📄 Steel frames - Plastic Analysis and Design
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Steel frames - Plastic Analysis and Design

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MasterFrame Plastic Analysis and Design workflow

In most cases, it is not logical to begin by assigning plastic hinges before an initial elastic analysis and design has been carried out. The engineer should first understand the elastic behaviour of the frame, then introduce plastic redistribution in a controlled way with a clear understanding of the intended mechanism.

The normal design work flow in MasterFrame would be to:

  1. Analyse and design the frame elastically first
    Begin with a normal elastic analysis and design check to establish sensible initial section sizes based on the elastic moment distribution.
  2. Review the elastic behaviour of the structure
    Examine the moment diagram, utilisation ratios, and general force distribution to identify whether limited plastic redistribution i.e. allowing plastic hinges to form at certain location will redistribute moment in such a fashion as to better utilise material to lead to a more efficient design.
  3. Decide where plastic redistribution may be beneficial
    Based on engineering judgement, identify the locations where a plastic hinge could form in a stable and meaningful way. The aim is usually to limit peak moments in highly stressed areas and encourage redistribution to parts of the frame with spare capacity.
    1. Example, in a typical portal frame (assuming a reasonable rafter pitch) the eaves moment is often significantly higher than the apex moment, so controlled hinge formation may help shift moment into less highly stressed regions. e.g. allowing a plastic hinge to form in the column (by over stressing/undersizing the column) limits the moment in both the column and eaves end of the rafter, forcing moment redistribution toward the apex, and better utilising the rafter section.
  5. Adjust member sizes to create the intended elastic overstress
    If redistribution is desired, modify the relevant section sizes so that the chosen locations are capable of reaching their plastic resistance and forming hinges under the applied loading.
  6. Define the plastic hinge locations in MasterFrame
    Back in MasterFrame place the potential plastic hinges at the intended positions. Then activate the 'plastic analysis option' for the required loadcases (described in more detail below).
  7. Reanalyse the frame using plastic analysis
    Reanalyse and check from the graphical output if the desired plastic hinges and plastic mechanism has formed, and that the resulting plastic mechanism is the one expected.
  8. Check the load factor and overall behaviour
    Within the Graphical Analysis Results > Plastic Hinges Tab, confirm that hinge formation is not occurring at an unreasonably low load factor, as this may indicate excessive overstress, excessive hinge rotation, or an unrealistic mechanism. Although design codes do not generally specify strict limits for this, very low plastic collapse factors may lead to serviceability concerns or difficulties when second-order effects such as P-Delta are considered.
  9. Recheck the member design
    Once the plastic analysis behaviour is understood, carry out the steel design check again using the revised force distribution.
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It's important to note the plastic analysis must always be a lower bound (i.e. stable) mechanism. If too many plastic hinge are placed and form, if this leads to an unstable upper bound plastic plastic mechanism, the analysis will not complete due to this instability.


Placing potential plastic hinges and activating load case Plastic Analysis

  1. In MasterFrame firstly go to Restraints (menu)> Potential Plastic Hinges.
    • Here you can place potential plastic hinges, i.e. the locations in you model where you allow a plastic hinge to for form if the class 1 steel section experiences moment above it's plastic capacity during the analysis of the load cases.
  3. You must have a node in the member at the location where you want the hinge to potentially form. For this you can the Modify Geometry> Split Member, with the 'Insert analytical node only' box checked
  4. The hinge is placed in a similar way to end releases in that you are clicking near the end of a member. THe hinge placement will depend on they type of plastic mechanism you wish to allow. In this example, we are splitting
    1. Column at the under side of the eaves haunch
    2. Rafter at the end of the eaves haunch

  6. Enter the Analysis > Second Order Analysis per Load Case to bring up Analysis options for each load case.

    1. The 'Plastic Analysis' option can be activated on a load case by load case basis by clicking on the 'Include Plastic Analysis' option.

    2. The 'Find Plastic load factor' is optional, and will determine the factor by which the load case loads need to be increased to produce a plastic collapse mechanism.

    3. You can use the 'Apply' button to quickly activate plastic analysis on multiple load cases in one action.

Viewing load case Plastic Hinges formed

Following your analysis you can determine if any plastic hinges have formed and at what load factor from the 'Results (menu)' Graphical analysis results.