Abstract
The standard design method (classical method) for reinforced concrete rectangular footings is: First, a dimension is proposed and should comply with the allowable stresses; subsequently, the effective depth is obtained from the maximum moment and is checked against the bending shear and the punching shear until, it complies with these conditions and, then, steel reinforcement is obtained, but it is not guarantee that the minimum cost will be obtained. This paper shows an optimal design for reinforced concrete rectangular footings using the new model. A numerical experimentation is presented to show the model capability to estimate the minimum cost design of the materials used for a rectangular footing that supports an axial load and moments in two directions in accordance to the building code requirements for structural concrete and commentary (ACI 318-13). Also, a comparison is made between the optimal design and current design for rectangular footings. The solutions show that the optimal design is more economical and more precise with respect to the current design, because standard design is done by trial and error. Then, the optimal design should be used to obtain the minimum cost design for reinforced concrete rectangular footings.
Highlights
The foundation is the part of the structure which transmits the loads to the soil
This paper shows an optimal design for reinforced concrete rectangular footings using a new model
General equation for any type of footings subjected to biaxial bending is: σ = P ± Mxy ± Myx where: σ is the stress exerted by the soil on the footing, A is the contact area of the footing, P is the axial load applied at the center of gravity of the footing, Mx is the moment around the axis “X”, My is the moment around the axis “Y”, x is the distance in the direction “X” measured from the axis “Y” to the fiber under study, y is the distance in direction “Y” measured from the axis “X” to the farthest under study, Iy is the moment of inertia around the axis “Y” and Ix is the moment of inertia around the axis “X”
Summary
The foundation is the part of the structure which transmits the loads to the soil. The foundations are classified into superficial and deep, which have important differences: in terms of geometry, the behavior of the soil, its structural functionality and its constructive systems (Das et al, 2006; Ha, 1993).The footings sizes are mostly governed by the axial load and moments, allowable soil pressure, unit weight of concrete, soil unit weight, and the depth of the footing base below the final grade (Al-Ansari, 2013).Optimum design of structures has been the topic of many studies in the field of structural design. The foundation is the part of the structure which transmits the loads to the soil. The foundations are classified into superficial and deep, which have important differences: in terms of geometry, the behavior of the soil, its structural functionality and its constructive systems (Das et al, 2006; Ha, 1993). The footings sizes are mostly governed by the axial load and moments, allowable soil pressure, unit weight of concrete, soil unit weight, and the depth of the footing base below the final grade (Al-Ansari, 2013). Optimum design of structures has been the topic of many studies in the field of structural design. A designer’s goal is to develop an “optimal solution” for the structural. Optimal design for rectangular isolated footings using the real soil pressure.
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