# Short columns

Short column h >

(a) Columns 'shortened' by beams

Short column

(a) Columns 'shortened' by beams

Short column

(b) A short column on a sloping site

▲ 9.8 Examples of short columns among longer columns of moment frames.

(b) A short column on a sloping site

▲ 9.8 Examples of short columns among longer columns of moment frames.

Having just been informed of configuration difficulties posed by long columns, prepare to learn of the dangers of short columns. Structural extremes are unacceptable in seismic resistant systems. Short columns are to be avoided just as assiduously as flexible columns.

There are two types of short column problems; firstly, where some columns are shorter than others in a moment frame, and secondly, where columns are so short they are inherently brittle. The short columns of the second group are usually normal length columns that are prevented from flexing and undergoing horizontal drift over most of their height by partial-height infill walls or very deep spandrel beams.

Figure 9.8 shows examples where columns, some shorter than others in the same frame, cause seismic problems. The structural difficulty arising from these configurations is illustrated in Fig. 9.9. Two columns together, one that is half the height of the other, resist a horizontal force. The stiffness of a column against a horizontal force is extremely sensitive to its length; in fact, inversely proportional to the column length cubed (L3). The shorter column is therefore eight times stiffer than the other, so it tries to resist almost eight times as much force as the longer column. It is unlikely to be strong enough to resist such a large proportion of the horizontal force and may fail.

Seismic force

Seismic force

▲ 9.9 Two unequal height columns resisting seismic force.

Frame elevation

Frame elevation

Ground level

Vertical section through pile sleeve and pile (Detail A)

Section (Detail A)

▲ 9.10 A method of avoiding a short column on a sloping site.

This type of short column problem can be overcome in several ways, some of which have already been described. An application of the differentiation approach will relieve the frame with one or more short columns of any responsibility for seismic resistance. Shear walls or braced frames are provided elsewhere in plan (Fig. 9.6) . If the beams that frame into the columns forming short columns in Fig. 9.8(a) are pinned at both ends, that effectively doubles the column lengths and makes them all of equal length as far as seismic resistance is concerned. Of course, that creates a soft storey scenario that then needs to be addressed. An alternative approach to structuring Fig. 9.8(a) is to neglect the seismic strength of the long columns altogether and to resist all seismic forces by four one-bay frames; two acting in each direction to achieve a symmetrical structural configuration.

On a sloping site, short columns can be lengthened by integrating them with the piles (Fig. 9.10). If the piles are monolithic with columns and protected from contact with the ground by sleeves or casings that allow unrestrained horizontal drift, then a short column is avoided. Finally, check that a soft storey does not result from this foundation modification.

Now we return to short columns which have a very short distance over which they can flex horizontally (Fig. 9.11). As a rule-of-thumb a

Drift

Drift

Pile

Movement gap

Sleeve

Drift

Drift

Shear cracking

Short column

Masonry or concrete infill restraining lower portion of column

Shear cracking

Short column

Masonry or concrete infill restraining lower portion of column

Elevation of a regular height column

Elevation of a short or captive column

▲ 9.11 Comparison between a regular and a short column subject to horizontal drift.

▲ 9.12 Typical short column damage. 1994 Northridge, California earthquake.

(Reproduced with permission from Andrew B. King).

▲ 9.12 Typical short column damage. 1994 Northridge, California earthquake.

(Reproduced with permission from Andrew B. King).

▲ 9.13 Short column failure. 2007 Pisco, Peru earthquake.

(Reproduced with permission from Darrin Bell).

▲ 9.13 Short column failure. 2007 Pisco, Peru earthquake.

(Reproduced with permission from Darrin Bell).

Seismic force

Seismic force

Opening Short column

Compression strut

(a) Elevation

Opening Short column

Compression strut

(a) Elevation

Length of raised infill to beam soffit

Reduced opening

(b) Elevation

▲ 9.14 Reduction in the width of an opening above a partial-height masonry or concrete infill to prevent a short column failure. The raised lengths of infill enable a compression strut to transfer force directly to the top of the column and avoids the need for the column to bend.

short column has an unrestrained or free-length less that twice its depth. The problem is that the free-length is too short to allow for the development of a ductile plastic hinges. In the event of seismic overload the column fails in shear. To simulate a column snapping in a completely brittle manner, break a carrot between your hands. Once opposing diagonal shear cracks form in a reinforced concrete column its reduced gravity carrying capacity often leads to collapse (Figs 9.12 and 9.13)'

Guevara and Garcia describe this type of short column where its free-length is restricted by infill walls as a ' captive-column' . They explain where short columns are typically located in buildings and why they are so popular.4 They also report on unsuccessful attempts by several international research groups to improve the seismic performance of short reinforced concrete columns, concluding that the best solution is to avoid them. If confined masonry or structural masonry walls (Chapter 5) are required to function as shear walls and the masonry is partial height, Guevara and Garcia suggest continuing a short length of masonry up the sides of columns so that diagonal compression struts can act at the beam-column joint and thereby avoid short column failure (Fig. 9.14).

Chapter 10 discusses how non-structural partial-height masonry infills are separated to prevent short column

Wall 2 Wall 1

Wall 2 Wall 1

(a) Building with a discontinuous shear wall

(a) Building with a discontinuous shear wall

Wall 1 Perimeter moment Wall 2

frame

Wall 1 Perimeter moment Wall 2

frame

(b) Floor plan at an upper storey
(c) Ground floor plan showing torsional rotation

Wall 1 Wall 2

(d) Drift profiles

▲ 9.16 A discontinuous wall and its torsion-inducing influence on a building.

Short column

Reinforced concrete infill

Elevation of a short column configuration

Concrete infill

Separation gap

Separation gap

Infills are separated from the moment frame

Reinforced concrete infill extended full height and connected to infill above to form a shear wall

One bay completely infilled to form a shear wall

▲ 9.15 Methods to avoid a short column configuration with reinforced concrete infills.

configuration. The same approach applies if infill walls are of reinforced concrete construction. Alternatively, designers can infill one or more windows to form shear walls which are strong and stiff enough to resist seismic forces without short columns being damaged (Fig. 9.15). Note that even if strong infills are separated from the moment frame as shown, the ductility of the frame is reduced due to the stiffening and strengthening effect the infills have on the beams. The beams cannot bend when the building sways, so large cracks form at column-beam interfaces. Some engineers specify thin horizontal slots, at least as long as the beam is deep, to be filled with soft material at each end of an infill. This detail avoids the extreme concentration of bending deformation at the ends of beams.