## Masonry wall design

Until relatively recently, masonry wall was the major load bearing component in a building structure. With the beginning of steel and concrete frame technologies, masonry has become a part of a building’s cladding envelope and as such is more subject to being exposed to lateral loads than vertical ones.

Before any design of a masonry element can be introduced, some understanding of its geometry, support conditions and material properties must be established. All these factors and facets have a significant effect on the design of masonry, and therefore must be established from the outset.

Once the basic geometry is configured an iterative process begins with an initial thickness of the wall considered and then checked against the applied stresses.

The material properties are entirely dependent on the type of masonry and mortar selected.

With masonry generally being constructed in slender forms, the geometric properties are of paramount importance. In recognition of this, the code applies coefficients to distribute the load between perpendicular directions through the masonry, based on its dimensions and support conditions.

One of the first checks carried out should be to determine whether the wall is too slender. This is based on the ratio of height verses thickness (h/t) of the wall. If it is more than 30 and the wall is spanning vertically, then it is too thin, and its thickness needs to be increased. The value of this ratio is referred to again when determining the bending moment coefficients.

The next item for review is the Serviceability Slenderness check. Depending on the support conditions of the wall, the ratio of height to length (h/l) is compared against the ratio of length to thickness (l/t) where (h) is the height of the wall, (l) is the length of the wall and (t) is the thickness of the wall.

Modelling the support conditions accurately is very important when designing masonry as their rigidity impacts on the capacity of the wall to resist lateral loads.

Typical restraint conditions for masonry walls.

Simply supported masonry walls Continuous support to masonry walls

In the case of laterally loaded walls, the bending moment capacity is dependent upon the geometry of the wall, its support conditions and the material it is constructed from. For failure that is parallel to bed joints f_{xk1} is the flexural strength based on the mortar and masonry type. Similarly, the value of f_{xk2} is the flexural strength of masonry based on failure that is perpendicular to bed joints.

Having found the values of fxk1 and fxk2 in the code, the Orthogonal Ratio μ can be calculated thus:

μ = f_{xk1 }/ f_{xk2}

Once this ratio is determined, you are directed to the code where a series of tables provide the value of bending moment coefficient α2. These tables plot the values of h/l against μ.

The bending moment capacity of a wall that is subject to lateral forces M_{Rd}

The applied bending moment M_{Ed} is calculated using the coefficients defined in the code.

The applied bending moment that is parallel to the bed joints is defined as:

M_{Ed1} = a _{1} W_{Ed} l^{2 }

α_{1} is the orthogonal ratio μ multiplied by the bending moment coefficient α_{2}.

W_{Ed} is the ultimate design load applied to the wall.

l is the length of the wall.

The bending moment that is perpendicular to the bed joint is defined as:

M_{Ed2} = a _{2} W_{Ed} l^{2 }

Bending parallel to the bed joint:

M_{Rd1} =((f_{xk1}/Ƴ_{m})+ Ơ_{4}) Z

Ơ_{4 }is the applied compressive stress in N/mm^{2}

Z is the elastic modulus of the wall

Bending perpendicular to the bed joint:

M_{Rd2} =(f_{xk2}/Ƴ_{m}) Z

For walls, the shear capacity V_{Rd }is defined thus:

V_{Rd} = f_{vd }t l_{c}

Where:

f_{vd} is the shear strength of the wall and those that have fully filled mortar joints are defined as f_{vk0}+0.4σd. The value of f_{vk0} is drawn from the code.

t is the thickness of the wall

l_{c} is the length of wall under compression

This is then compared against the applied shear load V_{Ed} and provided it is equal to or greater than the applied shear, the wall is adequate.

A h=2.3m high wall, spanning between piers at l= 2.2m centres must withstand a design wind action of

W_{k}= 1.2 kN/m^{2};. It is founded on a mass concrete strip footing and is bonded to the piers, forming a continuous connection. The top of the wall has no lateral support and is free to move. The wall is to be made from clay bricks with moisture absorption of 9% and a Class M2 mortar that is 10mm thick. Determine if a single skin of brick can withstand the wind action.

Thickness of the wall; t=102.5mm

**Serviceability check.**

l/t=**21.463**

h/t=**22.439**

**Actions on wall**

Self-weight; Sw=h*t*22kN/m^{3}=**5.187** kN/m

h/l=**1.045**

**From Table **

f_{xk1}=0.35

f_{xk2}=1

Orthogonal Ratio μ; m= f_{xk1 }/f_{xk2} =**0.350**

**Support condition “D“**

**a _{2}=0.048;** a

_{1}=m*a

_{2}=

**0.017**

**Applied Bending Moment;**

M_{Ed1}=a_{1}*W_{k}*l^{2}=**0.098** kNm/m

M_{Ed2}=a_{2}*W_{k}*l^{2}=**0.279** kNm/m

**Bending Moment Capacity **

**From table**

**Ƴ _{m}=2.7**

Compressive Strength Ơ_{d}; C=1m*h*22kN/m^{3}*1/1m=**0.051** N/mm^{2}

Z=1m*t^{2}/6=**1751041.667**mm^{3}

X= (f_{xk1}/ Ƴ_{m})N/mm^{2}=**0.130** N/mm^{2}

M_{Rd1}=(X+C) *Z/1m =**0.316** kNm/m Greater than M_{Ed1}=**0.098** kNm/m Therefore OK

;X_{2}=(f_{xk2}/ Ƴ_{m})N/mm^{2}=**0.370** N/mm^{2}

M_{Rd2}=X_{2}*Z/1m=**0.649** kNm/m Greater than; M_{Ed2}=**0.279** kNm/m Therefore OK

**Shear Capacity Check;**

**From table**

**f _{vko}=0.1 N/mm^{2}**

;f_{vk}= f_{vko}+0.4*C=**0.120**N/mm^{2}

l_{c}=l+2*h=**6.800**m

V_{Rd}= f_{vk}*t*l_{c}=**83.807** kN Greater than V_{Ed}=W_{k}*h*l=**6.072**kN Therefore OK