OPTIMUM DESIGN OF REINFORCED CONCRETE SHEAR WALLS

The recently published New Zealand Code of Practice for the Design of Concrete Structures (NZS 3101:1982) and the newly amended Code of Practice for General Structural Design and Design Loadings for Buildings (NZS 4203) permit a variety of possible design approaches for reinforced concrete shear wall structures. A series of wall designs for dimensionally similar four-storey and e i g h t storey buildings has been carried out and a comparison of c o n struction cost estimates obtained together with an assessment of the relative design effort required for the different design options.


ABSTRACT
The recently published New Zealand Code of Practice for the Design of Concrete Structures (NZS 3101:1982)  Two broad classes of shear walls are defined, namely, "ductile shear walls" and "shear walls of limited ductility".
The distinction is made on the basis of overall height to depth ratio, with walls having a value of this ratio of less than 1.0 being, ^classified as walls of limited ductility .Ductile shear walls have an aspect ratio 1.0 or more, and may have the form of cantilevers or of "coupled walls".
In the latter case, two or more ductile cantilever walls are connected by "a number of appropriately reinforced ductile coupling beams that are capable of dissipating a significant proportion of the seismic energy" The procedure for design of walls of limited ductility is less complicated particularly because explicit capacity design for shear is not required.
Instead, the dependable shear strength ( 0 V. ) must be able to resist twice the value of shear induced by code-prescribed seismic loading together with shear resulting from the, .appropriatelyfactored gravity loading (clause 14.4.2.1 ) .This procedure is used for shear wall systems where the overall height to depth ratio ("aspect ratio") is small.
However, walls of greater aspect ratio may, at the discretion of the designer, be designed as walls of limited ductility ( y2 (clause 3.3.6.1 ) with increased loadings (Table 5, item 4) .
The designer may also choose to design walls to respond elastically to earthquake loading through application of an equiva- The floor area for each building height was chosen such that the full dependable strength of each wall in the base region was mobilised when designed according to references (2) and (3) .As a result, wall thickness varied at the base between wall types but the tributary floor area was kept constant for each building height.
The wall outlines are shown in Figure 1.The buildings were assumed to be situated in seismic zone A, and the risk factor taken as unity.
In the third amendment to reference (2) , a materials factor of 0.8 is proposed for reinforced concrete.Thus the seismic base shear is However, in order to compare design approaches, both sets of 1 0 metre walls were also designed using the limited ductility procedure and an S-f actor of 2.0,

2)
Twin 5 Metre Cantilever Walls For both buildings, these walls are ductile with an S-factor determined from equation 2 as 1 .1 for the four storey building and 1 .0for the eight storey building.

3) Coupled Walls
In determining the geometry of this system the main constraint imposed was that the overall wall length be 1 0 metres, The size of the opening beneath the coupling beam was set at 2.1 metres high by 1 .7 metres wide so that it could serve as a doorway.
where A is the proportion of total overturning moment resisted by all beams, and Z is as defined previously.
The larger A, the more slender the walls for constant coupling beam geometry, and the more framelike the response of the system.
A value of S of 0.86 was determined for the four storey building.A lower S could have been achieved by widening the openings.However, if the openings were made wide enough to achieve S = 0.80, the structure would become too flexible and exceed the limitations on interst^orey drift imposed in the loadings code .
In the case of the eight storey structure, an S = 0.80 was obtained with 2.1 x 1.7 metre openings while still satisfying drift limitations.

DETERMINATION OF WALL THICKNESS 1) Analytical Model
It was assumed that both buildings contained a basement.
In such a situation, a large seismic shear is reacted at the ground floor level through the floor slab which acts as a "transfer diaphragm" and sheds load to the perimeter retaining walls.
A shear of reversed direction exists in the shear wall between basement and ground floor level.
The value of this force may be very high and it is very sensitive to the model -in particular, to whether the ground floor diaphragm has finite or infinite stiffness and to whether the base is fully fixed against, xptation, pinned, or modelled on springs .Further, particularly when the wall is longer than the interstorey height, it is important to explicitly model the shear stiffness as well as flexural stiffness rather than treat the wall total stiffness as that of an equivalent flexure-only cantilever .
The difference is shown for one example in Figure 5.

2) Stability of Wall Edge
For walls designed to the "ductile" re- In this study, the thicknesses within end regions were generally determined by the upper limit on v., the total shear stress, except for the "tour storey twin 5 metre walls.
The stability requirement will often be met in practice by adjoining walls or may be achieved by a local thickening at free edges of walls.

3) End Region
The "end region" of a shear wall is the region in which plastic hinges may be expected to form under severe seismic loading .For both ductile walls and walls of limited ductility, the end region is generally of height equal to the length of the wall or one-sixth of /its total height, whichever is the greater (clause 10.5.5.3 and 14.5.2).This distance is to be measured up from the point of maximum moment, and thus, for the walls considered in this study, from the level of the ground floor * The end region for the 10 metre walls, from the above criteria , extended to just under three storey heights above ground.
Even though there is a basement, the "end region" is correctly measured upwards from the level~pf the ground floor for the prescribed distance.This is the level where maximum curvature occurs in a cantilever shear wall and hence where the potential for initiation of a plastic hinge exists.
However The ,recent amendment to the Loadings Code (clause 3.3.6.1)permits slender walls (that is, in which flexural effects dominate due to their large total height to length ratio) to be designed using the approach for walls of limited ductility, should the designer so choose.
It is thus instructive to compare benefits between the two approaches from the point of view of minimising wall cross-section.
Let the base applied seismic shear force, L = KP, where P is the load at S = 1 and K is the multiplier necessary to obtain design applied shear, L at wall base.
From the preceding, for a wall of limited ductility K = 2 x S = 4 while for ductile walls Let wall length, I , and thickness, be fixed.
Hence, change in S res ul¥s from a change in total height, h , of wall through equation ( 2). as the coupled shear wall for the eight storey building.
For the design examples, the wall crosssection dimensions were not altered above ground floor level.
Clearly, there is greater scope for reduction here in the case of a ductile design approach but economies here would be partly offset by the need for more flexural and shear reinforcement .

The
Table 2 obtains the factor K/v. for both design approaches and for a range of aspect ratios (h /£ ), assuming two or more walls make up the w resisting system.These factors may be regarded as indicating the relative amounts of wall cross-sectional area needed, the higher value implying a greater are^.isrequired to satisfy code requirements .
In the case of the "ductile" design approach, the maximum total shear stress (v.) is allowed to increase substantially outside the end zone (up to nearly twice the value and depending on wall aspect ratio -see Table 2) .
The, -.commentary to the Concrete Design Code recommends that use of a magnification factor (w0 ) for applied shear be retained outside°the end zone and this has been followed in preparing Table 2.
There is little difference between values of wall cross-sectional areas required within the end zone for either design approach, but the advantage of a "ductile" design approach becomes rapidly apparent outside of the end zone with increasing aspect ratio.
A greater rate of reduction of wall area with height is therefore possible for the "ductile" design.
In the case of all the four storey wall designs, the basement to ground floor wall thickness was increased to 500 mm to accommodate shear strength requirements.A thickness of 600 mm was needed in this area for the 1 0 metre eight storey wall designed to either design approach.
The aspect ratio for these walls is 2.8 and Table 2 indicates that similar shear area would be required in the end region for the two approaches.
However, a 500 mm thickness at base was sufficient for the more slender twin 5 metre wall as well where w = dynamic shear magnification factor 0 = overstrength factor o M° = overstrength moment at base of wall i.
A more even division of shear can be obtained only by increasing the flexural strength of the tension wall without at the same time making it stronger when in compression.
This was thought desirable, and accordingly, longitudinal reinforcement was concentrated in the outer ends of the wall set as shown in Figure 3 for the four storey building.
The effect was to reduce the ratio of total shear stress between the two walls from 5.7:1 to 4.3:1.The end thickenings were terminated at the extent of the end zone (third floor level).
The additional overturning effect in the eight storey building is not compensated for by a greater gravity load on the walls because most of the gravity load is taken by columns.
However, all of the seismic load is assumed to be taken by shear walls and the difference between seismic and gravity-induced axial load increases with the number of stories.
Hence, a concentration of reinforcement at the outer edge would still not result in a significant value of flexural strength of the tension wall when compared to that of the compression wall..In addition, Paulay and Williams recommend an even distribution of vertical reinforcement at the wall base to help to prevent the situation of a few large cracks arising and forming a potential plane of sliding.Coupled with the requirement (reference

R/O T/es-
(3), clause 10,5.8.2) that "stagger between splices shall be not less than twice the splice length", the situation arises for a ductile wall in excess of about 1 1 metres in length, and requiring D28 vertical bars, that there is nearly a three storey interval between successive splices on a bar.This could impose a considerable demand on the cost of steel fixing.
The end region of a coupled shear wall would normally be related to the length of one of the walls coupled rather than the length of the assemblage.
The exception is when the coupling beam is so stiff that the deflected shape of the assemblage approaches that of a single cantilever wall of overall length equal to that of the assemblage.No such limitation on thickness is made in the "limited ductility" design approach.

CONFINING REINFORCEMENT TIES AND COMPRES-SION EDGE REQUIREMENTS
In that case, confinement reinforcement in the end region is always required over 20 percent of the wall length from either end when the percentage of longitudinal reinforcement in this region exceeds about 1 percent.A greater quantity of confinement reinforcement must be provided here when the estimated compressive stress in this portion of wall length exceeds 0.2 0f 1 , in order to prevent compression failure of the concrete.
In the case of walls of limited ductility, the need for special transverse reinforcement outside the end region is cancelled provided that the dependable flexural strength outside of the end zone is 50 percent greater, than that required by the Loadings Code (see reference (3) clause 14.4.2.2).
Figure 2 shows the two major options available: Procedure B is more attractive than prolonging the extent of the labourwise costly confining ties.
Table 3 indicates that the total weight of confining ties for the eight storey 10 metre wall is reduced by about 50 percent when the "limited ductility" design approach is used (Procedure B -see Figure 2) instead of the "ductile" approach.On the other hand, no ties were required in the case of the four storey 10 metre wall designed to the "ductile" provisions, and thus the most attractive of the two approaches changes with wall height.By far the smallest number of ties was required for the coupled shear walls.Cantilever walls of a lesser number of stories may, on the other hand, require fewer confining ties if designed by the "ductile" approach.
Owing to the significant reduction in bending at the base of the ductile coupled walls, fewer confining ties were required here than for the pure cantilever walls.
The ductile twin 5 metre walls have a lesser total height of ties, but the number tabulated allows for the four ends of the wall set.
A reduction in number of ties should facilitate wall construction and hence, logically, the cost.However, the total weight of ties is very small compared to the remainder of reinforcing steel and if the same unit cost (dollars/kilogram) for "supply and place" of ties is used as for the remainder of the reinforcement, then the reduction in difficulty of construction will not be completely reflected in the cost difference between the design approaches.
No differentiation in unit rate for various types of reinforcement was made in the quantity survey for the different walls designed in this study.is still in its beginnings , and designers will not be familiar with the detail of the document for several months to come.

IQ-OOO
Our experience was that requirements for both the "ductile" and "limited ductility" design approaches took some effort to assimilate the first time round.
However, the latter approach does contain sufficient simplifications to make it worthy of consideration for design of even moderately slender walls (overall height to length ratio of up to about 3) notwithstanding the additional flexural reinforcement that is to be expected.
With experience, a designer will not be daunted by either design approach, and he will be wise to give first consideration to the "ductile" approach for slender shear walls.
A Thus, for a given quantity of vertical reinforcement, the tension wall gains strength with height and the compression wall becomes weaker.A further detraction in the design procedure for ductile coupled shear walls is the calculation of the overstrength factor 0 , the effort for which is cono siderably greater than in the case of a cantilever wall.

For
the more common low-and moderaterise shear wall structures, the "limited ductility" approach is more attractive.
Table 5 shows the relative number of calculation pages required for the eight storey walls.
In the situation of designing a set of walls, the results of analysis for the "ductile" example were scaled directly for the "limited ductility" wall.The relative value for the latter example would only rise to a figure of about "0.67" (Table 5) had the benefit of the previous analysis not been taken advantage of.Hence, the "limited ductility" approach is attractive.
The procedure for "elastically responding structures" should appeal to designers of low-rise, low slenderness ratio shear wall structures.
However, a considerable increase in the quantity of vertical reinforcement may be required.
For example, nearly three times the amount is required at the base of the four storey example wall compared to the "ductile" design.Nevertheless, the situation will often arise in practice where a wall such as this may require little more than nominal reinforcement to respond elastically to the design earthquake, in which case the "elastically responding" design procedure is the most attractive.~i-1-1-r--1 1 1 1 1 r--t 1 1 r~ FIG I.WALL CONFIGURATIONS STUDIED

Thus
and the newly amended Code of Practice for General Structural Design and Design Loadings for

Comparison of Extent of Confining Ties with Different Design Approach usual
0 for shear must be used.

TABLE 5 Relative Design Effort for Eight-Storey Walls 3
. Standards Association of New Zealand."Code of Practice for the Design of Concrete Structures."NZS 31 01 :1 982,