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Building Design and Construction Handbook - Merritt - Ventech!

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6.48 SECTION SIX<br />

FIGURE 6.14 Definition of terms for Eqs. (6.17) <strong>and</strong><br />

(6.18).<br />

Figure 6.16 can be easily used to determine the pressure at the edge of a footing<br />

or can be used to determine the pressure under the center of the footing as described<br />

below. The values of m <strong>and</strong> n must be calculated. The value m is defined as the<br />

width of the loaded area (x) divided by the depth to where the vertical stress increase<br />

(� z) is to be calculated. The value n is defined as the length of the loaded<br />

area (y) divided by the depth (z). The chart is entered with the value of n <strong>and</strong> upon<br />

intersecting the desired m curve, the influence value (I) is then obtained from the<br />

vertical axis. As indicated in Fig. 6.16, vertical stress increase (� z) is then calculated<br />

as the loaded area pressure (q o) times the influence value (I). Figure 6.16 can also<br />

be used to determine the vertical stress increase (� z) below the center of a rectangular<br />

loaded area. In this case, the rectangular loaded area would be divided into<br />

four parts <strong>and</strong> then Fig. 6.16 would be used to find the stress increase below the<br />

corner of one of the parts. By multiplying this stress by 4 (i.e., 4 parts), the vertical<br />

stress increase (� z) below the center of the total loaded area is obtained. This type<br />

of analysis is possible because of the principle of superposition for elastic materials.<br />

To find the vertical stress increase (� z) outside the loaded area, additional rectangular<br />

areas can be added <strong>and</strong> subtracted as needed in order to model the loading<br />

condition.<br />

Figure 6.17 presents a chart for determining the change in vertical stress beneath<br />

a uniformly loaded circular area. Figure 6.18 shows a Newmark (1942) chart, which<br />

can be used to determine the vertical stress increase (� z) beneath a uniformly loaded<br />

area of any shape. There are numerous influence charts, each having a different<br />

influence value. Note that the chart in Fig. 6.18 has an influence value (I) of 0.005.<br />

The first step is to draw the loaded area onto the chart, using a scale where AB

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