Numerical method for analysis and design of isolated square footing under concentric loading

Abstract

Footing is an important part of a structure, because its repair is extremely difficult and cumbersome. Therefore, all structural parameters should be carefully considered when designing a footing. An isolated footing needs sufficient depth, when considering the fixed base assumption. Extensive research has previously been conducted to define and formalize the depth of a rigid footing, i.e., the depth required, such that footing behaves as a rigid. Alternatively, working stress method (WSM) and limit state method (LSM) provide a lower depth for low subgrades and a higher depth for high subgrades than that required by rigid condition if a unit width footing is considered for the design. This paper presents a simple approach for calculating the depth to meet the rigid condition under static loading. The proposed calculation method produced a better rigidity than the existing approaches and it correlated well to the finite-element method (FEM) for low subgrades. The reinforcement distribution is function of the bending moment (BM). Steel is uniformly embedded throughout the length or width of conventional footing methods, but this is inappropriate, because the bending moment is not uniform along the length or width of the footing. This paper proposes solutions to this by redefining the placement of steel in the central zone of the footing. The effective zone for reinforcement was based on the FEM results. This simple procedure was developed for calculating the maximum moment using the Diagonal Strip Method (DSM). DSM is a substitute for FEM, and it has been shown to correlate well. The BM at central zone as well as at the edges can be calculated to define the spacing of the reinforcements.

Mathematical Modeling of the Optimal Cost for the Design of Strap Combined Footings

“…If c 1 /2 is replaced by −a 1 /2 and the addition of P u1 a 1 /2 + M uy1 into Equation (17) to obtain the moment about the axis formed by q 2 and q 6 , the moment Mq 2 q 6 = 0. c.…”

“…Several models have been developed for the comprehensive design of reinforced concrete for circular, square and rectangular isolated footings subjected to biaxial bending [15][16][17][18][19][20]. Likewise, models for combined footings have been investigated for the complete design of reinforced concrete under biaxial bending in each column of trapezoidal-shaped [21], rectangular [22], L or corner [23], strap [24] and T [25] footing.…”

An Investigation into the Influence of a New Building on the Response of a Sheet Pile Wall Adjacent to an Existing Buried Pipe

“…Simulating strip footing was possible using a beam element [23][24][25] that possessed both bending stiffness (EI) and axial stiffness (EA). The material model for this element was linear elastic, and its characteristics were dependent on specific parameters.…”

The effect of geocell dimensions and layout on the strength properties of reinforced soil

“…A number of investigators [21,22] remarked that geocell confinement in soil induces apparent cohesion, whereas the reinforcement depth is replaced by an equivalent layer, with homogenous properties [33]. The induced cohesion in the soil is related to the increase in the confining pressure on the soil due to the geocell reinforcement, which is calculated through the following equation:…”

“…Less and more amounts of sand make the domination role for clay cohesion or friction between the sand particles in determining the shear strength of the mixture, respectively [19]. Numerical simulations demonstrated that the best redistribution of the load is achieved if reinforcements are placed up to a certain depth depending on the loading width [20][21][22]. Through experiments and numerical simulations, it was showed that confinement through geocell effectively increases the stiffness and strength of the ballast and decreases vertical settlement and lateral dispersion [11,23].…”