1. Strain of steel and concrete is proportional to distance from neutral axis (Fig. 9.50c). 2. Maximum usable compression strain of concrete is 0.003 in / in (Fig. 9.50c). 3. Stress, psi, in longitudinal reinforcing bars equals steel strain s times 29,000,000 for strains below yielding, and equals the steel yield strength y, tension or compression, for larger strains (Fig. 9.50). 4. Tensile strength of concrete is negligible. 5. Capacity of the concrete in compression, which is assumed at a maximum stress of , must be consistent with test results. A rectangular stress distribution 0.85
c (Fig. 9.50d) may be used. Depth of the rectangle may be taken as a
1c, where c is the distance from the neutral axis to the extreme compression surface and 1
0.85 for c
 4000 psi and 0.05 less for each 1000 psi that
c exceeds 4000 psi, but 1 should not be taken less than 0.65. In addition to these general assumptions, design must be based on equilibrium and strain compatibility conditions. No essential difference develops in maximum capacity between tied and spiral columns, but spiral-reinforced columns show far FIGURE 9.50 Stresses and strains in a reinforcedconcrete

Q q  ult  cN  1/2  BN  D N (6.24) ult BL c t  t q where qult  ultimate bearing capacity for a strip footing Qult  vertical load causing a general shear failure of the underlying soil (Fig. 6.24) B  width of the strip footing L  length of the strip footing t  total unit weight of the soil D  vertical distance from the ground surface to the bottom of the strip footing c  cohesion of the soil underlying the strip footing Nc, N, and Nq  dimensionless bearing capacity factors In order to calculate the allowable bearing pressure (qall), the following equation is used: qall qult /F, where qall  allowable bearing pressure, qult  ultimate bearing capacity from Eq. (6.24), and F  factor of safety (typically F  3). This allowable bearing pressure often has to be reduced in order to prevent excessive settlement of the foundation. In addition, building codes often list allowable bearing pressures versus soil or rock types, such as Table 6.14, which presents the allowable bearing pressures (qall) from the Uniform Building Code (1997). TABLE 6.14 Allowable Bearing Pressures

subsurface observation up to 9 m (30 ft) deep Costly, timeconsuming, requires shoring, only useful where dateable materials are present, depth limited to zone above the groundwater level Source: NAVFAC DM-7.1, 1982. to meet exact specifications, such as those stated by ASTM D 1587-94 (1998). The Shelby tube shown in Fig. 6.1 has an inside diameter of 6.35 cm (2.5 in). Many localities have developed samplers that have proven successful with local soil conditions. For example, in southern California, a common type of sampler is the California Sampler, which is a split-spoon type sampler that contains removable internal rings, 2.54 cm (1 in) in height. Figure 6.1 shows the California Sampler in an open condition, with the individual rings exposed. The California Sampler has a 7.6-cm (3.0 in) outside diameter and a 6.35-cm (2.50-in) inside diameter. This sturdy sampler, which is considered to be a thick-walled sampler, has proven successful in sampling hard and desiccated soil and soft sedimentary rock common in southern California. Three types of soil samples can be recovered from borings: FIGURE 6.1 Soil Samplers (no. 1 is the California Sampler in an open condition, no. 2 is a Shelby Tube, and no. 3 is the Standard Penetration Test sampler.) 1. Altered Soil. During the boring operations, soil can be altered due to mixing or contamination. For example, if the boring is not cleaned out prior to sampling, a soil sample taken from the bottom of the borehole may actually consist of cuttings from the side of the borehole. These borehole cuttings, which have fallen to the bottom of the borehole, will not represent in-situ conditions at the depth sampled. In other cases, the soil sample may become contaminated with drilling fluid, which is used for wash-type borings. These types of soil samples that have been mixed or contaminated by the drilling process should not be used for laboratory tests because they will lead to incorrect conclusions regarding subsurface conditions. Soil that has a change in moisture content due to the drilling fluid or heat generated during the drilling operations should also be classified as altered soil. Soil that has been densified by over-pushing or over-driving the soil sampler should also be considered as altered because the process of over-pushing or over-driving could squeeze water from the soil. 2. Disturbed Samples. Disturbed soil is defined as soil that has been remolded during the sampling process. For example, soil obtained from driven samplers, such as the Standard Penetration Test spilt spoon sampler, or chunks of intact soil brought to the surface in an auger bucket (i.e., bulk samples), are considered disturbed soil. Disturbed soil can be used for numerous types of laboratory tests. 3. Undisturbed Sample. It should be recognized that no soil sample can be taken from the ground in a perfectly undisturbed state. However, this terminology has been applied to those soil samples taken by certain sampling methods. Undisturbed samples are often defined as those samples obtained by slowly pushing thinwalled tubes, having sharp cutting ends and tip relief, into the soil. Two parameters, the inside clearance ratio and the area ratio, are often used to evaluate the disturbance potential of different samplers, and they are defined as follows: D
D inside clearance ratio (%)  100 i e (6.1)