D14.B.6 Member Resistances
D14.B.6.2 Axial Compression
The compressive resistance of columns is determined based on Clause 13.3 of the code. The equations presented in this section of the code assume that the compressive resistance is a function of the compressive strength of the gross section (Gross section Area times the Yield Strength) as well as the slenderness factor (KL/r ratios). The effective length for the calculation of compression resistance may be provided through the use of the parameters KX, KY, KZ, LX, LY, and LZ (see D14.B.7 Design Parameters). Some of the aspects of the axial compression capacity calculations are:
For frame members not subjected to any bending, and for truss members, the axial compression capacity in general column flexural buckling is calculated from Cl.13.3.1 using the slenderness ratios for the local Y-Y and Z-Z axis. The parameters KY, LY, KZ, and LZ are applicable for this.
For single angles, asymmetric or cruciform sections are checked as to whether torsional-flexural buckling is critical. But for KL/r ratio exceeding 50,as torsional flexural buckling is not critical, the axial compression capacities are calculated by using Cl.13.3. The reason for this is that the South African code doesn’t provide any clear guidelines for calculating this value. The parameters KY, LY, KZ, and LZ are applicable for this.
The axial compression capacity is also calculated by taking flexural-torsional buckling into account. Parameters KX and LX may be used to provide the effective length factor and effective length value for flexural-torsional buckling. Flexural-torsional buckling capacity is computed for single channels, single angles, Tees and Double angles.
While computing the general column flexural buckling capacity of sections with axial compression + bending, the special provisions of 13.8.1(a), 13.8.1(b) and 13.8.1(c) are applied. For example, Lambda = 0 for 13.8.1(a), K=1 for 13.8.1(b), etc.)
The laterally unsupported length of the compression flange for the purpose of computing the factored moment resistance is specified in STAAD with the help of the parameter UNL. If UNL is less than one tenth the member length (member length is the distance between the joints of the member), the member is treated as being continuously laterally supported. In this case, the moment resistance is computed from Clause 13.5 of the code. If UNL is greater than or equal to one-tenth the member length, its value is used as the laterally unsupported length. The equations of Clause 13.6 of the code are used to arrive at the moment of resistance of laterally unsupported members. Some of the aspects of the bending capacity calculations are:
The weak axis bending capacity of all sections except single angles is calculated as:
For Class 1 & 2 sections
For Class 3 sections
- Phi = Resistance factor = 0.9
- Py = Plastic section modulus about the local Y axis
- Sy = Elastic section modulus about the local Y axis
- Fy = Yield stress of steel
Single angles sections are not designed by STAAD, as the South African code doesn’t provide any clear guidelines for calculating this value.
For calculating the bending capacity about the Z-Z axis of singly symmetric shapes such as Tees and Double angles, SAB0162-1: 1993 stipulates in Clause 13.6(b), page 31, that a rational method.
D14.B.6.4 Axial compression and bending
The member strength for sections subjected to axial compression and uniaxial or biaxial bending is obtained through the use of interaction equations. In these equations, the additional bending caused by the action of the axial load is accounted for by using amplification factors. Clause 13.8 of the code provides the equations for this purpose. If the summation of the left hand side of these equations exceeds 1.0 or the allowable value provided using the RATIO parameter (see D14.B.7 Design Parameters), the member is considered to have FAILed under the loading condition.
D14.B.6.5 Axial tension and bending
Members subjected to axial tension and bending are also designed using interaction equations. Clause 13.9 of the code is used to perform these checks. The actual RATIO is determined as the value of the left hand side of the critical equation.
The shear resistance of the cross section is determined using the equations of Clause 13.4 of the code. Once this is obtained, the ratio of the shear force acting on the cross section to the shear resistance of the section is calculated. If any of the ratios (for both local Y & Z axes) exceed 1.0 or the allowable value provided using the RATIO parameter (see D14.B.7 Design Parameters), the section is considered to have failed under shear. The code also requires that the slenderness ratio of the web be within a certain limit (See Cl.188.8.131.52, page 29 of SABS 0162-1:1993). Checks for safety in shear are performed only if this value is within the allowable limit. Users may by-pass this limitation by specifying a value of 2.0 for the MAIN parameter.