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Column subjected to axial column load and uplift Column subjected to both axial column load and moment or eccentric loading
Column subjected to axial column load onlySince factor of safety is included in determining allowable soil bearing capacity, there is no need to add addition factor of safety in determine the footing sizes. But, since the bottom of footing is at a depth below ground surface, the weight of soil and footing above the bearing area should be subtracted from the allowable soil capacity. The required footing area is column load divided by the net allowable soil bearing capacity. A = P / Qanet [2.1] Where A: required footing area. P: Axial column load Qa net = net allowable soil bearing capacity. The weigh of footing and the soil above should be heavy enough to offset the uplift forces from wind or seismic. Wt ³ U * F.S. [2.2] Where: Wt: Total weight of footing U: uplift force F.S.: factor of safety. This situation usually occurs at column at building bracing location. The factor of safety for uplift force in most of building codes is 1.5.
Example 1: Determine footing sizes for axial loads and uplift.
Given:
Requirement: Determine footing sizes for axial loads and uplift.
Solution:
Column subjected to both axial column load and moment or eccentric loadingColumns at the base of a moment revisiting frame are often subjected to moment in addition to axial load. Columns that at edge of buildings often have to be designed with eccentricity due to limitation of property line. The bearing pressure at the bottom of footing will distribute in trapezoidal or triangular shape. The footing has to be sized so that maximum footing pressure does not exceed allowable soil bearing capacity. Eccentricity is within 1/6 width of footing
Figure 2.1 Footing pressures with eccentricity not more than 1/6 footing width When eccentricity is less than 1/6 width of footing, footing pressure under the footing is distributed in trapezoidal shape. When eccentricity equals to 1/6 width of footing, footing pressure distributes triangularly with zero pressure at one end of the footing. The soil bearing capacity can be calculated as Q = P / A ± M / S [2.3] P: Axial column Load A: footing area M = P*e, column moment in the x direction, e is eccentricity in x direction. S = LB2/6 section modulus of footing area in x direction For a rectangular footing, the equation can be written as Q= P / A ± M / S = P/(BL) ± P*e/(LB2/6) = (P/A) [1±e*B/6] [2.4] L, B are length and width of footing. When footing is subjected to moments or eccentricities in both direction, the equations become Q = P / A ± Mx / Sx ± My / Sy [2.5] Or Q = (P/A) [1±ex*B/6±ey*L/6] [2.6] Example 2: Determine maximum and minimum footing pressure for footing with eccentricity < B/6.
Given:
Requirement: Determine maximum and minimum footing pressure.
Solution:
Eccentricity exceeds 1/6 width of footingWhen eccentricity exceeds 1/6 width of footing, soil pressure under pressure distributes in a triangular shape with a portion of the footing have zero pressure. The resultant of footing pressure, R coincides with column load, P as shown below. Since the center of the resultant is at 1/3 length of the triangle, the length of the bearing area is three times of the distance from the center of the column load to the edge of footing.
Figure 2.2 Footing pressure with eccentricity greater than 1/6 footing widthTherefore, P = Qmax [3(B/22)L/2] Then, Qmax = 2P/[3(B/2e)L] [2.7]
Example 3: Determine maximum footing pressure for footing with eccentricity > B/6
Given:
Requirement: Determine maximum and minimum footing pressure.
Solution:
