The Chartership Forum

Structural Steel Design / Multi-storey steel buildings

Lateral stability: comparing four systems

Compare lateral stiffness, connection demands and space requirements using four illustrative stability systems.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

  • Ratio examples distinguish braced-frame and core baselines; illustrative ratios no longer presented as transferable structural properties, and ductility is not assigned solely by system label.

Checks needed for project use

  • A steel-design reviewer must check the first-generation calculation profiles, second-order analysis assumptions, connection rules and execution references against the applicable standards and amendments.
  • Actual geometry, cracked stiffness, connection behaviour, lateral analysis and applicable global stability criterion.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

The lateral system must provide stiffness and resistance while fitting the building layout. Braces use axial action, moment frames use bending, and cores act as vertical cantilevers. Compare actual geometries, connections, foundations and construction sequences before ranking the options.

By the end of this lesson you should be able to

  • Describe the four common lateral systems and how each resists sway
  • Compare them on stiffness, cost and plan freedom
  • Say why a braced bay is so much more efficient
  • Say when a moment frame or an eccentric brace is nevertheless right

What you should already know

  • Frame stability, αcr and the amplified sway method (Module 9)
  • Joint stiffness and classification (Modules 3 and 13)
  • Base fixity (Module 14)

Four lateral systems

A concentric brace develops an axial force; its horizontal stiffness depends on EA/L and the square of the horizontal direction cosine. A moment frame develops beam and column bending and depends on joint and base stiffness. A concrete core depends on wall geometry, cracking, openings and foundation rotation. An eccentric braced frame relies on a deliberately designed yielding link and capacity-protected surrounding members.

For the arithmetic exercise below, assume relative stiffnesses of 1.0, 0.15, 2.5 and 0.6, and relative costs of 1.0, 2.5, 0.6 and 1.4 respectively. These invented comparison inputs are not published system properties. Ductility requires appropriate detailing in every system.

Try it

Four systems, compared on the terms that decide

Relative lateral stiffness for each system, with the two you are comparing highlighted. The readout gives what each costs in the other's currency — including what it does to αcr.

System A

System B

12.5
Relative lateral stiffness of the four systemsbraced bay1.00moment frame0.15concrete core2.50eccentric bracing0.60green = A · red = B · bar length is relative lateral stiffnessstiffness per unit cost, A over B: 16.7
A relative stiffness
1.00
B relative stiffness
0.15
Stiffness ratio
6.67 ×
Cost ratio
0.40 ×
Stiffness per unit cost
16.7 ×
A obstructs the plan
yes
B obstructs the plan
no
A is ductile
no
B is ductile
yes
αcr with A
12.5
αcr with B
1.9
Second-order needed with A
no
Second-order needed with B
YES

A braced bay is 6.7 times stiffer than a moment frame and 2.5 times cheaper — 16.7 times the stiffness per unit cost. But one obstructs the floor plate and the other does not, and on a letting plan that is frequently the whole argument.

Things worth trying

  • Start with braced bay against moment frame. 6.7 times the stiffness at 0.4 times the cost — nearly 17 times the stiffness per unit cost, which is not a marginal preference.
  • Now look at the αcr rows. A building at 12.5 on a braced bay would be at 1.9 on a moment frame: second-order effects need careful assessment for the moment-frame model.
  • That factor of six is why the stability system is chosen before anything else. Every member depends on αcr, and αcr depends almost entirely on this choice.
  • Compare the concrete core with the braced bay. The core is stiffer AND cheaper, because it is already being built for the lifts — 4.2 times the stiffness per unit cost.
  • But look at the note: it fixes the stability system's position at the design's earliest stage and has to be built ahead of the steel. The cost is programme, not material.
  • Compare eccentric with concentric bracing. The eccentric option is less stiff and dearer, and it is chosen anyway where energy dissipation matters — the link beam is a designed fuse.
  • Look at the 'obstructs the plan' rows for the braced bay. That single yes is why the best engineering answer is regularly rejected, and why braced bays end up round lift cores.
  • Drop the base αcr to 6 and compare again. On a marginal building the choice stops being economic and becomes a question of whether the frame stands up at all.

Worked example

Choosing a stability system for the ten-storey office

Given

  • The building from the last lesson: ten storeys, 1200 m² per floor, 3.5 m storey height
  • A central core containing lifts and stairs, 8 m × 6 m in plan
  • The client requires clear, column-free letting floors outside the core zone
  • Total vertical load at the lowest storey 21 000 kN; wind 900 kN at that level
  • Assume the trial arrangement is the reference braced-bay system: storey drift under the stated wind is 12 mm. This fixes the stiffness-ratio baseline.

Find

Compare illustrative stiffness scenarios; identify the checks required before selecting a stability system.

Assumptions

  • Relative stiffness and cost figures are invented arithmetic inputs, not engineering recommendations.
  • The αcr threshold is calibrated and unverified here
  • The core is assumed available for stability — a programme assumption as much as a structural one

    Practice

    A braced bay has relative stiffness 1.0 at relative cost 1.0; a moment frame has 0.15 at 2.5. How many times more stiffness per unit cost does the braced bay give?

    Practice

    A storey carries V = 21 000 kN, is 3.5 m high, and drifts 12 mm under a horizontal load of 900 kN. What is αcr?

    Practice

    That building is rebuilt on a moment frame with 0.15 times the lateral stiffness. What is αcr now?

    Practice

    A concrete core has relative stiffness 2.5 at relative cost 0.6. How many times the stiffness per unit cost of a braced bay is that?

    Check yourself

    Why can a suitably arranged brace provide high lateral stiffness?

    Summary

    • Four systems: concrete core, braced bay, eccentric bracing, moment frame
    • Bracing uses axial action; a moment frame relies on bending and joint stiffness.
    • The exercise assumes a 6.67 stiffness ratio; it does not establish one for real systems.
    • And it is rejected whenever the floor plate must stay clear
    • So braced bays cluster round cores and stairs, where the plan is obstructed anyway
    • A core requires its own structural and cost assessment.
    • The reference braced-bay model gives αcr = 12.5; the assumed moment-frame scenario gives 1.875.
    • So the stability system is chosen FIRST, because everything else follows from αcr