Differential Shortening Of Columns

Columns in tall buildings experience large axial displacements because they are relatively long and accumulate gravity loads from a large number of floors. A 60-story interior column of a steel building, for example, may shorten as much as 2 to 3 in. (50 to 76 mm) at the top, while a concrete column of similar height may experience an additional 2 to 3 in. (50 to 76 mm) of shortening due to creep and shrinkage of concrete. If such shortening is not given due consideration, problems may develop in the performance of building cladding systems. Proper awareness of this problem is necessary on the part of structural engineer, architect, and curtain wall supplier to avoid unwelcome arguments, lost time, and money.

The maximum shortening of a column occurs at the roof level, reducing to zero at the base. In a concrete frame it may take several years for the shortening to occur because of the long-term effect of creep, although a major part of it occurs within the first few months of construction. Very little can be done to minimize shortening, but the design team should be aware of the magnitude of frame shortening so that soft joints are properly detailed between the building frame and cladding to prevent axial load from being transferred into the building facade. Before fabrication of cladding, the in-place elevations of structural frame should be measured and used in the fabrication of cladding. The design should provide for sufficient space between the cladding panels to allow for the movement of the structure. Insufficient space may result in bowed cladding components or, in extreme cases, the cladding panels may even pop out of the building.

A similar problem occurs when mechanical and plumbing lines are attached rigidly to the structure. Frame shortening may force the pipes to act as structural columns resulting in their distress. A general remedy is to make sure that nonstructural elements are not brought in to bear the vertical loads by separating them from the structural elements.

The axial loads in all columns of a building are seldom the same, giving rise to the problem of so-called differential shortening. The problem is more acute in a composite structure because steel columns that are later encased in concrete are typically slender, and are therefore subject to large axial loads during construction. Determining the magnitude of axial shortening in a composite system is complicated because many of the variables that contribute to the shortening cannot be predicted with sufficient accuracy. Consider, for example, the lower part of the composite column that is continually undergoing creep. The steel column during construction is partly enclosed in concrete at the lower floors, with the bare steel column projecting beyond the concreted levels by as many as 8 or 10 floors. Another factor that is difficult to predict is the gravity load redistribution due to frame action of columns and, if the building is founded on compressible material, foundation settlement is another factor that influences the relative changes in the elevations of the columns. The magnitude of load imbalance continually changes, making an accurate assessment of column shortening rather challenging. For concrete buildings, the method of construction more or less takes care of the immediate column shortening and, to a limited extent, the creep effects. This is because as each floor is leveled at the time of its construction, the column shortening that has occurred prior to the construction of that floor is compensated. Also, the creep and shrinkage effects tend to be small because dead load accumulates incrementally over a 12- to 15-month construction period.

Creep is difficult to quantify because it is time-dependent. Initially the rate of creep is significant; it diminishes as time progresses until it eventually reaches zero. Because of sustained loads, the stress in concrete gradually gets transferred to the reinforcement with a simultaneous decrease in concrete stress.

Columns with different percentages of reinforcement and different volume-to-surface ratios creep and shrink differently. An increase in the percentage of reinforcement and volume-to-surface ratio reduces the strain due to creep and shrinkage under similar stresses. Differential shortening of columns induces moments in frame beams, resulting in gravity load transfer to adjacent columns. A column that has shortened less receives more load, thus compensating for the initial imbalance.

Differential rather than the absolute shortening of column is more significant. Relative displacement between columns occurs because of the difference between the P/A ratios of columns. P is the axial load on and A is the area of the column under consideration. If all columns in a building have the same area and are sized for gravity load requirement only, there will be no relative vertical movement between the columns. All columns will undergo the same displacement because the P/A ratio is nearly constant for all columns. In a building, this condition is seldom present. This is because typically in building design, not all columns are designed for the same combination of loads. For example, the design of frame column is governed by the combined gravity and lateral loads while nonframe columns are designed for gravity loads only. This results in a large difference in the P/A ratios between the two sets of columns. Differential column shortening between perimeter and interior columns can produce floors that slope excessively. Since architectural partition walls, doors, and ceilings are normally built plumb and level, respectively, problems will result. Also, see Section 8.5, Floor-Leveling Problems.

Consider, for example, a steel tubular system with closely spaced exterior columns and widely spaced interior columns. High-strength steel up to 65 ksi is used for the interior column design, and because of large tributary areas and the desire to minimize column sizes, the resulting P/A ratios are large. The exterior columns, on the other hand, usually have a small P/A ratio for two reasons. First, their tributary areas are small because of their close spacing of usually 5 to 12 ft (2.44 to 3.66 m). Second, the columns are sized to limit lateral displacements, resulting in areas much in excess of those required for strength consideration alone. Because of this imbalance in the gravity stress level, these two groups of columns undergo different axial shortenings; the interior columns shorten much more than the exterior columns.

A reversed condition occurs in buildings with interior-braced core columns and widely spaced exterior columns; the exterior columns experience more axial shortening than the interior columns. The behavior of columns in buildings with other types of structural systems, such as interacting core and exterior frames, tends to be somewhere in between these two limiting cases.

In all these cases, it is relatively easy to evaluate the shortening of columns. The procedure requires a step-by-step manipulation of the basic PL/AE equation.

Having obtained the axial shortening values of all columns in a building, the next step is to assign column length correction Ac for each column. The objective is to attain as level a floor as practical. Ac is thus the difference between the specified theoretical height of a given column and its actual height after it has shortened. The magnitude of correction in a typically tall building of 30 to 60 stories is rather small, perhaps 1/8 in. (3.17 mm) per floor, at the most. Therefore, instead of specifying this small correction at each level, in practice it is usual to lump the corrections of a few floors to stipulate the required correction. For example, in lieu of )8-in. correction at every level one would specify 1 in. (25.4 mm) at every eighth floor.

Let us consider a typical column of a tall building with variations in story heights, gravity loads, and areas up the height, as shown in Fig. 8.32a. The axial shortening of the column at level n, denoted as An, is given by the following equation:

An = axial shortening at level n Pi = axial load increment Lk = column height at story k Ak = column area at story k NS = number of stories

To illustrate this rather trivial procedure, consider a column that is N stories high, with a constant cross-sectional area A, subjected to a constant load P at each floor. See Fig. 8.32b. The above simplifications are not valid in a practical column but keep the explanation simple.

Figure 8.32a. Axial shortening computations for a practical column.

It is evident that the axial shortening A1 at level 1 is equal to the total load at that level multiplied by L. Thus,

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