be sure we shall test you with something of fear and hunger, some loss in goods, lives and fruit of...

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• Be sure we shall test you with something of fear and hunger, some loss in goods, lives and fruit of your toils, but give glad tidings to those who patiently persevere. Who say when afflicted with calamity “To Allah we belong and to Him is our return”. They are those on whom descend the Blessings from their Lord and Mercy and they are the ones that receive guidance.

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SHORT COLUMNS

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GENERALBack to reinforced concrete columns, with passing reference to short, stocky columns subjected to small bending moments, often said to be “axially loaded.” We have already discussed the same during last semester. Columns with large bending moments and slender columns will now be discussed.

To be on same page, concrete columns can be roughly divided into the following three categories:

Short compression blocks or pedestals. If the height of an upright compression member is less than three times its least lateral dimensions, it may be considered to be a pedestal. The ACI (2.1 and 10.17) states that a pedestal may be designed with unreinforced or plain concrete with a maximum design compressive stress equal to 0.85 Øf’c, where Ø is 0.65. Should the total load applied to the member be larger than 0.85 Øf’c Ag, it will be necessary either to enlarge the cross-sectional area of the pedestal or to design it as a reinforced concrete column, as described later.

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Short reinforced concrete columns. Should a reinforced concrete column fail due to initial material failure, it is classified as a short column. The load that it can support is controlled by the dimensions of the cross section and the strength of the materials of which it is constructed. We think of a short column as being a rather stocky member with little flexibility.

Long or slender reinforced concrete columns. As slenderness ratios are increased, bending deformations will increase, as will the resulting secondary moments. If these moments are of such magnitude as to significantly reduce the axial load capacities of columns, those columns will be referred to as being long or slender.

When a column is subjected to primary moments (those moments caused by applied loads, joint rotations, etc.), the axis of the member will deflect laterally, with the result that additional moments equal to the column load times the lateral deflection will be applied to the column. These latter moments are called secondary moments or P moments and are illustrated.

GENERAL

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A column that has large secondary moments is said to be a slender column, and it is necessary to size its cross section for the sum of both the primary and secondary moments. The ACI’s intent is to permit columns to be designed as short columns if the secondary or PΔ effect does not reduce their strength by more than 5%. Effective slenderness ratios are described and evaluated in lectures to follow and are used to classify columns as being short or slender. When the ratios are larger than certain values (depending on whether the columns are braced or un-braced laterally), they are classified as slender columns.

The effects of slenderness can be neglected in about 40% of all un-braced columns and about 90% of those braced against side-sway. These percentages are probably decreasing year by year, however, due to the increasing use of slenderer columns designed by the strength method, using stronger materials and with a better understanding of column buckling behavior.

GENERAL

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GENERAL

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TYPES OF COLUMNS

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TYPES OF COLUMNS A plain concrete column can support very little load, but its load-carrying capacity will be greatly increased if longitudinal bars are added. Further substantial strength increases may be made by providing lateral restraint for these longitudinal bars. Under compressive loads, columns tend not only to shorten lengthwise but also to expand laterally due to the Poisson effect. The capacity of such members can be greatly increased by providing lateral restraint in the form of closely spaced closed ties or helical spirals wrapped around the longitudinal reinforcing.

Reinforced concrete columns are referred to as tied or spiral columns, depending on the method used for laterally bracing or holding the bars in place. If the column has a series of closed ties, it is referred to as a tied column. These ties are effective in increasing the column strength. They prevent the longitudinal bars from being displaced during construction, and they resist the tendency of the same bars to buckle outward under load, which would cause the outer concrete cover to break or spall off. Tied columns are ordinarily square or rectangular, but they can be octagonal, round, L-shaped, and so forth.

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TYPES OF COLUMNS

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TYPES OF COLUMNS The square and rectangular shapes are commonly used because of the simplicity of constructing the forms. Sometimes, however, when they are used in open spaces, circular shapes are very attractive. The forms for round columns are often made from cardboard or plastic tubes, which are peeled off and discarded once the concrete has sufficiently hardened.

If a continuous helical spiral made from bars or heavy wire is wrapped around the longitudinal bars, the column is referred to as a spiral column. Spirals are even more effective than ties in increasing a column’s strength. The closely spaced spirals do a better job of holding the longitudinal bars in place, and they also confine the concrete inside and greatly increase its resistance to axial compression. As the concrete inside the spiral tends to spread out laterally under the compressive load, the spiral that restrains it is put into hoop tension, and the column will not fail until the spiral yields or breaks, permitting the bursting of the concrete inside. Spiral columns are normally round, but they also can be made into rectangular, octagonal, or other shapes.

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TYPES OF COLUMNS

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For spiral columns, circular arrangements of the bars are still used. Spirals, though adding to the resilience of columns, appreciably increase costs. As a result, they are usually used only for large heavily loaded columns and for columns in seismic areas due to their considerable resistance to earthquake loadings. (In non seismic zones, probably more than 9 out of 10 existing reinforced concrete columns are tied.) Spirals very effectively increase the ductility and toughness of columns, but they are much more expensive than ties.

Composite columns, are concrete columns that are reinforced longitudinally by structural steel shapes, which may or may not be surrounded by structural steel bars, or they may consist of structural steel tubing filled with concrete (commonly called lally columns).

TYPES OF COLUMNS

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AXIAL LOAD CAPACITY OF

COLUMNS

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AXIAL LOAD CAPACITY OF COLUMNS In actual practice there are no perfect axially loaded columns, but a discussion of such members provides an excellent starting point for explaining the theory involved in designing real columns with their eccentric loads. Several basic ideas can be explained for purely axially loaded columns, and the strengths obtained provide upper theoretical limits that can be clearly verified with actual tests.

It has been known for several decades that the stresses in the concrete and the reinforcing bars of a column supporting a long-term load cannot be calculated with any degree of accuracy. You might think that such stresses could be determined by multiplying the strains by the appropriate moduli of elasticity. But this idea does not work too well practically because the modulus of elasticity of the concrete is changing during loading due to creep and shrinkage. Thus, the parts of the load carried by the concrete and the steel vary with the magnitude and duration of the loads. For instance, the larger the percentage of dead loads and the longer they are applied, the greater the creep in the concrete and the larger the percentage of load carried by the reinforcement.

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Though stresses cannot be predicted in columns in the elastic range with any degree of accuracy, several decades of testing have shown that the ultimate strength of columns can be estimated very well. Furthermore, it has been shown that the proportions of live and dead loads, the length of loading, and other such items have little effect on the ultimate strength. It does not even matter whether the concrete or the steel approaches its ultimate strength first. If one of the two materials is stressed close to its ultimate strength, its large deformations will cause the stress to increase quicker in the other material.

For these reasons, only the ultimate strength of columns is considered here. At failure, the theoretical ultimate strength or nominal strength of a short axially loaded column is quite accurately determined by the expression that follows, in which Ag is the gross concrete area and Ast is the total cross-sectional area of longitudinal reinforcement, including bars and steel shapes:

AXIAL LOAD CAPACITY OF COLUMNS

Pn = 0.85f 'c (Ag - Ast ) + fy Ast

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FAILURE OF TIED AND SPIRAL COLUMNS

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FAILURE OF TIED AND SPIRAL COLUMNS Should a short, tied column be loaded until it fails, parts of the shell or covering concrete will spall off and, unless the ties are quite closely spaced, the longitudinal bars will buckle almost immediately, as their lateral support (the covering concrete) is gone. Such failures may often be quite sudden, and apparently they have occurred rather frequently in structures subjected to earthquake loadings.

When spiral columns are loaded to failure, the situation is quite different. The covering concrete or shell will spall off, but the core will continue to stand, and if the spiral is closely spaced, the core will be able to resist an appreciable amount of additional load beyond the load that causes spalling. The closely spaced loops of the spiral together with the longitudinal bars form a cage that very effectively confines the concrete. As a result, the spalling off of the shell of a spiral column provides a warning that failure is going to occur if the load is further increased.

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American practice is to neglect any excess capacity after the shell spalls off since it is felt that once the spalling occurs the column will no longer be useful—at least from the viewpoint of the occupants of the building. For this reason the spiral is designed so that it is just a little stronger than the shell that is assumed to spall off. The spalling gives a warning of impending failure, and then the column will take a little more load before it fails. Designing the spiral so that it is just a little stronger than the shell does not increase the column’s ultimate strength much, but it does result in a more gradual or ductile failure.

The strength of the shell is given by the following expression, where Ac is the area of the core, which is considered to have a diameter that extends from out to out of the spiral:


Shell strength = 0.85f 'c (Ag - Ac)

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By considering the estimated hoop tension that is produced in spirals due to the lateral pressure from the core and by tests, it can be shown that spiral steel is at least twice as effective in increasing the ultimate column capacity as is longitudinal steel. Therefore, the strength of the spiral can be computed approximately by the following expression, in which ps is the percentage of spiral steel:

Equating these expressions and solving for the required percentage of spiral steel, we obtain


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To make the spiral a little stronger than the spalled concrete, the code (10.9.3) specifies the minimum spiral percentage with the expression to follow, in which fyt is the specified yield strength of the spiral reinforcement up to 100,000 psi.

Once the required percentage of spiral steel is determined, the spiral may be selected with the expression to follow, in which ps is written in terms of the volume of the steel in one loop:


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In this expression, Dc is the diameter of the core out to out of the spiral, as is the cross-sectional area of the spiral bar, and db is the diameter of the spiral bar. The designer can assume a diameter for the spiral bar and solve for the pitch required. If the results do not seem reasonable, he or she can try another diameter. The pitch used must be within the limitations listed next. Actually, Table A.14, which is based on this expression, permits the designer to select spirals directly.


TABLES A-14Size and Pitch of Spirals, ACI Code—U.S. Customary Units

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CODE REQUIREMENTS FOR

CAST-IN-PLACE COLUMNS

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CODE REQUIREMENTS FOR CAST-IN-PLACE COLUMNS The ACI Code specifies quite a few limitations on the dimensions, reinforcing, lateral restraint, and other items pertaining to concrete columns. Some of the most important limitations are as follows.

The percentage of longitudinal reinforcement may not be less than 1% of the gross cross-sectional area of a column (ACI Code 10.9.1). It is felt that if the amount of steel is less than 1%, there will be a distinct possibility of a sudden no inductile failure, as might occur in a plain concrete column. The 1% minimum steel value will also lessen creep and shrinkage and provide some bending strength for the column. Actually, the Code (10.8.4) does permit the use of less than 1% steel if the column has been made larger than is necessary to carry the loads because of architectural or other reasons. In other words, a column can be designed with 1% longitudinal steel to support the factored load and then more concrete can be added with no increase in reinforcing and no increase in calculated load-carrying capacity. In actual practice the steel percentage for such members is kept to an absolute minimum of 0.005.

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The maximum percentage of steel may not be greater than 8% of the gross cross-sectional area of the column (ACI Code 10.9.1). This maximum value is given to prevent too much crowding of the bars. Practically, it is rather difficult to fit more than 4% or 5% steel into the forms and still get the concrete down into the forms and around the bars. When the percentage of steel is high, the chances of having honeycomb in the concrete is decidedly increased. If this happens, there can be a substantial reduction in the column’s load-carrying capacity. Usually the percentage of reinforcement should not exceed 4%when the bars are to be lap-spliced. It is to be remembered that if the percentage of steel is very high, the bars may be bundled.

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The minimum numbers of longitudinal bars permissible for compression members (ACI 10.9.2) are as follows: 4 for bars within rectangular or circular ties, 3 for bars within triangular-shaped ties, and 6 for bars enclosed within spirals. Should there be fewer than 8 bars in a circular arrangement, the orientation of the bars will affect the moment strengthof eccentrically loaded columns. This matter should be considered in design according to the ACI Commentary (R10.9.2).

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CODE REQUIREMENTS FOR CAST-IN-PLACE COLUMNS

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The Code does not directly provide a minimum column cross-sectional area, but to provide the necessary cover outside of ties or spirals and to provide the necessary clearance between longitudinal bars from one face of the column to the other, it is obvious that minimum widths or diameters of about 8 to 10 in. are necessary. To use as little rentable floor space as possible, small columns are frequently desirable. In fact, thin columns may often be enclosed or “hidden” in walls.

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When tied columns are used, the ties shall not be less than #3, provided that the longitudinal bars are #10 or smaller. The minimum size is #4 for longitudinal bars larger than #10 and for bundled bars. Deformed wire or welded wire fabric with an equivalent area may also be used (ACI 7.10.5.1).

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The center-to-center spacing of ties shall not be more than 16 times the diameter of the longitudinal bars, 48 times the diameter of the ties, or the least lateral dimension of the column. The ties must be arranged so that every corner and alternate longitudinal bar will have lateral support provided by the corner of a tie having an included angle not greater than 135. No bars can be located a greater distance than 6 in. clear on either side from such a laterally supported bar. These requirements are given by the ACI Code in its Section 7.10.5. Next slide shows tie arrangements for several column cross sections. Some of the arrangements with interior ties, such as the ones shown in the bottom two rows of the figure, are rather expensive. Should longitudinal bars be arranged in a circle, round ties may be placed around them and the bars do not have to be individually tied or restrained otherwise (7.10.5.3). The ACI also states (7.10.3) that the requirements for lateral ties may be waived if tests and structural analysis show that the columns are sufficiently strong without them and that such construction is feasible.


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There is little evidence available concerning the behavior of spliced bars and bundled bars. For this reason, Section R7.10.5 of the Commentary states that it is advisable to provide ties at each end of lap-spliced bars and provides recommendations concerning the placing of ties in the region of end-bearing splices and offset bent bars.

Ties should not be placed more than one-half a spacing above the top of a footing or slab and not more than one-half a spacing below the lowest reinforcing in a slab or drop panel. Where beams frame into a column from all four directions, the last tie may be below the lowest reinforcing in any of the beams.


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The Code (7.10.4) states that spirals may not have diameters less than ⅜ in. and that the clear spacing between them may not be less than 1 in. or greater than 3 in. Should splices be necessary in spirals, they are to be provided by welding or by lapping deformed uncoated spiral bars or wires by the larger of 48 diameters or 12 in. Other lap splice lengths are also given in ACI Section 7.10.4 for plain uncoated bars and wires, for epoxy-coated deformed bars and wires, and so on. Special spacer bars may be used to hold the spirals in place and at the desired pitch until the concrete hardens. These spacers consist of vertical bars with small hooks. Spirals are supported by the spacers, not by the longitudinal bars. Section R7.10.4 of the ACI Commentary provides suggested numbers of spacers required for different-size columns.


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The ACI 318 Code (Section 7.10.5.4) states that where longitudinal bars are located around the perimeter of a circle, a complete circular tie is permitted. The ends of the circular tie must overlap by not less than 6 in. and terminate with standard hooks that engage a longitudinal column bar. Overlaps at ends of adjacent circular ties shall be staggered around the perimeter enclosing the longitudinal bars. The code commentary for this provision warns that vertical splitting and loss of tie restraint are possible where the overlapped ends of adjacent circular ties are anchored at a single longitudinal bar. Adjacent circular ties should not engage the same longitudinal bar with end hook anchorages. While the transverse reinforcement in members with longitudinal bars located around the periphery of a circle can be either spirals or circular ties, spirals are usually more effective.


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SAFETY PROVISIONS FOR COLUMNS

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The values of ɸ to be used for columns as specified in Section 9.3.2 of the Code are well below those used for flexure and shear (0.90 and 0.75, respectively). A value of 0.65 is specified for tied columns and 0.75 for spiral columns. A slightly larger ɸ is specified for spiral columns because of their greater toughness.

The failure of a column is generally a more severe matter than is the failure of a beam because a column generally supports a larger part of a structure than does a beam. In other words, if a column fails in a building, a larger part of the building will fall down than if a beam fails. This is particularly true for a lower-level column in a multistory building. As a result, lower ɸ values are desirable for columns.

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There are other reasons for using lower ɸ values in columns. As an example, it is more difficult to do as good a job in placing the concrete for a column than it is for a beam. You can readily see the difficulty of getting concrete down into narrow column forms and between the longitudinal and lateral reinforcing. As a result, the quality of the resulting concrete columns is probably not as good as that of beams and slabs.

The failure strength of a beam is normally dependent on the yield stress of the tensile steel—a property that is quite accurately controlled in the steel mills. On the other hand, the failure strength of a column is closely related to the concrete’s ultimate strength, a value that is quite variable. The length factors also drastically affect the strength of columns and thus make the use of lower ɸ factors necessary.


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It seems impossible for a column to be perfectly axially loaded. Even if loads could be perfectly centered at one time, they would not stay in place. Furthermore, columns may be initially crooked or have other flaws, with the result that lateral bending will occur. Wind and other lateral loads cause columns to bend, and the columns in rigid frame buildings are subjected to moments when the frame is supporting gravity loads alone.


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DESIGN FORMULAS

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DESIGN FORMULAS

In the slides that follow, the letter e is used to represent the eccentricity of the load. No reference to e has been made earlier only load Pu and a bending moment Mu have been talked of, but no specific eccentricity e for a particular column. The term e represents the distance the axial load Pu would have to be off center of the column to produce Mu. Thus

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Nonetheless, there are many situations where there are no calculated moments for the columns of a structure. For many years the Code specified that such columns had to be designed for certain minimum moments even though no calculated moments were present. This was accomplished by requiring designers to assume certain minimum eccentricities for their column loads. These minimum values were 1 in. or 0.05h, whichever was larger, for spiral columns and 1 in. or 0.10h for tied columns. (The term h represents the outside diameter of round columns or the total depth of square or rectangular columns.) A moment equal to the axial load times the minimum eccentricity was used for design.

In today’s Code, minimum eccentricities are not specified, but the same objective is accomplished by requiring that theoretical axial load capacities be multiplied by a factor sometimes called α, which is equal to 0.85 for spiral columns and 0.80 for tied columns. Thus, as shown in Section 10.3.6 of the code, the axial load capacity of columns may not be greater than the following values:

DESIGN FORMULAS

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It is to be clearly understood that the preceding expressions are to be used only when the moment is quite small or when there is no calculated moment.

The equations presented here are applicable only for situations where the moment is sufficiently small so that e is less than 0.10h for tied columns or less than 0.05h for spiral columns. Short columns can be completely designed with these expressions as long as the e values are under the limits described. Should the e values be greater than the limiting values and/or should the columns be classified as long ones, it will be necessary to use the procedures described in the next two chapters.

DESIGN FORMULAS

For tied columns (φ = 0.65)

For spiral columns (φ = 0.75)

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