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Location with Respect to Depth
The depth below ground level at which the bottom of a foundation structure is located depends on number of factors, the most important of which is the stability of soil and permissible settlements (total, differential and angular).
In the case of cohesion less soils, it is imperative that the foundation cannot be placed at the top as there is no confining effect. Even in the case of cohesive soils, a minimum depth is necessary to take into account possibilities of erosion, shrinkage and influence of organic matter. The topography of the ground will decide on the minimum depth. In the case of sloping ground or partially filled up ground, special provisions like stepping may be necessary. (Figure). The nearness of adjacent structures will have to be taken into account in location of the new footing. If the structure is to contain vibrating machinery, the foundations of the building have to be taken to levels lower than that of the foundation of the machine to avoid transmission of vibration.
(a) Prove that the fourier series expansion for the function x(t) described in the finite interval -π ≤ t≤ π x(t) = 0 -π ≤ t ≤ 0 x(t) = sint 0 ≤ t ≤ π (b) Represent t
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