Stability Sample

7/25/2019 Stability Sample

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Part 1: General philosophy

2 Stability

2.1 Definition of stability

The word stability is synonymous with steadiness,poise and balance. It is a time-based characteristic

meaning resistance to change; a concept illustratedin Figure 2.1.

In the context of structural engineering a stablesystem is one that, when displaced by a smallamount, will return to its equilibrium position.Conversely, an unstable system is one which, when

displaced by a small amount, will continue to moveaway from the equilibrium position to the point whereit fails.

The European Council Construction ProductsDirective 89/106/EEC2.1 defines a building to bestable when, The loadings that are liable to act on it

during its construction and use will not lead to:(a) Collapse of the whole or part of the work.

(b) Major deformations to an inadmissible degree.(c) Damage to other parts of the works or to fittings

or installed equipment as a result of majordeformation of the loadbearing construction.

(d) Damage by an event to an extentdisproportionate to the original cause.

It should be clear from these statements that stabilityconcerns both safety and function. This Guidefocuses on statements (a), (b) and (c); meanwhilestatement (d) is the focus of the InstitutionspublicationPractical guide to structural robustness

and disproportionate collapse in buildings2.2.

2.2 Forms of instability

There are six degrees of freedom for any single pointwithin a static system: three orthogonal component

axes for linear displacements and three orthogonalcomponent axes for rotations (see Figure 2.2).

Actions and reactions must be in equilibrium in each

of the six degrees for stability to be maintained;otherwise the system is a mechanism subject to thelaws of motion.

Instability can occur in an element (local), or asub-frame or whole structure (global). Where

allowed to manifest, it would be perceived as eitherrigid body movement or deformation of the part orwhole. Overturning is a bold example of globalinstability (see Box 2.1), though each of sliding,

racking, and twisting are further lateral instabilitymodes illustrated in Figure 2.3.

It should be noted that buoyancy, uplift, slope failureand foundation settlement are each causes of globalinstability that can be attributed to vertical actions.While consideration of these is of equal importance to

the lateral modes, vertical instability is not the focusof thisGuide.

Local instability includes Euler and lateral torsionalbuckling. These modes can occur in elements of alateral load resisting system but are also more widelyapplicable to any element subject to the necessary

actions and restraint conditions.

2.3 Responsibility of design engineers

It should always be the case that one structuralengineer is responsible for the overall design of anybuilding structure, with a duty to oversee that the

designs and details of all elements and assembliescomply with the stability requirements. Thisresponsibility applies equally where some or all of thestructural design and details are developed by others,

to new buildings as well as alterations, and to bothpermanent and temporary structures.

The Institution of Structural Engineers Stability of buildings Parts 1 and 2 3

Stable Unstable

Figure 2.1 Inherently stable and unstable massing

z

y

x

Figure 2.2 Degrees of freedom


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4 Stability systems

4.1 Load paths for lateral actions

A structure is a system that transfers actions from the

point of action to points of reaction, adhering to thelaws of statics. Load paths are required for allactions (vertical and horizontal) and must be

continuous through elements and connections.

Planned load paths should be communicated in thedesign calculations, clearly illustrating the primary

systems of resistance (see Box 4.1). At least one loadpath is needed to resist each action, though many

actions will share common load paths or parts of loadpaths.

Full load paths to resist lateral forces will often

include: the facade, cladding rails, windposts, beams

and columns, horizontal stability systems, verticalstability systems, substructure and foundations, and

all connections/interfaces between these elementslisted (see Figure 4.1).

For the ultimate limit state, it is good practice toestablish simple load paths that may neglect thecontributions of redundant elements (e.g. two wallsconnected by a monolithic beam may be designed as

independent elements ignoring the coupling effect ofthe beam). This is an upper lower bound approachto modelling that allows the design to be completed

with only limited concern for each of relativestiffnesses, locked in stresses, tolerances and theconstruction sequence. It tends to result in

conservative solutions that are simple to erect androbust.

Even when planning simplified load paths the true

distribution of stresses can remain critical, at least at

the serviceability limit state. In reality, load paths willdevelop through all elements that resist movement ofthe structure and unintentional load paths can lead to

premature failure of inadequate elements. While thesefailures will seldom threaten the adequacy of thestructure (provided adequate upper lower bound

load paths have been designed), they are rarelyacceptable.

To overcome any unintentional load paths, manyvertical planar elements including partitions, glazingand cladding (each of high in-plane stiffness but low

failure strength) are often installed with connections

14 The Institution of Structural Engineers Stability of buildings Parts 1 and 2

Box 4.1 Sketching load paths

The practice of sketching load paths is recommended andwidely regarded fundamental to design, both forcommunicating and exploring/developing ideas. Load path

sketches can be global (see Figure 4.1) or narrowed down toshow a specific system or detail (see Figures 10.7 and 10.8by way of examples).

Foundations

Vertical

bracing

Horizontal bracing

Wind posts

Beams

Load

Floor slab

diaphragms

Figure 4.1 Load paths from facade to ground (shown for horizontal loads in the single axis only)


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It should be noted that the tied system shows only

tension taken in the ties. This is representative ofrecommended modelling practice (see Section 9.3)for systems where the ties are able to bow or goslack.

Figure 8.4 illustrates how braced systems arecompatible with simple foundation connectionswithout moment transfer. Uplift, shown owing to the

applied lateral forces, must be resisted by either the

permanent mass of the structure (including theweight of the foundation) or a tensile resistance of thesoil-foundation interface. Meanwhile the lateral shear

force (often concentrated through one of thecolumns) must be resisted by friction and passive soilpressure on the foundation. It is common practice to

provide a reinforced concrete ground beam acrossthe column set to ensure the shear always acts onthe more heavily loaded column, irrespective of load

direction or brace configuration. A beam will alsoprevent differential lateral movement of the columns.Ground beams are included in Figure 8.3.

While not included in Figure 8.4, local actionsshould not be overlooked. These may result fromeccentric connections (see Section 10.3) or fromactions applied directly to the constituent elements

(see Figure 8.5 by way of example). In manyinstances, they will induce moments or torsionaleffects in elements which can critically impact the

axial and shear capacities and must not beneglected.

It is not advisable to have significant actions, such asthose from a floor slab, acting on a bracing structureaway from a braced node. A situation where this may

be mistakenly overlooked is that of a braced staircore with half landing beams in the plane of thebracing (see Figure 8.6). Similar situations include

multi-storey car parks with split level slabs and foldedor pitched roofs.

8.5 Bracing angle

Bracing is most efficient where diagonal elements areinclined between 358and 508 to the horizontal. Thisensures relatively modest element forces and

compact connection details. Narrow bracing systemswith steeply inclined diagonal elements have lessflexural stiffness, increased column forces and will

increase the sway sensitivity; meanwhile widerbracing systems will increase element effectivelengths (critical to diagonal struts and unrestrainedhorizontal beams) and often result in greatereccentricity at the nodes.

Slack ties sagging

under self weight

Pinned

connections

Strut system Tied system

Note

Ties are shown slack and sagging under self weight where not subject to tension.

This is intentionally shown exaggerated.

Figure 8.4 Load path diagrams for tie and strut bracing systems (foundations not shown)

Note

The bending moment in the cladding rails is not shown.

Wind

Local wind suction

on side walls

Bending moment in

columns, loaded by

cladding rails

Figure 8.5 Local bending on facade columns coincident with bracing actions

The Institution of Structural Engineers Stability of buildings Parts 1 and 2 35

Vertical framed bracing 8.5

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