Its definition is derived from the Mohr-Coulomb failure criterion and is used to describe the friction shear resistance of soils together with the normal effective stress. In the stress plane of Shear stress-effective normal stress, the soil friction angle is the angle of inclination with respect to the horizontal axis of the Mohr-Coulomb shear resistance line. Concepts and Formulas. Granular soil has no cohesive strength. Some moist granular soils exhibit apparent cohesion.
Granular soil cannot be molded when moist and crumbles easily when dry. TABLE 5. N mm Combined footings: This type is used to support two or more column loads. They may be continuous with a rectangular or trapezoidal plan. The combined footing becomes necessary in situations where a wall column has to be placed on a property line that may be common in urban areas. Under such conditions, an isolated footing may not be suitable since it would have to be eccentrically loaded.
It is more economical to combine the exterior column footings with an interior column footing as shown in Figure 5. The combined footings are more economical to construct in the case of closely spaced columns.
Cantilever footings: They are basically the same as combined footings except that they are isolated footings joined by a strap beam that transfers the effect of the bending moment produced by the eccentric column load at the exterior column possibly located along the property line to the adjacent interior column footing that lies at a considerable distance from it. Figure 5. Mat, raft, or continuous footing: This is a large continuous footing supporting all of the columns and walls of a structure as shown in Figure 5.
A mat or a raft footing is used when the soil conditions are poor and a pile foundation is not economical. In this case, the superstructure is considered to be theoretically floating on a mat or raft. This type of structure is basically an inverted floor system.
Pile foundation: a plan; b elevation. Pile foundations: This type of foundation becomes essential when the supporting soil consists of poor layers of material to an extended depth such that an individual or mat foundation is not feasible.
A concrete footing on cohesionless sandy soil will exhibit a pressure distribution similar to the one shown in Figure 5. The sand near the edges of the rigid footing tends to displace outward laterally when the footing is loaded whereas the rigid footing tends to spread pressure uniformly. On the other hand, the pressure distribu- tion under a rigid footing in cohesive clay soil is similar to that shown in Figure 5. When the footing is loaded, the clay under the footing deflects in a bowl-shaped depression, relieving the pressure under the middle of the footing.
However, for design purposes it is customary to assume that the soil pressures are linearly distributed, such that the resultant vertical soil force is collinear with the resultant applied force as shown in Figure 5.
To simplify the foundation design, footings are assumed to be rigid and the supporting soil layers elastic.
Hence, the soil pressure under a footing is determined assuming linearly elastic action in compression. If a column footing is loaded with axial load P at or near the center of the footing, as shown in Figure 5. If e is the eccentricity of the load relative to the centroidal axis of the area A, the moment M can be expressed as Pe.
The maximum eccentricity e for which Equation 5. However, the larger eccentricities will cause a part of the footing to lift of the soil.
Generally, it is not preferred to have the footing lifted since it may produce an uneconomical solution. This is referred to as the kern distance. Therefore, the load applied within the kern distance will produce compression under the entire footing. The base area of the footing or the number and the arrangement of piles are established after the permissible soil pressure or the permissible pile capacity has been determined by the principles of soil mechanics as discussed in Chapters 3, 4, and 6, on the basis of unfactored service loads such as dead, live, wind, and earthquake, whatever the combination that governs the specific design.
In the case of footings on piles, the compu- tation of moments and shear could be based on the assumption that the reaction from any pile is concentrated at the pile center. The critical section for punching shear has a perimeter b0 around the supported member with the shear strength computed in accordance with applicable provision of codes such as ACI Tributary areas and corresponding critical sections for both wide-beam and two-way actions for isolated footing are shown in Figure 5. For footing design with no shear reinforcement, the shear strength of concrete Vc i.
Design Example 5. Solution The base area of the footing is determined using service unfactored loads with the net permissible soil pressure. Depth required for shear usually controls the footing thickness.
Both wide-beam action and two-way action for strength computation need to be investigated to determine the controlling shear criteria for depth. Hence, it is good practice to have rebars bent up at the end so that it provides a mechanical means of locking the bar in place. But in reality the bar has a hook at the end. Hence it is satisfactory. It is advised to provide at least the minimum area of steel required in both directions.
The soil pressure causes the cantilever to bend upward and, as a result, reinforce- ment is required at the bottom of the footing, as shown in Figure 5. The critical sections for design for flexure and anchorage are at the face of the wall section A—A in Figure 5.
One-way shear is critical at the section at a distance d from the face of the wall section B—B in Figure 5. Example 5. The wall carries a service unfactored dead load of 1. The allowable soil net bearing pressure is 5. The floor-to-floor height is 10 ft including the roof. Solution 1 Estimate the total service load. Only one-way shear is significant for a wall footing.
We need to check it at a distance d away from the face of the wall section B—B in Figure 5. The tributary area for moment is shown shaded in Figure 5. Maximum spacing allowed in the ACI section 7.
Applies with a factor of 0. Provide 5 at in. Provide 6 4 at in. It is required that the footings are designed for equal settlement under live loading. The footings are subjected to dead and live loads given below. Determine the area of footing required for a balanced footing design. It is given that the allowable net soil bearing pressure is 5 ksf Table 5. Note that this ratio is 1. Note that the soil pressure under footing 5 is 5 ksf, whereas under other footings it is less than 5 ksf.
When an exterior column is relatively close to a property line in an urban area and a special spread footing cannot be used, a combined footing can be used to support the perimeter column and an interior column together. The size and the shape of the footing are chosen such that the centroid of the footing coincides with the resultant of the column loads. By changing the length of the footing, the centroid can be adjusted to coincide with the resultant loads.
The deflected shape and the reinforcement details are shown for a typical combined footing in Figure 5. At the same time the nearby 24 square interior column carries a service dead load of kips and a live load of 80 kips at each floor. The architects have hired you as an engineer to design the footing for these columns.
The specific site condition dictates that a combined footing be chosen as an economical solution. Both columns carry three floors above them and are located 18 ft apart. The geotechnical engineer has advised that the soil bearing pressure at about 4 ft below the ground is 5 ksf. Determination of moist-soil consistency Field test for moist-soil consistency Testing is done when the soil is moist but not wet, as, for example, 24 hours after a good rainfall. Try to crush a small amount of moist soil by pressing it between your thumb and forefinger or by squeezing it in the palm of your hand.
Rate moist soil consistency as follows:. Determination of dry-soil consistency Field test for dry-soil consistency Testing is done when the soil has been air-dried. Try to break a small amount of dry soil by pressing it between your thumb and forefinger or by squeezing it in the palm of your hand. Rate dry soil consistency as follows:. Friday, October 9, Shear strength of soil. Typical values of shear strength parameters. Typical relationships for estimating the angle of internal friction, f , are as follows:.
Empirical values for f , of granular soils based on the standard penetration number, from Bowels, Foundation Analysis. Relationship between f , and standard penetration number for sands, from Peck , Foundation Engineering Handbook. Density of Sand. Very loose. Very dense. Relationship between f , and standard penetration number for sands, from Meyerhof , Foundation Engineering Handbook. Soi packing.
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