The analysis of a framed building with shear walls subjected to horizontal and vertical load is essentially a three-dimensional problem. With the proliferation of computer programs available a three-dimensional analysis presents no great difficulty provided the modeling techniques fully reflect the behavior of the structure. The only penalty is time. Sometimes, especially where a dynamic analysis is required, it is the only method that can be used.

However, in many cases, the problem can be simplified into several two-dimensional components, thus resulting the amount of work. But to do this, the designer must understand fully the behaviour of the structure.

The intention to discuss is:

- The behaviour of combined shear wall and framed structures,
- Methods of apportioning loads, and
- Failure modes of shear walls.

**Load sharing of shear wall:**

The load attracted to each component (shear wall, core, frame) is a function of position and relative stiffness.

It is assumed that the floors are rigid in-plane and that the stiffness of each component, **j** is represented by a single parameter, **K _{j.}**

_{ }The centre of rotation can be determined statically, thus,

The force per component, **F _{j} **resulting from the total force on the wall,

**F**is given by

_{t}The torsional stiffness, **K**** _{j}** can be ignored except for core walls without substantial openings. This simplified approach is valid where the centre of rotation is close to the centre of building.

It may be assumed that **K _{j}** is directly related to the in-plane inertia of the components when the horizontal deflections are due predominantly to the effects of flexure.

#### Frame and Shear Wall Behaviour**:**

Rigid frames and short shear walls subjected to horizontal load mainly deform in a pure shear manner that is with concave in the upper part. Cantilever shear walls deform in a flexural manner, that is convex curvature throughout the height of the wall. Squat and coupled shear walls deform in a shear-flexure manner, exhibiting a combination of the two extreme deflection shapes.

A symmetrical arrangement of walls and frame will deflect in the direction of the horizontal load. The high in-plane stiffness of the floors forces the walls and frame to adopt identical deflection profiles.

Frames and walls do not simply attract a fixed percentage of the load throughout their height. The shapes of the deflection curves show that a rigid frame can attract a high proportion of the load at the top of the structure, but will attract very little at its base where it is more flexible.

Non-symmetrical arrangements of shear walls cause the structure to rotate about a vertical axis. The centre of rotation will vary from floor to floor and the rotation will not increase continuously in one direction over the height of the structure. A three-dimensional analysis is required.

#### Coupled Shear Walls:

A coupled shear wall structure consists of two or more shear walls in a single place connected by beams or slabs at each floor level. Generally they are a single pierced shear wall.

If the flexural stiffness of the beam is small compared to that of the shear wall, or the stiffness of the beam-wall connection is small such that it behaves like a hinge, then the structure acts as individual cantilever walls linked by a member which transmits only axial load (i.e. it behaves like a truss member). This results in the individual walls developing similar deflection profiles (they will not be identical because the tension in the ties increases with height and this puts restraining forces on the walls).

It the beam-wall connection is moment resisting then the structure behaves partly as individual cantilever walls, and partly as a single wall bending about a common neutral axis. The proportion of each action depends on the degree of moment connection.

**Failure Modes of Shear Walls:**

Possible shear wall failure modes due to horizontal loads are:\

- Flexural
- Horizontal shear
- Vertical shear

The figure below shows the failure modes of the shear walls: