# Moment frames

Although each system is also capable of resisting gravity forces, its primary function, in the context of this book, is to provide horizontal resistance. Acting as a vertical cantilever each system is grounded by its foundations and rises up a building to receive horizontal forces from each floor and roof diaphragm (Fig. 5.3). It experiences horizontal shear forces and bending moments which give rise to vertical compression and tension forces concentrated at each end of the wall or frame. Listed in order of decreasing stiffness, shear walls, braced frames and moment frames can be thought of as vertical cantilever structural walls with different degrees and geometries of penetrations to realize cross-braced and

Triangular penetration

Shear wall

Triangular penetration

Shear wall

Braced frame

Rectangular penetration

Moment frame

▲ 5.4 Penetrations of a shear wall lead to braced or moment frame systems.

moment frame forms (Fig. 5.4). A brief overview of each of these three structural systems precedes more in-depth discussions that follow.

A shear wall resists horizontal forces acting in its plane by virtue of its length and to a lesser extent its thickness. Its strength and stiffness against horizontal forces usually requires a rigid connection to its foundations. Like any of the three systems providing seismic resistance it should be continuous from foundation to roof. The material of a wall can consist of any recognized structural material provided it has sufficient strength to resist the forces that the diaphragms transfer into it. Usually the wall material will be as strong if not stronger than that of the diaphragms.

Braced frames come in a variety of configurations. In their most basic form they consist of posts, beams and one or two diagonal bracing members per storey that generally fully triangulate the structure. Essentially, braced frames are vertical trusses. All their joints can be pinned. Depending on the type of frame and the cross-sectional dimensions of its members, diagonal members resist tension forces only or both tension and compression.

Reaction from shear wall

Torsion moment

Reaction from shear wall

Torsion moment

Horizontal off-set or lever-arm x

### Horizontal off-set or lever-arm

▲ 5.5 Seismic force in the y direction is resisted by two shear walls. Because of the off-set or lever-arm between them they also resist torsion. Structure acting in the x direction is not shown.

By contrast, a moment frame requires rigid connectivity between beams and columns. Rigid and strong joints enable bending moments to be transferred between adjacent column and beam members without any relative rotation. Horizontal forces are resisted mainly by bending and shear forces in the beams and columns. Due to the ever-present overturning moment causing toppling that acts upon any primary vertical structure, end columns of a frame experience compression and tension forces in addition to the gravity forces present. A frame can consist of any number of bays and storeys.

One of these three systems must be present in each orthogonal direction when considering the plan of a building. Then earthquake attack from any direction is resisted (see Fig. 2.13). Strive for symmetry of structural layout to reduce torsion. Ideally the lengths and thicknesses of shear walls acting in one direction should be similar. Where two or more elements of any system, say shear walls, are off-set in plan creating a lever-arm between them they can resist both horizontal forces and any in-plan torsion (Fig. 5.5) as discussed further in Chapter 9. The numbers of structural elements necessary in each direction depends upon a number of factors including site seismicity, the weight of the y x building, and its height. Architects also decide upon the numbers of elements to meet their design criteria bearing in mind the fewer the elements the larger the force each one is required to carry. It is also necessary to integrate the seismic force resisting systems with the gravity resisting structure and with the architectural concept and program or design brief.

It is recommended that just one structural system only is used in each orthogonal direction. It is permissible, and in fact sometimes desirable, to place different structural systems in parallel but because mixed-systems - as they are known - lead to more complex force paths, they are best avoided until those implications are studied later in this chapter.