Cumulative tutorial 14
A frame that is allowed to yield
Ductility demand, the strength it buys, and the displacement it does not reduce.
A single-storey steel frame is designed to yield in a severe event rather than to resist it elastically. The detailing has been checked and a ductility of 3.2 is reliably available.
Establish what that buys in strength, what it costs in displacement, and how much energy the frame absorbs in doing it. The third answer is the one that explains why ductile detailing is worth its trouble; the second is the one most often forgotten.
What you are given
- Lateral stiffness 9.5 MN/m
- Yield force 420 kN
- Post-yield stiffness ratio α = 0.03
- Elastic period 0.75 s
Tutorial 14
Work the problem
4 questions
Question 1
What is the yield displacement, in millimetres?
Question 2
At a ductility demand of 3.2, what peak displacement does the frame reach, in millimetres?
Question 3
Using the equal-energy rule appropriate below the corner period, what strength reduction factor does μ = 3.2 give?
Question 4
How much energy does one full symmetric cycle at that ductility dissipate, in kJ? Use the elastic–perfectly plastic expression.
What this establishes
Strength down by a factor of 2.3; displacement unchanged at 141 mm; energy dissipation up by a factor of eighteen. The behaviour factor is a strength reduction and nothing more, and every drift-sensitive detail in the building sees no benefit from it whatever.