📄 Elastic Critical Load Factor Buckling Analysis in MasterPort

Elastic Critical Load Factor Buckling Analysis in MasterPort

The Elastic Critical Load Factor (αcr or Alpha Crit) in MasterPort is a stability check used to assess the frame's sensitivity to second-order effects (deformed geometry). This check determines whether a first-order analysis is sufficient or if the structure requires a second-order (P-Delta) analysis to account for sway effects.

Calculation Methods

The Elastic Critical load factor in MasterPort can be assessed either by the sway deflection method or by a Buckling Analysis. In both cases we are exclusively interested in the main portal frame in-plane Elastic Critical load factor value.  

  1. Sway Deflection Method (Approximate): This uses the Equivalent Horizontal Notational Loads (EHNL) method. When using the sway deflection method for Elastic Critical load factor, the EHNL (equivalent horizontal notational loads) are only applied in the plane of the portal frame, therefore automatically excluding the out of plane assessment. 
  2. Buckling Analysis: This uses the MasterFrame analysis engine. However, MasterPort treats this as a special case to prevent the analysis from returning critical modes related to out-of-plane buckling (e.g., a rafter buckling laterally), which are typically restrained by purlins and rails but might not be fully physically modelled as restraints during the analysis phase. Out of plane buckling is generally of no concern as the portal frame members are typically laterally restrained by purlins/side rails.

MasterPort Specific Behaviour

When determining αcr via Buckling Analysis in MasterPort, the geometric stiffness matrix components are modified only for the major axis of main portal frame members (Rafters, Columns, Lean-To Beams, Props, Mezzanine members). This ensures the analysis focuses exclusively on the in-plane Elastic Critical load factor of the main frame. All other members are excluded from this specific buckling stiffness modification.

Note: This differs from the standard MasterFrame environment, where all members in both major and minor axes are considered in the buckling analysis, potentially requiring the manual modelling of lateral restraint members to achieve accurate results.

Interpretation and SCI Guidance

The resulting αcr value dictates the analysis requirements based on best practice and safety standards.

  • Elastic Analysis: If αcr < 10$, the influence of deformed geometry is significant, and you must account for this by enabling P-Delta analysis or using amplified moments,.
  • Plastic Analysis: Based on SCI guidance, for plastically designed frames subject only to gravity loads, second-order effects can typically be ignored if αcr≥5. If αcr<5, second-order analysis is required.

Important: While MasterSeries provides these calculated factors, users must refer to SCI P292 / P399 (or current relevant SCI guidance) independently to fully understand the derivation of these limits and ensure the structure complies with the specific clauses regarding frame stability and pattern loading sensitivity.

Application and Refinement

  • Automatic Briefs: Upon entering the design module, an Elastic Critical Load Factor check is automatically applied to all members.
  • Excluding Members: Occasionally, minor members (e.g., parapet posts or canopies) may return a low αcr value that does not reflect the overall stability of the main building. You can manually exclude these members from the check by selecting the "Elastic Critical Load Factor" brief and clicking on the members you wish to omit.
  • P-Delta: If your frame returns an αcr below the critical limits (e.g., < 10), you should return to the General tab in the Editor and enable P-Delta Analysis for the critical load cases,.

When determining the Elastic Critical load factor by the alternative buckling analysis, at the analysis stage the presence of the lateral restraints may be be fully represented as these are specified at design time. Therefore, with consider the general buckling analysis approach may produce a more critical out of plane buckling mode. When using MasterPort, to circumvent this problem we treat this as a special case, in that the geometric stiffness matrix components are only modified for the major axis of main portal frame rafters, columns and beams. These are the members that have the following naming member attribute  applied

  • UT (Rafter...
  • UT (Column...
  • UT (Lean-To Beam...
  • UT (Lean-To Column...
  • UT (Prop...
  • UT (Mezzanine...

These names are applied automatically by MasterPort, however when outside the simplified interface they can be edited, which would potentially will affect if the members qualify for buckling stiffness adjustments. All other members are excluded from the buckling stiffness modification. 

If using MasterFrame, no such consideration is made and all members in both major and minor axis are considered in the buckling analysis, ignoring any design time lateral restraint. In such cases it would be common for engineers to include at least some lateral restraints member in the model to accommodate for this restraint.