Skip to content
Queensferry

Module 09

Beam-columns and frame stability

Almost every real column carries moment as well as axial force, and the two do not simply add. The axial force bends the member further, and the same effect scales up to whole frames — where it becomes a question about stiffness, not strength.

What this module covers

  • Explain why a member under N and M is worse than the sum of the two checks
  • Derive the amplification factor 1/(1 − N/Ncr) and say what it does not depend on
  • Distinguish cross-section interaction, member amplification and the code's interaction factors
  • Calculate αcr for a storey from its drift, and say what it means physically
  • Apply the amplified sway method to the right moments and not to the wrong ones
  • Say what to change when a frame is too flexible, and by how much

Lessons

  1. 9.1

    Why N and M do not simply add

    The axial force does not just eat into the moment capacity. It also increases the moment — and that second effect is the one people miss.

    Start lesson →
  2. 9.2

    Frame stability, and which moments get amplified

    The same effect at the scale of a whole frame. It turns into a question about lateral stiffness — and about which moments the amplifier is allowed to touch.

    Start lesson →

Module checkpoint

Check what you have taken in

8 questions

  1. Question 1

    A member has NEd = 600 kN and Ncr = 2400 kN in the plane of bending. What is the amplification factor?

  2. Question 2

    A first-order moment of 80 kNm sits on that member, with Cm = 1.0. What design moment does the amplification give, in kNm?

  3. Question 3

    A storey 3.5 m high carries VEd = 3000 kN and sways 14 mm under a horizontal force of 120 kN. What is αcr?

  4. Question 4

    A storey has αcr = 5. By what factor are its sway moments amplified?

  5. Question 5

    At what value of N/Ncr does the amplification factor reach 1.25?

  6. Question 6

    A storey has αcr = 5 and drifts 40 mm. What drift is needed for αcr = 10, in mm?

  7. Question 7

    Which quantity drives the second-order amplification of a beam-column's moment?

  8. Question 8

    A frame is analysed with a genuine second-order analysis that includes the sway imperfections. The sway moments are then amplified by 1/(1 − 1/αcr). What is wrong?