Shear walls are plain or reinforced concrete walls that augment structural stiffness and provide lateral stability to building structures. According to clause 9.6.1 of Eurocode 2, a shear wall is an element that has its cross-section length to thickness ratio to be equal to 4 or greater.

 

Types of Shear wall

Shear walls can be categorized based on their cross-section geometry

Planar walls

Flange walls

Couples Shear walls

Core walls

 

Behavior of shear walls

The behavior of shear walls is greatly influenced by the aspect ratio of the wall. Short walls which have their height-to-depth ratio to be less than 1 are greatly dominated by shear deformation. Slender (cantilever) walls which have their height-to-depth ratio to be greater than four are subjected dominantly to flexural deformation. Squat walls which are neither short nor slender are subjected to both flexural and slender deformations, their height-to-depth ratio is greater than 1 but less than 4.

It is however worth noting that for very tall buildings of more than about 25 storeys, shear walls struggle to stabilize such buildings. At that height, the overall aspect ratio of shear wall becomes so high it loses its flexural rigidity and start behaving like a typical frame. For such tall buildings, other lateral load stabilizing system would have to be incorporated to complement shear walls.

Allowable Horizontal Deflection

Although Eurocode 2, and Eurocode 0 do not specify allowable limit for horizontal deflections of shear walls or overall building, nevertheless the overall horizontal displacement over the building and horizontal displacement over a storey (drift) can be taken as hw/500 and 1/500 respectively (ie: hw is the overall height of the wall or building).

Forces acting on Shear walls

There are three major forces that act on shear walls. These are:

Axial Load: Shear walls are subjected to axial loads from roofs, slabs, or beams which are supported by the wall. Axial loads acting on a shear wall can be estimated by assuming the members on the wall are simply supported.

In-plane Moments: Lateral loads from primarily from wind or earthquake act on shear walls. The effect of this lateral load is in-plane moment in the wall. When estimating the in-plane moments, it is also necessary to estimate in-plane moments due to imperfections.

Transverse Moment: Shear walls are also subjected to transverse unbalanced moment from slabs, roof, and beams they support along the wall’s major axis.  The magnitude of the transverse moment can be calculated by creating an appropriate sub-frame and using simple elastic method like moment distribution method. There is also transverse moment due to imperfection which should also be considered.

Load combinations for Shear wall Design

The load combination on shear wall should be according to equation 6.10, 6.10a, 6.10b, table A1.1, and table A1.2(B) of EN 1990:2002 + A1: 2005.

Layout of Shear walls

It is encouraged that the layout of shear walls is symmetrical in plan. Symmetric distribution of shear walls ensures the line of action of horizontal force acting on the building coincides with the center of stiffness of the walls; hence torsional rigidity is achieved, and the behavior of the building is uncomplicated.

If, however, the center of stiffness of the shear walls does not coincide with the line of action, then the horizontal load will induce torsion in the building. This causes the building to twist about its center of stiffness rather than deflect translationally. In this case, the twisting moment (torsion) induced in the building is also distributed to the shear walls in proportion to their stiffnesses and the shear walls are designed accordingly.

Shear walls are generally preferred to be located at the perimeter, away from the center of gravity of buildings. This allows the shear walls to better resist deformation from lateral load more efficiently. Locating shear walls at the perimeter is also encourage when the arrangement of shear walls in plan is not symmetrical, and torsional force has to be resisted.

Estimation of in-plane lateral load acting on a shear wall

When there is a single shear wall in form of a core wall in a building, it can be assumed that all lateral loads are to be resisted by the wall alone. However, when there are more than one shear walls, especially of different section, in a building then the lateral load shall be shared amongst them in proportion to their stiffnesses. This can easily be calculated by simple statics for identical planar walls that are symmetrically distributed across the building plan. Things however become complicated and requires further number crunching if the walls are not identical – planar walls combined with cores for example. The computation required becomes much more demanding should the walls be arranged asymmetrically on plan.

According to Annex I of the Eurocode 2, when a wall in a building of up to 25 storeys is reasonably symmetrical and does not have significant openings that can cause large shear deformation, the lateral load resisted by a shear wall can be calculated thus:

$P_n=\frac{P(E I)_n}{\sum E I} \pm \frac{(P e) y_n(E I)_n}{\sum(E I) y_n^2}$

P_n is the lateral load on wall n

(EI)n is the stiffness of wall n

P is the applied load (1.1)

e is the eccentricity of P with respect to the centroid of the stiffnesses (see Figure 1.3)

Y_n is the distance of wall n from the centroid of stiffnesses.

 

Design Concept of Shear walls

The basic design concept of a shear wall is that it is designed as a typical column. As the main purpose of incorporating shear walls in building is to provide stability against in-plane horizontal forces, then it will always be subjected to moment. Therefore, shear walls are basically designed as wide columns subjected to moment and axial force.

Deign Approach of shear walls

There are several methods for designing shear wall for main reinforcement. Eurocode 2 in clause 9.6.1 suggests struct-and-tie method but does not give further guidance.  There is also an approach of determining the extreme fiber stresses in a shear wall due to combine axial load and in-plane moment using simple elastic analysis. Another method is resolving the in-plane moment into equivalent vertical couple acting on the end zones of the wall. The latter two methods are further discussed below.

The couple Method (Shear walls with End Zones)

In this method, only the end sections of the wall on both sides of its length are made to resist the in-plane moment and the axial load is assumed to be distributed over the entire length of the wall, thereby leading to concentration of reinforcements at the ends.

When lateral load acts parallel to the plane of a shear wall, the rear end of the wall is subjected to tensile stress and the far end of the wall is subjected to compressive stress (see fig 1). This basic concept is exploited such that the in-plane moment acting on the wall is converted to equivalent concentrated tensile and compressive forces acting in the end zones of the walls (see fig 2). The concentrated compressive force is added to the axial force acting on the section of the end zones while the concentrated tensile force is subtracted from the axial force (see fig 3).

The reinforcement alone resists the tensile force when the end zone is in tension, while the reinforcement plus concrete resist the compressive force when the end zone is in compression. The wall can be subjected to in-plane moment from either side at any point in time, so both end zones are designed to resist the resultant compressive force and also resultant tensile force.

The width of the end zone is determined using engineering judgement; however, it is recommended to use 1m especially for planar walls. If the in-plane moment is very large, there might be concentration of reinforcement at the end zones plus, sometimes, a much thicker section at the end zones than the web section of the shear wall which result in a flanged shear wall

The axial loads are estimated assuming the slabs and beams are simply supported on the wall. The in-plane moment is converted to equivalent axial couple by dividing the moment by the lever arm between the end zones

Transverse Moment

The transverse moment is estimated using simple elastic analysis. Moment due to imperfection or eccentricity should be taken care of just like in the case of a column. The slenderness effect should be allowed for when appropriate.

End Zones reinforcement

As stated earlier, since the in-plane moment can originate from either end of the wall, the endzones should be reinforced for the most critical between the tensile reinforcement and compressive reinforcement.

Compressive reinforcement

The equivalent compressive force due to axial load and in-plane moment should be combined together with the transverse moment and the area of steel required should be taken from design chart or N-M interaction diagram as in the case for columns. The resulting area of reinforcement can be provided for both the end zone (if compression is more critical for the end zones than tension) and web of the shear wall.

Tensile reinforcement

For tensile stress in the end zones, the reinforcement area should be based on the tensile force and the transverse moment. The expression below should be used to calculate the area of reinforcement.

$A_s=\frac{N_{E d}}{\sigma_{s t 1}}+\frac{M_{E d}}{\left(d-d_2\right) \sigma_{s t 1}}$

Where;

Ned = Axial tensile force due to in-plane moment and axial load

Med = transverse moment

d = effective depth

d2 = depth of compression reinforcement

σst1 = design strength of steel rebar (fyk /γm)

Wall’s Web reinforcement

The wall’s web can me designed to resist only the axial load and the transverse moment using column design chart or Interaction diagram. For simplicity, the web can be reinforced conservatively for compressive force due to both axial and in-plane moment, and transverse moment just like for end zones in compression.

Elastic Stress Method

This is a simplified method where the extreme fiber stress from the combination of in-plane moment and axial load are computed using simple elastic analysis. This stress is then assumed to act on every meter length of the wall having divided the wall into meter strips and the forces acting on it is estimated per meter. Each of this strip is treated as a column as explained further below.

The extreme fiber stress due to axial load and in-plane moment $=\frac{N_{E d}}{A} \pm \frac{M_{E d}}{z}$

A = L x h

$\mathrm{Z}=\mathrm{I} / \mathrm{Z}=\frac{h x L^3}{12 x \frac{L}{2}}=\frac{h L^2}{6}$

Substituting A and z into the equation, the extreme fiber stress becomes:

$f_t=\frac{N_{E d}}{L h} \pm \frac{6 M_{E d}}{h L^2}$

Where;

f_t  = fiber stress in N/mm²

N_Ed = design ultimate axial load in Newton

M_Ed = ultimate in-plane moment in Nmm

L = length of wall in mm

h = thickness of wall in mm.

This resulting axial stress is multiplied by the wall thickness (f_t x h) to obtain stress per meter length (N/m) on the wall. This axial stress is combined with the transverse moment (calculated as earlier explained) from slab and beams and the wall is designed just like columns per meter strip length.

Click here to Study a Worked Example on Design of Planar Shear Wall using Elastic Stress Method

Shear walls subjected to only in-plane moment and axial loads

Shear walls are sometimes subjected to insignificant transverse moment such as in the case of internal walls where adjoining slabs and beams are of symmetrical spans. In such cases, the shear wall can be designed for equivalent axial force from combined axial force and in-plane moment, plus the effect of imperfection or eccentricity, whichever is greater, of the equivalent axial force on the column.

Alternatively, the simplified approach in “manual for the design of reinforced concrete building structures to Eurocode 2” can be adopted where extreme fiber stress for compressive, and tensile loads are express in the following expressions:

Compressive Load

f_th = 0.43 f_ckh + 0.67 f_yk A_sc

where;

f_ck = characteristic concrete cylinder strength in N/mm²

f_yk = characteristic strength of reinforcement in N/mm²

A_sc = area of reinforcement in mm² per mm length of wall

 

Tensile Load

$$
\frac{0.5f_tL_t}{0.87f_{yk}}
$$

where L_t is the length of the wall in mm over which tension occurs.

The area of reinforcement should be placed within 0.5L_t from the end of the wall where the maximum tension occurs

 

Detailing requirement for Shear walls.

• The minimum area of vertical reinforcement (As,vmin) in a shear wall should be 0,002 Ac
• The maximum area of vertical reinforcement (As,vmax) in a shear wall should be 0,04 Ac
• The maximum area of vertical reinforcement (As,vmax ) at laps should not exceed 0,08 Ac
• The area of reinforcement required whether As,vmin or otherwise should be equally divided between the two faces of the wall
• The distance between two adjacent vertical bars shall not exceed 3 times the wall thickness or 400 mm whichever is the lesser.
• Horizontal reinforcement should be provided and made to run parallel to the faces and edges of the wall
• The recommended value of the horizontal reinforcement is either 25% of the vertical reinforcement or 0,001 Ac, whichever is greater.
• The spacing between two adjacent horizontal bars should not be greater than 400mm
• If the vertical reinforcement in both faces in any part of the wall exceeds 2% of the gross cross-sectional area of the concrete, then transverse reinforcement in the form of links should be provided in accordance with the requirement for columns (see 9.5.3)
• Diagonal bar reinforcement should be positioned at the corners of the openings in the shear wall and should be designed to resist a tensile force equal to twice the shear force in the vertical components of the wall but should not be less than two 16mm diameter.

 

 

References

EN 1992-1-1:2004 – Design of concrete structures – Part 1-1: General rules and rules for buildings

Design of Shear wall Buildings – CIRIA Report 102

Manual for the design of reinforced concrete building structures to EC2 – IstructE EC2 Design Manual