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The National Building Code of Canada (NBC) 2020 Article 4.1.8.7 provides a clear procedure for earthquake methods of analysis. The more advanced method, the Dynamic Analysis Procedure in Article 4.1.8.12, should be used for all structure types except those that meet the criteria set forth in 4.1.8.7. The more simplistic method, the Equivalent Static Force Procedure (ESFP) in Article 4.1.8.11, can be used for all other structures.
The response spectrum analysis is one of the most frequently used design methods in the case of earthquakes. This method has many advantages. The most important is the simplification: It simplifies the complexity of earthquakes so far that the design can be performed with reasonable effort. The disadvantage of this method is that a lot of information is lost due to this simplification. One way to moderate this disadvantage is to use the equivalent linear combination when combining the modal responses. This article explains this option by describing an example.
For the stability verification of members using the equivalent member method, it is necessary to define effective or lateral-torsional buckling lengths in order to determine a critical load for stability failure. In this article an RFEM 6-specific function is presented, by which you can assign an eccentricity to the nodal supports and thus influence the determination of the critical bending moment considered in the stability analysis.
The Steel Joist Institute (SJI) previously developed Virtual Joist tables to estimate the section properties for Open Web Steel Joists. These Virtual Joist sections are characterized as equivalent wide-flange beams which closely approximate the joist chord area, effective moment of inertia, and weight. Virtual Joists are also available in the RFEM and RSTAB cross-section database.
The stability checks for the equivalent member design according to EN 1993-1-1, AISC 360, CSA S16, and other international standards require consideration of the design length (that is, the effective length of the members). In RFEM 6, it is possible to determine the effective length manually by assigning nodal supports and effective length factors or, on the other hand, by importing it from the stability analysis. Both options will be demonstrated in this article by determining the effective length of the framed column in Image 1.
The new RFEM software generation provides the option to perform stability design of tapered timber members in line with the equivalent member method. According to this method, the design can be performed if the guidelines of DIN 1052, Section E8.4.2 for variable cross-sections are met. In various technical literature, this method is also adopted for Eurocode 5. This article demonstrates how to use the equivalent member method for a tapered roof girder.
In RF-/STEEL EC3, sets of members are calculated according to the General Method (EN 1993-1-1, Cl. 6.3.4) together with the stability analysis. To do this, it is necessary to determine the correct support conditions for the equivalent structure with four degrees of freedom. In most 3D models today, you can quickly lose track of the location of a set of members in the system.
Sections are an excellent way to display and evaluate results clearly. In the RFEM and RSTAB section dialog boxes, you can display several result types at the same time.
For the stability design of members and sets of members with a uniform cross-section, you can use the equivalent member method according to EN 1993-1-1, 6.3.1 to 6.3.3. However, as soon as a tapered cross-section is available, this method can no longer be used, or only used to a limited extent. The RF-/STEEL EC3 add-on module can automatically recognize these cases and switch to the general method.
RF-/DYNAM Pro - Equivalent Loads allows you to determine the loads due to equivalent seismic loads according to the multi‑modal response spectrum method. In the example shown here, this was done for a multi‑mass oscillator.
The National Building Code of Canada (NBC) 2015 Article 4.1.8.7 provides a clear procedure for earthquake methods of analysis. The more advanced method, the Dynamic Analysis Procedure in Article 4.1.8.12, should be used for all structure types except those that meet the criteria set forth in 4.1.8.7. The more simplistic method, the Equivalent Static Force Procedure (ESFP) in Article 4.1.8.11, can be used for all other structures.
The response spectrum analysis is one of the most frequently used design methods in the case of earthquakes. This method has many advantages. The most important is the simplification: It simplifies the complexity of an earthquake to such an extent that an analysis can be carried out with reasonable effort. The disadvantage of this method is that a lot of information is lost due to this simplification. One way to mitigate this disadvantage is to use the equivalent linear combination when combining the modal responses. This article explains this option by describing an example.
The wind load of rectangular rounded structural components is a complex matter. The equivalent forces from wind load depend on the strength of the circulating wind load and the component geometry.
In RF-DYNAM Pro - Equivalent Loads, the equivalent seismic loads can be calculated according to different standards. By calculating the equivalent loads for each eigenmode, it is not directly possible to obtain the transversal shear for each story to perform an analysis afterwards. The following example describes the option to calculate the transversal shear quickly and efficiently.
The Steel Joist Institute (SJI) previously developed Virtual Joist tables to estimate the section properties for Open Web Steel Joists. These Virtual Joist sections are characterized as equivalent wide-flange beams which closely approximate the joist chord area, effective moment of inertia, and weight. Virtual Joists are also available in the RFEM and RSTAB cross-section database.
According to EN 1993‑1‑1 [1], it is necessary to use the equivalent geometric imperfections with values that reflect the possible effects of all types of imperfections. EN 1993‑1‑1, Section 5.3, specifies basic imperfections for the global analysis of frames as well as member imperfections.
According to EN 1993-1-1 [1], it is necessary to use the equivalent geometric imperfections with values that reflect the possible effects of all types of imperfections. EN 1993-1-1, Section 5.3, specifies basic imperfections for the global analysis of frames as well as member imperfections.
As an alternative to the equivalent member method, this article describes the possibility to determine the internal forces of a wall at risk of buckling according to the second-order analysis, taking imperfections into account, and to subsequently perform the cross-section design for bending and compression.
The following article describes a design using the equivalent member method according to [1] Section 6.3.2, performed on an example of a cross-laminated timber wall susceptible to buckling described in Part 1 of this article series. The buckling analysis will be performed as a compressive stress analysis with reduced compressive strength. For this, the instability factor kc is determined, which depends primarily on the component slenderness and the support type.
Pushover analysis is a nonlinear structural calculation for seismic analysis of structures. The load pattern is inferred from the dynamic calculation of equivalent loads. These loads are increased incrementally until global failure of the structure occurs. The nonlinear behaviour of a building is usually represented by using plastic hinges.
In RF-/DYNAM Pro – Equivalent Loads, a signed result option in accordance with the dominant eigenmode has been available since version X.06.3039. For the modal combination of results corresponding to the single eigenvalues, a quadratic combination rule has to be used. In RFEM and RSTAB, the SRSS and the CQC rule are available. Only results, not loads, are allowed to be combined directly. The reason is the mode shapes, which are arbitrarily scaled and signed.
In RF‑/DYNAM Pro – Equivalent Loads the CQC (Complete Quadratic Combination) rule has been available since version X.06.3039.
When performing the stability analysis of members according to the equivalent member method, considering internal forces according to the linear static analysis, it is very important to determine the governing equivalent member lengths.
In the DYNAM Pro add‑on module for RSTAB, you can now neglect masses that may have a negative effect on the equivalent mass factor when calculating eigenvalues. To do this, you can disable the masses under [Details]. These include primarily mass points located in the support of the structures.
The stability analysis of the steel frame described in my previous post can also be performed in RF‑/FE‑LTB according to the Equivalent Imperfection Method. This post describes how to calculate or determine the critical load factor.
Result combinations exported from RF‑/DYNAM Pro – Equivalent Loads are generated by superimposing the results from the individual modal responses. For this, the SRSS rule can be used as "equivalent linear combination". When result combinations are used in RF‑/STEEL, two options are available for calculating stresses. In the first option, the results from the result combinations are used directly. This is done line by line, for each maximum and minimum controlling internal force. In the second option, stresses are determined from the individual load cases. The quadratic superposition rule is then performed again in RF-/STEEL.
Damage equivalent factors depend on the respective components to be designed in RF‑/STEEL Fatigue Members, and they are explained in the corresponding standards. The following list shows an overview of the standards describing the calculation of the damage equivalent factors in detail.
When accidental torsion is considered in the RF-/DYNAM Pro - Equivalent Loads module, the module exports two load cases for each eigenvalue: one with positive torsional moment, the other with negative torsional moment. The generated equivalent loads themselves do not differ in these two load cases.
The modal results of a response spectrum analysis are combined with quadratic combination rules, and in RF‑/DYNAM Pro, the SRSS and the CQC rules are available. The default setting modifies the quadratic expressions into equivalent linear combinations. The advantage of this option is that the corresponding internal forces keep their signs and are often much smaller, compared to the standard SRSS or CQC rules. The standard SRSS and CQC rules are on the conservative side and the "equivalent linear combinations" are recommended.
With the latest version of RF‑/DYNAM Pro, you can exclude the mode shapes from the seismic design. In most standards, there are provisions to exclude the effective modal mass factors that are too small. The "Mode Shapes" tab offers the option to specify the factor and to disregard the mode shapes automatically.