## Verification for the nolocalcollapse requirement

What was said in Section 2.2.2.1 concerning seismic design for energy dissipation (normally through ductility) with a q factor greater than 1.5, and in Section 2.2.2.2 on design without energy dissipation or ductility and with a q factor not greater than 1.5 for overstrength, applies to buildings. The specific rules for the fulfilment of the no-(local)-collapse requirement within the framework of design for energy dissipation and ductility are elaborated further here.

4.11.2.1. Verification in force-based dissipative design with linear analysis

In the standard case of force-based seismic design based on linear analysis with a q factor value greater than 1.5, the following verifications are performed:

9 Dissipative zones are dimensioned so that the design resistance of the ductile mechanism(s) of force transfer, Rd, and the design value of the corresponding action effect due to the seismic design situation, Ed, from the analysis satisfy equation (D2.3).

• Regions of the structure outside the dissipative zones and non-ductile mechanisms of force transfer within or outside the dissipative zones are dimensioned to remain elastic until and beyond yielding of the ductile mechanism(s) of the dissipative zones. This is pursued through overdesign of the regions not considered as dissipative zones and of the non-ductile mechanisms of force transfer relative to the corresponding action effect due to the seismic design situation, Ed, from the analysis. Normally this overdesign is accomplished through 'capacity design'. In capacity design, the ductile mechanisms of force transfer in dissipative zones are assumed to develop overstrength capacities, 7Rdi?d, and equilibrium of forces is employed to provide the action effect in the regions not considered as dissipative zones and in the non-ductile mechanisms of force transfer. Capacity design is also used to spread the inelastic deformation demands over the whole structure and to prevent their concentration in a limited part of it. In frames, this is achieved according to the rules and procedures outlined in Section 4.11.2.2

9 Dissipative zones are detailed to provide the deformation and ductility capacity that is consistent with the demands placed on them by the design of the structure for the chosen q factor value.

• The foundation is also capacity designed on the basis of the overstrength of ductile mechanisms of force transfer in dissipative zones of the superstructure. Foundation elements are either capacity designed to remain elastic beyond yielding in dissipative zones of the superstructure or are dimensioned and detailed for energy dissipation and ductility, like the superstructure.

4.11.2.2. Design strategy for spreading inelastic deformation demands throughout the structure According to Section 2.2.1 and equations (D2.1) and (D2.2), buildings designed on the basis Clause 4.4.2.3(3) of q values higher than 1.5 should be capable of sustaining ductility demands corresponding to a value of the global displacement ductility factor, fj,6, about equal to q. In a multi-storey

building, the global displacement ductility factor is defined on the basis of the horizontal displacement of the building (drift) either at the roof or - preferably - at the height of application of the resultant lateral force. The global displacement ductility demand, in terms of ¡jls, should be spread as uniformly as possible to all storeys of the building. In other words, a storey-sway (or soft-storey) mechanism should be avoided and a beam-sway mechanism should be promoted instead. As shown in Fig. 4.4a, if a soft-storey mechanism develops, the entire inelastic deformation demand will be concentrated there: chord rotations at the ends of the ground storey columns will be equal to 0st = S/Hst, where S is the top displacement (the magnitude of which is essentially determined from the properties of the elastic structure and the elastic response spectrum of the seismic action, irrespective of the inelastic response) and Hst is the height of the ground storey; for buildings of more than two storeys, inability of the ground-storey columns to sustain such chord rotation demands will most likely lead to local failures and global collapse. In contrast, in a beam-sway mechanism the global displacement demand is uniformly spread to all storeys, and inelastic deformations and energy dissipation takes place at all beam ends; the kinematics of the mechanism require that vertical elements - which are not only more important for global stability but also inherently less ductile than beams - develop plastic hinging only at the base (Figs 4.4b and 4.4d). Even that hinging may be replaced by rotation of the column footing (Figs 4.4c and 4.4e). In the beam-sway mechanisms of Figs 4.4b to 4.4e the chord rotation at the ends of members where plastic hinges form will be equal to 9 = 6/Htot, where the top displacement S is essentially the same as in the soft-storey mechanism of Fig. 4.4a if the properties of the elastic structure and the elastic spectrum of the seismic action are the same, and Htot is the full height of the building.

Eurocode 8 pursues the development of beam-sway mechanisms in multi-storey buildings by providing a stiff and strong vertical spine to them that remains elastic above the base during the response. This is pursued through:

• choices in the structural configuration

8 rules for the dimensioning of vertical members so that they form a stiff and strong vertical spine above the base.

More specifically:

(1) In concrete buildings, wall systems (or wall-equivalent dual systems) are promoted, and their walls are (capacity-)designed to ensure that they remain elastic above the base, both in flexure and in shear. In steel and composite (steel-concrete) buildings, frames with concentric or eccentric bracings are promoted, and all members except the few intended for energy dissipation (i.e. except the tension diagonals in frames with concentric bracings or the 'seismic links' in those with eccentric bracings) are designed to remain elastic above the base during the response. These systems are indirectly promoted through the strict interstorey drift limits for the damage limitation seismic action (see Section 4.11.1), which are difficult to meet with frames alone - especially in concrete frames, where the cracked stiffness of members is used in the analysis.

(2) In moment-resisting frame systems (and frame-equivalent dual concrete frames) strong columns are promoted, indirectly through the interstorey drift limits mentioned above, and directly through the capacity design of columns in flexure described in Section 4.11.2.3, so that formation of plastic hinges in columns before beam hinging is prevented.

4.11.2.3. Capacity design of frames against plastic hinging in columns Clauses The objective of the Eurocode 8 rules for the design of (concrete, steel or composite)

4.4.2.3(4), moment-resisting frames is to force plastic hinges out of the columns and into the beams, so

4.4.2.3(5), that a beam-sway mechanism develops and a soft storey is prevented. To this end, at their

4.4.2.3(6) joints with beams, primary seismic columns are (capacity) designed to be stronger than the beams, with an overstrength factor of 1.3 on beam design flexural capacities:

lMRdjC>1.3lMRd,b (D4.23)

H-H | |

3--1 |
a--8 |

v!--B |
a_-a |

-v., --rf-*- |
a__« |

e |
0 | ||

1 6 |
TZI—^f5 | ||

0 |
0 |
Htot | |

I _0 | |
0 |

L |
i — |
" ' I |

si ffl |
S b | |

fa |
M b | |

if li |
b | |

_--r-n |

Fig. 4.4. Plastic mechanisms in frame and wall systems: (a) soft-storey mechanism in a weak column/strong beam frame; (b, c) beam-sway mechanisms in a strong column/weak beam frame; (d, e) beam-sway mechanisms in a wall system where MRd c and Mm b denote the design value of the flexural capacity of columns and beams, respectively. The summation on the left-hand side extends over the column sections above and below the joint; the summation on the right-hand side extends over all beam ends framing into the joint, regardless of whether they are primary or secondary seismic beams.

Equation (D4.23) has to be verified in each of the two main horizontal directions of the building in plan, or at least in the direction in which the structural type has been characterized as a frame or a frame-equivalent dual system. In each horizontal direction in which equation (D4.23) should be fulfilled, it has to do so first with the column flexural capacities in the positive (clockwise) sense about the normal to the horizontal direction of the frame (or frame-equivalent dual) system and then in the negative (anticlockwise) sense, with the beam flexural capacities always taken to act on the joint in the opposite sense with respect to the column capacities.

If a beam framing into a joint is at an angle 9 to the horizontal direction in which equation (D4.23) is checked, the value of MRd b enters into equation (D4.23) multiplied by cos 9. On the other hand, if the two cross-sectional axes in which the flexural capacities of the column, MRd c, are expressed are at angles <9, and f)2 = 90 + with respect to the horizontal direction in which equation (D4.23) is checked, these capacities should enter equation (D4.23) multiplied by sin 9X and sin 92, respectively.

Fulfilment of equation (D4.23) is not required at the joints of the top floor. In fact, it does not make any difference to the plastic mechanism whether the plastic hinge will form at the top of the top storey column or at the ends of the top floor beams. After all, it is difficult to satisfy equation (D4.23) there, as only one column enters in the summation of the left-hand side.

4.11.2.4. Verification of the foundation and design and detailing of foundation elements Due to the importance of the foundation for the integrity of the whole building structure, and the difficulty to access, inspect and repair damaged foundation systems, the verification of the foundation of buildings designed for energy dissipation is based on seismic action effects derived from capacity design, on the basis of the overstrength capacity of the yielding elements of the superstructure. This always applies to the verification of the foundation soil and, in general, for the dimensioning of the foundation elements. This is in the opposite direction to US codes,39'40 which allow reduction of overturning moment at the base due to uplift by 25% for linear static analysis or by 10% for a response spectrum analysis.

Wherever the seismic action effects determined for the foundation or its elements according to capacity design exceed the corresponding value from the analysis for the design seismic action without reduction by the behaviour factor q, then this latter - smaller - value may be used as seismic demand in the verifications. This applies to individual parts of the foundation and individual foundation elements. Moreover, the option is given to calculate the seismic action effects for the entire foundation system from the analysis for the design seismic action using q = 1.5 and completely neglecting capacity design. This option is consistent with the way seismic action effects are calculated in buildings which are designed as 'low-dissipative' according to Section 2.2.2.2. This is not a viable alternative, though, in high-seismicity regions, especially for medium- or high-rise buildings, as the seismic action effects resulting from the application of q = 1.5 in the entire foundation system may be so high that verification of some parts of the foundation system may be unfeasible.

Clause 4.4.2.6(4) For the foundation of individually founded vertical elements (essentially for individual footings) the seismic action effects determined through capacity design are calculated assuming that seismic action effects from the elastic analysis increase proportionally until the dissipative zone or element that controls the seismic action effect of interest reaches the design value of its force capacity, Rd]1 and is, indeed, increased by an overstrength factor 7Rd, which is taken equal to 7Rd = 1.2 if the value of the q factor used in the design of the superstructure exceeds 3. This is achieved by multiplying all seismic action effects from the analysis by the value 7Rdi2 = 7Rd(i?di/Edi) ^ q, where is the seismic action effect from the elastic analysis in the dissipative zone or element controlling the seismic action effect of interest.

In individual footings of walls or of columns of moment-resisting frames, & is taken as the minimum value of the ratio MRd/AfEd in the two orthogonal principal directions at the lowest cross-section of the vertical element where a plastic hinge can form in the seismic design situation, as it is in that direction that the element will first develop its force capacity. The value of MRd should be determined assuming that the axial force in that section of the vertical element is equal to the value from the analysis for that particular seismic design situation. In individual footings of columns of steel or composite braced frames, Q is taken as the minimum value of the force capacity to the corresponding value from the analysis in the seismic design situation, among all intended dissipative zones in the braced frame. If it is a concentric braced frame, Q is the minimum value of the ratio Nph Rd/NBd over all diagonals of the entire braced frame which are in tension for that particular seismic design situation, as only the tensile diagonals are intended for energy dissipation in such frames. If the braced frame is eccentric, Q is the minimum value of the ratio FpI Rd/FEd over all plastic shear zones and of Mpl Rd/MEd over all plastic hinge zones in this particular braced frame, where FpI Rd and Mpl Rd denote the design value of the plastic shear or moment resistance, respectively, of seismic links in the eccentric frame, as these may depend on the axial load in the seismic link from the analysis for the particular seismic design situation. Implicit in such calculations of Q is the assumption that the action effect of gravity loads present in the seismic design situation is negligible in comparison to Rdi and Edi. In connecting beams between individual footings, seismic action effects from the analysis should also be multiplied by the value of 7Rdi2 derived from the nearest individual footing for that particular seismic design situation.

For common foundations of more than one vertical element (e.g. in rafts, foundation beams and strip footings) the value of Q derives from the vertical element that develops the largest seismic shear in the seismic design situation. Alternatively, the value of 7Rdi? may be taken equal to 1.4, meaning that the seismic action effects from the analysis are magnified by 1.4, without any capacity design calculations.

All seismic action effects in the foundation system or element of interest are multiplied by the value of 7Rdi? applicable to that particular design situation. For an individual footing this includes the seismic action effects transmitted from the vertical element and any tie beams to the footing and all components of the reaction from the ground. The implication is that if the vertical seismic reaction is tensile, the eccentricity of the total vertical reaction due to the combination of gravity loads and the vertical seismic reaction multiplied by 7Rdi2 may be large.

4.11.2.5. Verification in displacement-based dissipative design on the basis of non-linear analysis

EN 1998-1 allows design on the basis of non-linear analysis (mainly of the pushover type) without the use of the behaviour factor q. In that case, verification for the no-(local-)collapse requirement comprises the following:

(1) Brittle elements or mechanisms of force transfer are verified via equation (D2.3) expressed in terms of forces, with design action effects, Ed, as obtained from the non-linear analysis for the seismic design situation (taking into account second-order effects, as appropriate), and design resistances, Rd, determined as for linear analysis, including the same partial factors for the materials.

(2) Dissipative zones, which are designed and detailed for ductility, are verified via equation (D2.3) expressed in terms of member deformations (e.g. plastic hinge or chord rotations), taking as design action effects, Ed, the deformations obtained from the non-linear analysis for the seismic design situation (including second-order effects, as appropriate), and as design resistances, Rd, the design values of member deformation capacities (including appropriate partial factors on deformation capacities).

(3) All the material-specific rules given in Sections 5-9 of EN 1998-1 for dissipative seismic design should be verified. These rules include the minimum requirements for materials, member geometry and detailing, etc. for DCM, as well as fulfilment of equation (D4.23)

Clauses

at the joints of moment resisting frames (or frame-equivalent dual concrete systems). They also include the magnification of shear forces in concrete walls of DCM, but do not include the determination of design shears in concrete beams or columns by capacity design, as this is explicitly covered by point 1 above. They do not include, either, the determination of confinement reinforcement in the plastic hinge or other dissipative zones of concrete walls or columns as a function of the curvature ductility factor, as this is determined from the behaviour factor q, because this factor is not relevant in this case. The deformation-based verification of dissipative zones according to point 2 covers this requirement in a more direct way. (4) The plastic mechanism predicted to develop in the seismic design situation is satisfactory, in the sense that soft-storey plastic mechanisms or similar concentrations of inelastic deformations are avoided.

Fulfilment of the requirements and verification according to point 3 above may appear as superfluous or even onerous, in view of the fulfilment of all the other conditions. However, this requirement has been introduced to ensure that the final design will possess the global ductility and deformation capacity which is implicitly required as a safeguard against global collapse under a seismic action much stronger than the design earthquake. With the accumulation of experience of design on the basis of non-linear analysis without the q factor, these minimum requirements may be refined, revised or even abolished.

By allowing design on the basis of non-linear analysis (mainly of the pushover type) without the use of the behaviour factor q, EN 1998-1 is taking the bold step of introducing displacement-based design for new buildings. However, this step is incomplete, as specific information on capacities in terms of deformations is not given and the task is delegated to National Annexes, in which individual countries are requested to specify (through reference to relevant sources of information) these capacities, along with the associated partial factors on deformation capacities. Fortunately, in the meantime, Part 3 of Eurocode 852 has filled this gap. Being fully displacement based, that part of Eurocode 8 gives in informative annexes the ultimate deformation capacities of concrete, steel (and composite) and masonry elements, as well as partial factors on these capacities for the 'significant damage' limit state, which is defined (in a note in the normative part of EN 1998-352) as equivalent to the ultimate limit state for which the no-(local-)collapse requirement should be verified in new buildings according to EN 1998-1. The information in these annexes may provide guidance for the National Annexes to EN 1998-1, or even be directly adopted by them for the deformation capacities of members and the associated partial factors.

4.11.2.6. Verification of seismic joint with adjacent structures or between structurally independent units of the same building Clauses Buildings are designed as separate structural units, independent from adjacent ones. To

4.4.2.7(1), make sure that the structural model adopted for the analysis applies and to prevent any

4.4.2.7(2) unforeseen consequences of dynamic interaction of the response with that of adjacent structures, EN 1998-1 requires securing a minimum spacing from such structures. The space is meant to be provided between the structures and may be filled, locally or fully, by a non-structural material which offers little resistance to compression in the event of an earthquake.

If the building being designed and that adjacent to it belong to the same property, or is a structurally independent unit of the same building, then the designer has full access to the information necessary for the construction of a full structural model of both buildings or structurally independent units and their analysis for the design seismic action. Then, he or she may compute the maximum horizontal displacements of both buildings or units normal to the vertical plane of the joint between them under the design seismic action. If the analysis for the design seismic action is linear, based on the design response spectrum (i.e. the elastic spectrum with 5% damping divided by the behaviour factor q), then the value of the floor displacement under the design seismic action is that from the analysis multiplied by the behaviour factor q adopted in the horizontal direction normal to the vertical plane of the seismic joint. If the analysis is non-linear, the floor displacements are determined directly from the analysis for the design seismic action. The rules of Section 4.9 should be applied to take into account the effect of the two simultaneous horizontal components of the seismic action on floor drifts. Unless the analysis is of the response time-history type, it only provides the peak value(s) of floor drifts during the response. To account for the fact that these peak values do not take place simultaneously, the width of the seismic joint is taken as the SRSS of the peak horizontal displacements of the two buildings or units at the corresponding level normal to the vertical plane of the joint.

If the building being designed and that adjacent to it do not belong to the same property, the owner and the designer normally do not have the information necessary for the calculation of the peak horizontal displacement of the other building or unit normal to the vertical plane of the joint. Even if they have access to such information, they normally have no control over future developments on the other side of the property line. So, EN 1998-1 simply requires the designer to provide a distance from the property line to the potential points of impact at least equal to the peak horizontal displacement of his or her building at the corresponding level, calculated according to the previous paragraph. This ends his or her responsibility, even when the structure of the adjacent building or unit has been built up to the property line.

Apart from the uncertainty created about the validity of the structural model and of the Clause 4.4.2.7(3) predictions of the seismic response analysis, dynamic interaction with adjacent buildings normally does not have catastrophic effects. On the contrary, given that it is only a few buildings that collapse even under very strong earthquakes, weak or flexible buildings may be spared by being in contact with adjacent strong and stiff buildings on both sides. For this reason, EN 1998-1 allows reducing the width of the seismic joint calculated according to the previous two paragraphs by 30%, provided that there is no danger of the floors of one building or independent units ramming vertical elements of the other within their clear height. So, if the floors of the two adjacent buildings or units overlap in elevation, just 70% of the width of the seismic joint calculated according to the previous two paragraphs needs to be provided.

## Greener Homes for You

Get All The Support And Guidance You Need To Be A Success At Living Green. This Book Is One Of The Most Valuable Resources In The World When It Comes To Great Tips on Buying, Designing and Building an Eco-friendly Home.

## Post a comment