Sabah Shawkat Cabinet of Structural Engineering 2017 3.4 Reinforced concrete column Design of reinforcement in reinforced concrete elements loaded concentric and eccentric compression with a small eccentricity Although the column is essentially a compression member, the manner in which it tends to fail and the amount of load that causes failure depend on: 1. The material of which the column is made. 2. The shape of cross-section of the column. 3. The end conditions of the column. As the loads on columns are never perfectly axial and the columns are not perfectly straight, there will always be small bending moments induced in the column when it is compressed. Determining the buckling length of the column lo Figure: 3.4-1 1. One end fixed in direction and position, the other free k = 2 2. Both ends pinned k = 1 3. One end pinned, the other fixed in direction and position k = 0.707 4. Both ends fixed in direction and position k = 0.5 The consideration of the two end conditions together results in the following theoretical values for the effective length factor (the factor usually used in practice). Columns and struts with both ends fixed in position and effectively restrained in direction would theoretically have an effective length of half the actual length. Sabah Shawkat Cabinet of Structural Engineering 2017 However, in practice this type of end condition is almost never perfect and therefore somewhat higher values for k are used and can be found in building codes. In fact, in order to avoid unpleasant surprises, the ends are often considered to be pinned (k = 1.0) even when, in reality, the ends are restrained or partially restrained in direction. In this case, the end conditions for buckling about the x-x axis are not the same as about the y-y axis. There-fore both directions must be designed for buckling (Where the end conditions are the same, it is sufficient to check for buckling in the direction that has the least radius of gyration). Although the buckling of a column can be compared with the bending of a beam, there is an important difference in that the designer can choose the axis about which a beam bends, but normally the column will take the line of least resistance and buckle in the direction where the column has the least lateral unsupported dimension Determination of basic characteristics ‘ slenderness: radius of gyration: i lo i I A c´ ‘ Ac‘= b . h - rectangle: - where I is the moment of inertia of I = 1/12.b.h3 the cross section determine the minimum cross-sectional dimension columns in terms of buckling Figure 3.4-2 Sabah Shawkat Cabinet of Structural Engineering 2017 Design of reinforcement in reinforced concrete columns Stress in concrete [MPa] : c = Nsd / Ac’ Total required area of reinforcement v [cm2] : Arequired = c‘ .10 2 where can be obtained from the following graph: =5 =7,5 0.1 0.2 12.84472 13.14803 12.76732 13.06879 13.75465 13.67173 0.3 0.4 =10 13.28918 Minimum amount of reinforcement: =c 13.5888 • Determination of the maximum carrying capacity of cross-section The maximum capacity of the cross section can be determined using the following graph: Aprovided . 10 2 / (Ac‘) =5 =7,5 0.1 0.2 12.84472 13.14803 12.76732 13.06879 13.75465 13.67173 0.3 0.4 =10 13.28918 =b < 0,6 . fck 13.5888 sdv Ac‘ v lo v i v Areq, Aprovided v MN m2 m m cm2 When the load on a column is not axial but eccentric, a bending stress is induced in the column as well as a direct compressive stress. This bending stress will need to be considered when designing the column with respect to buckling. The relationship between the length of the column, its lateral dimensions and the end fixity conditions will strongly affect the column’s resistance to buckling. Sabah Shawkat Cabinet of Structural Engineering 2017 Many countries have their own structural design codes, codes of practice or technical documents which perform a similar function. It is necessary for a designer to become familiar with local requirements or recommendations in regard to correct practice. Figure 3.4-3 In low and normal strength concrete, significant non-linearities in the stress-strain behaviour start to develop at about 0.001 strain and the slope of the curve is close to zero at about 0.002 strain. The steel is therefore still in the elastic range, and is able to carry an increasing part of the load, when the non-linearities in the concrete start to develop. The usual range of the yield strength of ordinary reinforcement is 400 to 500 N/mm2. The reinforcement thus starts to yield at about the same strain level as the concrete reaches its maximum strength. In high strength concrete the stress-strain curve is more linear, and the strain at maximum stress is higher compared to lower strength concrete. The reinforcement in HSC columns will therefore yield before the concrete reaches its maximum strength and will continue to yield at about the same stress level until the concrete reaches its ultimate strain level. Precast Concrete Columns can be circular, square or rectangular. For structures of five storeys or less, each column will normally be continuous to the full height of the building. For structures greater than five storeys two or more columns are spliced together. Precast concrete columns may be single or double storey height. The method of connection to the foundation Sabah Shawkat Cabinet of Structural Engineering 2017 and to the column above will vary with manufacturer. Foundation connection may be via a base plate connected to the column or by reinforcing bars projecting from the end of the column passing into sleeves that are subsequently filled with grout. Alternatively, a column may be set into a preformed hole in a foundation block and grouted into position. Column-column connections may be by threaded rods joined with an appropriate connector; with concrete subsequently cast round to the dimensions of the cross-section of the column. Alternatively, bars in grouted sleeves, as described above, may be used. This results in a thin stitch between columns while the previous approach requires a deeper stitch. Connections may be located between floors, at a point of contra-flexure, or at floor level. Columns are provided with necessary supports for the ends of the precast beams (corbels or cast-in steel sections). There will also be some form of connection to provide beam-column moment connection and continuity. For interior columns this may be by holes through which reinforcing bars pass from one beam to another. For edge columns, some form of bracket or socket is required. During erection columns must be braced until stability is achieved by making the necessary connections to the beams and slabs. Figure 3.4-4 Sabah Shawkat Cabinet of Structural Engineering 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-5 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-6 Figure 3.4-7 2017 Sabah Shawkat Cabinet of Structural Engineering 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-8 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-9 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-10 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-11 2017 Sabah Shawkat Cabinet of Structural Engineering Figure 3.4-12 2017 Sabah Shawkat Cabinet of Structural Engineering 2017