Black plate (3,1) 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 illustrated in Figure 2.1. In the context of structural engineering a stable system is one that, when displaced by a small amount, will return to its equilibrium position. Conversely, an unstable system is one which, when displaced by a small amount, will continue to move away from the equilibrium position to the point where it fails. The European Council Construction Products Directive 89/106/EEC2.1 defines a building to be stable 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 major deformation of the loadbearing construction. (d) Damage by an event to an extent disproportionate to the original cause.’’ It should be clear from these statements that stability concerns both safety and function. This Guide focuses on statements (a), (b) and (c); meanwhile statement (d) is the focus of the Institution’s publication Practical guide to structural robustness and disproportionate collapse in buildings2.2. 2.2 Forms of instability There are six degrees of freedom for any single point within a static system: three orthogonal component axes for linear displacements and three orthogonal component 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 the laws of motion. Instability can occur in an element (‘local’), or a sub-frame or whole structure (‘global’). Where allowed to manifest, it would be perceived as either rigid body movement or deformation of the part or whole. Overturning is a bold example of global instability (see Box 2.1), though each of sliding, racking, and twisting are further lateral instability modes illustrated in Figure 2.3. It should be noted that buoyancy, uplift, slope failure and foundation settlement are each causes of global instability that can be attributed to vertical actions. While consideration of these is of equal importance to the lateral modes, vertical instability is not the focus of this Guide. Local instability includes Euler and lateral torsional buckling. These modes can occur in elements of a lateral load resisting system but are also more widely applicable 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 structural engineer is responsible for the overall design of any building structure, with a duty to oversee that the designs and details of all elements and assemblies comply with the stability requirements. This responsibility applies equally where some or all of the structural design and details are developed by others, to new buildings as well as alterations, and to both permanent and temporary structures. z y Stable x Unstable Figure 2.1 Inherently stable and unstable massing Figure 2.2 Degrees of freedom The Institution of Structural Engineers Stability of buildings Parts 1 and 2 3 and Box 4.1 Load paths from fac¸ade to ground (shown for horizontal loads in the single axis only) 14 The Institution of Structural Engineers Stability of buildings Parts 1 and 2 . clearly illustrating the primary systems of resistance (see Box 4. at least at the serviceability limit state. locked in stresses. horizontal stability systems.8 by way of examples).1).1) or narrowed down to show a specific system or detail (see Figures 10. While these failures will seldom threaten the adequacy of the structure (provided adequate ‘upper lower bound’ load paths have been designed). though many actions will share common load paths or parts of load paths. ‘Load paths’ are required for all actions (vertical and horizontal) and must be continuous through elements and connections. Even when planning simplified load paths the true distribution of stresses can remain critical. load paths will develop through all elements that resist movement of the structure and unintentional load paths can lead to premature failure of inadequate elements. Load path sketches can be global (see Figure 4. tolerances and the construction sequence. beams and columns. This is an ‘upper lower bound’ approach to modelling that allows the design to be completed with only limited concern for each of relative stiffnesses. windposts. substructure and foundations.1) 4 Stability systems 4. Horizontal bracing all connections/interfaces between these elements listed (see Figure 4. it is good practice to establish simple load paths that may neglect the contributions of redundant elements (e. both for communicating and exploring/developing ideas. adhering to the laws of statics. many vertical planar elements including partitions.g. For the ultimate limit state. To overcome any unintentional load paths. It tends to result in conservative solutions that are simple to erect and robust. Planned load paths should be communicated in the design calculations. they are rarely acceptable. In reality. vertical stability systems.1 Sketching load paths The practice of sketching load paths is recommended and widely regarded fundamental to design. Full load paths to resist lateral forces will often include: the fac¸ade. two walls connected by a monolithic beam may be designed as independent elements ignoring the coupling effect of the beam).Black plate (14. cladding rails. At least one load path is needed to resist each action. glazing and cladding (each of high in-plane stiffness but low failure strength) are often installed with connections Beams Wind posts Floor slab diaphragms Vertical bracing Load Foundations Figure 4.7 and 10.1 Load paths for lateral actions A structure is a system that transfers actions from the point of action to points of reaction.1). In many instances.5 Wind Bending moment in columns.5 Slack ties sagging under self weight Figure 8.5 Local bending on fac¸ade columns coincident with bracing actions The Institution of Structural Engineers Stability of buildings Parts 1 and 2 35 .Black plate (35. Figure 8. such as those from a floor slab. meanwhile wider bracing systems will increase element effective lengths (critical to diagonal struts and unrestrained horizontal beams) and often result in greater eccentricity at the nodes. It is common practice to provide a reinforced concrete ground beam across the column set to ensure the shear always acts on the more heavily loaded column. These may result from eccentric connections (see Section 10. they will induce moments or torsional effects in elements which can critically impact the axial and shear capacities and must not be neglected. Narrow bracing systems with steeply inclined diagonal elements have less flexural stiffness. Ground beams are included in Figure 8. must be resisted by either the permanent mass of the structure (including the weight of the foundation) or a tensile resistance of the soil-foundation interface. shown owing to the applied lateral forces. 8.3) or from actions applied directly to the constituent elements (see Figure 8.3. increased column forces and will increase the sway sensitivity.4 illustrates how braced systems are compatible with simple foundation connections without moment transfer. loaded by cladding rails Bracing angle Bracing is most efficient where diagonal elements are inclined between 358 and 508 to the horizontal.1) Vertical framed bracing It should be noted that the tied system shows only tension taken in the ties. A situation where this may be mistakenly overlooked is that of a braced stair core with half landing beams in the plane of the bracing (see Figure 8. A beam will also prevent differential lateral movement of the columns.3) for systems where the ties are able to bow or go slack. Similar situations include multi-storey car parks with split level slabs and folded or pitched roofs. This is representative of recommended modelling practice (see Section 9. Local wind suction on side walls Note The bending moment in the cladding rails is not shown. Pinned connections 8. This ensures relatively modest element forces and compact connection details.6). local actions should not be overlooked. This is intentionally shown exaggerated. Meanwhile the lateral shear force (often concentrated through one of the columns) must be resisted by friction and passive soil pressure on the foundation. irrespective of load direction or brace configuration. Uplift. While not included in Figure 8. acting on a bracing structure away from a braced node. Figure 8.4 Load path diagrams for tie and strut bracing systems (foundations not shown) It is not advisable to have significant actions.4.5 by way of example). Strut system Tied system Note Ties are shown slack and sagging under self weight where not subject to tension.