress is often lower than the yield point of steel, that is, the column will lose stability before reaching the ultimate strength state. The ratio of critical stress to yield point is called the stability coefficient of axially compressed column. In the three cases of axial compression column losing stability, the most common is bending instability (Figure 3a).
The main factor affecting the critical stress of column buckling is the slenderness ratio of the column, that is, the ratio of the calculated length of the column to the radius of gyration of the section. For a given steel, the longer or thinner the column, that is, the greater the slenderness ratio, the smaller the critical stress, and the more prone to buckling. When the slenderness ratio of the column in the x and y directions of the two main axes is not equal, its bending instability always occurs in the direction of weak stiffness, that is, large slenderness ratio (see the basic theory of columns). When a steel column has an open section and a small section wall thickness, torsional instability or flexural torsional instability may occur under axial pressure due to the poor torsional stiffness of the section. When the section is biaxial symmetry (such as cross section) or point symmetry (such as Z-section), the centroidal axis of the axial pressure coincides with the shear central axis. When the length of the column is small, torsional instability may occur (Figure 3b); When the section is uniaxially symmetric (such as slot shaped or T-shaped section), the centroidal axis where the axial pressure is located does not coincide with the shear central axis, and the column may suffer from bending torsional instability (Figure 3c); When the section has no symmetry axis, the instability of the column under axial pressure is generally flexural torsional instability. The critical stress of torsional instability and flexural torsional instability is related to the section form and size of the column, torsional stiffness and flexural stiffness, column length and support conditions.
The smaller the wall thickness of the open thin-walled section is, the smaller the torsional stiffness is, and the more prone to torsion. Steel columns used in engineering often have defects, such as the residual stress of the section caused by uneven heating and cooling during steel hot rolling and structural welding, manufacturing deviation such as initial bending of components, and installation deviation such as initial eccentricity of component connection. These defects will reduce the critical stress and stability coefficient. For steel columns with different sections, the reduction of stability coefficient is different. The stability calculation formula of axial compression column is σ ＝ N/A ≤ φ f, where σ is the compressive stress of gross section; N is the axial pressure; A is the gross sectional area; φ is the stability coefficient; F is the design strength.
Stability of eccentric compression columns with solid webs
Eccentric compression columns bear both axial pressure and bending moment. Because of the action of bending moment, the column has bending deformation at the beginning in the action plane of bending moment. If the axial pressure and bending moment increase gradually at the same time, the bending deformation also increases gradually. However, when the load increases to a certain size, even if the load remains unchanged or even gradually decreases, the deformation will continue to increase rapidly. At this time, the column has lost its bearing capacity. This phenomenon is called the instability of eccentrically compressed columns in the bending moment action plane (Figure 3d), which belongs to bending instability. If the lateral stiffness of the column is small and the lateral support is poor, when the load increases to a certain size, the column may also suddenly bend outward from its original plane in the lateral direction, and at the same time, torsion will occur, and then the bending torsion deformation will rapidly increase, so that the column will lose its bearing capacity. This phenomenon is called the loss of stability of the eccentrically compressed column outside the bending moment action plane (Figure 3e), It belongs to flexural torsional instability.
Stability of the eccentrically compressed columns in and out of the bending moment plane is not only related to slenderness ratio of the columns, but also depends on eccentricity. Eccentricity is usually measured by eccentricity (the ratio of eccentricity to section core distance). For a given steel and column section form, the greater the slenderness ratio and eccentricity of the column, the lower the critical average compressive stress when the column is unstable, that is, the more vulnerable the column is to instability.
Allowable slenderness ratio
The slenderness ratio of a column is a sign to measure the stiffness of the column. Too large slenderness ratio is not only detrimental to the stability of the column, but also makes the column prone to bending during transportation and installation, and prone to vibration under dynamic load during service life. Therefore, the allowable slenderness ratio of the column shall be specified in the design, usually 150.
Local stability of solid web column
When the thickness of the web, flange plate or other components of a solid web column is relatively small, local buckling may occur under a small load before the column loses its overall stability, that is, the compressed web or flange plate deviates from its original plane position, resulting in wavy buckling, which is called column loss of local stability. After the local loss of stability of the column, the stress condition of the column will deteriorate, which may lead to the early loss of the overall stability of the column. In order to ensure sufficient local stability of each component of the steel column, the width thickness ratio is usually limited to a certain value according to the stress and support of the plate. The calculation of lattice column shall also calculate the strength, stability, slenderness ratio limit and the stability of each single limb and component of lattice column; The calculation method is similar to that of solid web column.
However, the shear stiffness of the batten or batten plate system in the lattice column is much worse than that of the web of the solid web column. When the column is buckling around the imaginary axis (the axis intersecting the batten or batten plate plane in the section, Figure 2), in addition to bending deformation, the column will also have considerable shear deformation. The role of batten strip and batten plate is to connect the column limb of lattice column into a whole, to ensure that each column limb bears the force together, and to bear the shear force perpendicular to the virtual axis of the column. The lacing and column limb constitute a plane truss system. Under the shear force of the column, the lacing and column limb will only bear the axial force, and the stiffness is generally large. The batten plate and column limb constitute a multi-layer plane rigid frame system. Under the shear force of the column, the batten plate and column limb will bear bending moment and shear force.
Diaphragm
In order to meet the stress requirements, ensure that the geometric shape of the column section remains unchanged and increase the torsional stiffness of the column, diaphragms should be set at the places where the steel column is subjected to large horizontal forces and at the ends and middle of each transport unit. The diaphragm can be made of steel plate or angle steel. Column base and anchor bolt column base are column components that transmit the load on the column shaft to the foundation.
The column base not only fixes the column to the foundation, but also plays a role in transmitting and distributing loads. The column base is generally composed of bottom plate and shoe beam; When the column body is small, the boot beam can also be omitted; When the column body is large and the bottom plate is wide, in order to strengthen the stiffness of the bottom plate and reduce its bending moment and thickness, it is also necessary to properly arrange diaphragms or rib plates. The anchor bolt is a connector that fixes the column to the foundation. For axially compressed columns and eccentrically compressed columns with small bending moments, anchor bolts are used as installation and fixing positions. Generally, two anchor bolts are used according to the structure, with a diameter of 20~30mm. For eccentrically compressed columns with large bending moment, the anchor bolt should also resist the bending moment transmitted from the column body; When the anchor bolt is under tension, its diameter and number shall be calculated and determined according to the maximum bending moment and minimum axial pressure at the bottom of the column. [1]
