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Queensferry

Module 04

Analysis methods, imperfections and second-order effects

Seven analysis methods, four stability effects, and one piece of bookkeeping that decides whether the design is safe, wasteful, or wrong in a way nothing reveals.

What this module covers

  • Say what each analysis method can and cannot answer
  • Derive the moment magnification factor as a geometric series
  • Explain what αcr is and why the threshold is a calibrated judgement
  • Convert an initial sway imperfection into equivalent horizontal forces
  • Allocate each stability effect to exactly one place in the design
  • Recognise both the omission error and the double-counting error

Lessons

  1. 4.1

    Second-order effects, from first principles

    A frame leans, the vertical load acts through the lean, the frame leans further. Where that stops — and where it does not — is the whole of stability analysis.

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  2. 4.2

    Where every stability effect belongs

    Four effects, three possible homes, and two symmetrical errors that no individual calculation will ever reveal.

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Module checkpoint

Check what you have taken in

6 questions

  1. Question 1

    A frame has αcr = 6. What is the moment amplification factor?

  2. Question 2

    A frame carries 3 200 kN of vertical load and has an elastic critical load of 11 200 kN. What is αcr?

  3. Question 3

    A level carries 5 000 kN with an initial sway imperfection of 1/300. What equivalent horizontal force applies, in kN?

  4. Question 4

    A first-order sway moment of 150 kNm is found in a frame with αcr = 4. What is the design moment, in kNm?

  5. Question 5

    In the geometric series for a frame with αcr = 5, what fraction of the first-order sway does the SECOND increment add?

  6. Question 6

    A portal frame carrying gravity loads only has αcr = 7. It is analysed ELASTICALLY, where the threshold is 10. What amplification factor applies?