Dimensioning for the ULS in bending with axial force

Large walls should be dimensioned for the ULS in flexure without any increase of the design Clauses moments above the base over those obtained from the analysis for the seismic design, situation. Moreover, the vertical reinforcement placed in the cross-section should be tailored

to the requirements of the ULS in flexure with axial force - e.g. without excess reinforcement and with less minimum web vertical reinforcement than required in ductile walls. The objective is to spread flexural yielding at several floor levels and not just at the base of the wall. This will increase the overall lateral deflections of the wall and will mobilize better, through uplift, the contribution to earthquake resistance of masses and transverse beams supported by the wall at intermediate floors. Moreover, the minimization of flexural overstrengths reduces shear force demands and helps in avoiding pre-emptive shear distress.

Due to their small thickness relative to the in-plane dimensions, large walls may be Clauses susceptible to out-of-plane instability. Section 5 requires limiting the magnitude of compression (2), stresses due to bending with axial force, to avoid such out-of-plane instability, without giving (3) detailed guidance for the implementation of this requirement. It opens the door, though, for complementary guidance provided via the National Annex. It refers also to the rules of Eurocode 2 on second-order effects. The rules in Eurocode 2 pertinent to out-of-plane instability are:

• the rules against lateral instability of the laterally unrestrained compression flange of beams (clause 5.9 in EN 1992-1-1)

• the rules for second-order effects in plain (i.e. unreinforced) or lightly reinforced walls (clause 12.6.5 in 1992-1-1).

Deemed-to-satisfy rules in Eurocode 2 against lateral instability of the compression flange of beams include a condition that the product (hJb^Q.Jb^y3 is less than 70, plus another one that ljbvm is less than 3.5. This second condition is not meaningful in walls.

The rules for second-order effects in plain or lightly reinforced walls comprise:

• Reduction of the compressive strength of concrete by a factor tp< 1 equal to ip = min[1.14(l - 2e/bwo) - 0.021 Jb^, (1 - 2e/bw0)), where l0 is the unbraced length of the wall and e is the eccentricity of loading in the direction of the thickness of the wall, with a default value of e = IJA00. The unbraced length lQ is taken as equal to the clear storey height, hst, divided by [1 + (hJ3lVJ)2] or by [1 + (hjlxv)2}, if the wall is connected at one or at both ends of its length Zw, respectively, to a transverse wall with a length of at least hJ5 and thickness of at least £>wo/2.

• (Only for cast-in-situ walls of plain concrete) a lower limit of /0/25 on bwo, with l0 being the unbraced length of the wall defined above.

A characteristic feature of the seismic response of large lightly reinforced walls is their Clauses rigid-body rocking with respect to the ground (if they are on footings), or their flexural, response as a system of storey-high rigid blocks. This type of response entails hard impact(s), either upon closing of horizontal cracks at floor levels, or of the uplifting footing to the

ground. Such hard impacts excite high-frequency vertical vibrations of the whole of the large wall, or of certain storeys of it. Being of high frequency, these vibrations die out fast and do not have significant global effects. However, they may induce significant fluctuation of the axial force in each individual wall. In view of the inherent uncertainty and the complexity of the local phenomena, Section 5 allows taking into account this fluctuation in a simplified and safe-sided way, namely by increasing or decreasing the design axial force of each individual wall by half its axial force due to the gravity loads present in the seismic design situation. It also allows neglecting this additional force if the value of the q factor used in the design does not exceed the value q = 2. The vertical reinforcement is normally conditioned by the case in which the additional axial force is taken in the ULS verification for flexure with axial load as tensile, whilst a compressive additional axial force is more critical for the concrete and for wall lateral instability.

Due to the high frequency of these vertical vibrations, the ULS verification for flexure with axial load may be performed with a value of the ultimate strain of concrete increased to ecu2= 0.005 for unconfined concrete. The beneficial effect of confinement on ecu2 may be taken into account according to equation (D5.6). If the positive effect of confinement is considered, the unconfined concrete should be neglected if its strain exceeds 0.005. Due to this, and as in thin walls, the (effectively) confined part of the section is normally quite small, taking into account the beneficial effect of confinement on the value of ecu2 in the confined part of the section will normally not increase the flexural capacity of the wall and is not worth doing.


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