CONCRETE COLUMNS 119. Plain Concrete Columns.—The strength of plain concrete in compression has been discussed in Section 94. The failure of a short block under compression occurs through lateral expansion and the shearing of the material on surfaces making angles of about 30° with the line of pressure as shown in Fig. 57 (a). As the height of block becomes greater in proportion to its diameter, the resistance of the concrete becomes less certain and plain columns in which the length is more than four times the height frequently fail by shearing diagonally across the column as shown in Fig. 57 (b). This usually occurs where the concrete is of good quality and shows high crushing strength. Weaker concrete usually fails by local crushing.
Columns in which the lengths are more than six or eight times the diameters are usually reinforced. The Joint Committee recommends that all columns more than four diameters be reinforced, and that the stress on plain be limited to 22.5 per cent of the ultimate crushing strength of the concrete.
The use of concrete rich in cement is nearly always advisable in the construction of columns, on account of the greater reliability uf such concrete, as well as because of the economy of reduced section allowable with rich concrete. In reinforced columns, concrete of high compressive strength also admits of more economical use of steel, through employing higher unit stresses than are admissible with less rich concrete. Concrete less rich than 1 to 6 (2000 pounds) mixtures (see Section 94) is undesirable in column work and richer mixtures are commonly preferable.
120. Longitudinal Reinforcement.—Longitudinal bars in the corners of square columns, or near the exterior surfaces of round columns, diminish the uncertainty of action of the columns through preventing the material yielding at points of local weakness. Such reinforcement should always be stayed by light band reinforcement at frequent intervals as shown in Fig. 5S (a). This will prevent the longitudinal bars breaking away from the column through bending when loaded.
When a column containing longitudinal steel is loaded, the con crete and steel are shortened by the compression to the same extent and the stress carried by each material is proportional to its modulus of elasticity.
Let A = cross-section of column; As = cross-section of steel; p=steel ratio =As/A; n= ratio of moduli of elasticity = Es/ P= total load on columns; compression on concrete; .
fs = unit compression on steel = rz The total area of concrete is _1(1—p), and The Joint Committee recommends the following working stresses: (a) Columns with longitudinal reinforcement to the extent of not less than 1 per cent and not more than 4 per cent, and with lateral ties of not less than inch in diameter 12 inches apart, nor more than 16 diameters of the longitudinal bar: the unit stress recommended for axial compression, on concrete piers having a length not more than four diameters.
The Committee also recommends that the ratio of unsupported length of column to its least width be limited to 15, and that the hoops or bands are not to be counted on directly as adding to the strength of the cohmnn.
Example 22.—A square column is to carry a load of 95,000 pounds, and to be reinforced with 2 per cent of longitudinal steel. If f.=450 lb./in. and n=15, find dimensions for column and steel.
Solution.—From Table XVI, for ii =15 and p= .020, we find Z=1.280. Then A 165, and side of column =13 inches. .020X165=3.30 From Table X, four Winch square bars may he used, 3.52 inches.
If 1 to 3 concrete of 3000 pounds compressive strength (see Section 94) were used in the above problem, we would have = 675, n = 10, 7=11S, A = 119 and 2.3S The quantities of materials required would be reduced about 25 per cent, while the proportion of cement in the concrete would be about doubled.
Example 23. — A column 14 in. X 14 in. section is to carry a load of 130 000 pounds. If and 11=15 find area of steel required_ P 130000 Solution.—Z= f!_l X _ and from Table XV'I, p=.034. Then This might be four 11-inch round bars at the corners or eight 16-inch square bars at corners and middle of sides or four 1-inch round bars at corners and four ;-inch round bars at middle of sides. 6.6S The Joint Committee recommends a minimum of 1 per cent of longitudinal steel for columns of more than four diameters in length. This gives rigidity to the column, and security against local yielding in the concrete. IIigh percentages of longitudinal steel are not usually economical, because of the greater cost of steel as compared with concrete for resisting compression, particularly when the stresses in the steel are limited by those in the concrete.