The design of wall footing, also known as strip footing, is based on the principles of beam action with some slight modifications. Its purpose is to safely support either structural or nonstructural walls and to transmit and distribute loads to the soil in a way that does not exceed the load-bearing capacity of the soil. The design must also prevent excessive settlement and rotation while maintaining sufficient safety against sliding and overturning.
The orientation of the wall footing is aligned with the direction of the wall it is supporting. The size of the footing and the thickness of the foundation wall are determined based on the type of soil at the construction site and the expected loading conditions. The reinforcement area and distribution for the wall footing are carried out in accordance with the requirements of ACI 319-19, which is the Building Code Requirements for Structural Concrete.
Analysis of Wall Footing
The basic principles of beam action can be applied to wall footings with minor adjustments. In Figure 1, the forces acting on a wall footing are depicted. If bending moments were calculated based on these forces, the maximum moment would be expected to occur at the middle of the width.
However, the significant rigidity of the wall actually modifies this situation. It is acceptable to compute the moment at the face of the wall section 1-1, as tension cracks are more likely to form under the face of the wall rather than in the middle. This indicates that the very large rigidity of the wall influences the distribution of bending moments in the wall footing.
Fig. 1: Critical Sections for Moment and Shear Force in Wall Footing
The maximum moment, denoted as Mu, for footings that support masonry walls is calculated at a point midway between the middle and the face of the wall. This approach is taken because masonry is considered to be less rigid compared to concrete. On the other hand, for footings that support concrete walls, the maximum bending moment is determined using equation 1.
The ultimate bearing capacity of soil under a wall footing, denoted as “qu”, is determined by dividing the ultimate distributed load by the required area of the footing. The width of the wall footing is represented as “b”, while the width of the wall supported by the footing is denoted as “a”. The vertical shear force, “Vu”, can be calculated at section 2-2, which is located at a distance “d” from the face of the wall, using equation 2. The development length calculation is based on the section of maximum moment, denoted as section 1-1.
The distance denoted as “d” refers to the measurement between the face of the wall and the location where the vertical shear force is applied. This distance is also known as the effective depth of the wall footing section.
Footing size
The size of footings is calculated based on unfactored loads and effective soil pressure (qe), which is determined from the allowable bearing pressure (qa). Unfactored loads are used in footing design because overall safety factors provide the necessary safety margin. The allowable bearing pressure is established in accordance with the principles of soil mechanics, taking into account load tests and other experimental data. For service loads, the allowable bearing pressure is calculated with a safety factor of 2.5 to 3. This safety factor ensures that the bearing capacity of the soil is not exceeded and that settlement remains within tolerable limits. The required area of the footing (Areq) is calculated by dividing the total service loads by the allowable bearing pressure using equation 3.
Equation 3 relates to the calculation of the area of a footing in structural engineering. It takes into account the dead load (D) and live load (L) on the footing, as well as the effective bearing pressure (qe) which is determined by subtracting the weight of fill and weight of concrete from the allowable bearing capacity. However, if there are other loads such as wind loads and seismic loads acting on the footing, equation 4 should also be used to compute the area of the footing. In this case, the larger value obtained from these two equations should be considered as the final area of the footing. This approach ensures that the footing is designed to withstand the maximum loads that it may be subjected to, including both dead and live loads as well as other external loads such as wind and seismic loads.
The width of the wall footing is determined based on the required area, and the length of the footing is standardized at 1 meter. The wind load (denoted as W) is calculated using a coefficient (w), which is set to 1.3 if computed based on the ASCE (American Society of Civil Engineers) standards, otherwise it is set to 1. Similarly, seismic forces (denoted as E) are also considered in the calculation. By using these coefficients and taking into account the required area and standardized footing length, the width of the wall footing can be accurately determined.
Footing Depth
ACI 318-19 section 13.3.1.2 specifies that the overall depth of a foundation should be chosen in such a way that the effective depth of bottom reinforcement is at least 150 mm. This means that the depth of the foundation should be such that the reinforcement placed at the bottom of the foundation is at a sufficient depth to ensure the stability and strength of the structure.
For sloped, stepped, or tapered foundations, it is important to ensure that the design requirements are met at every section. This requires careful consideration of the depth and location of steps, or the angle of slope, to ensure that the foundation can provide the necessary support for the structure.
In other words, if the foundation has a slope, step, or taper, the depth and location of these features must be designed in such a way that the foundation meets the necessary requirements for strength and stability at every point along its length. This ensures that the structure will remain safe and secure, even when subjected to external loads and other stresses.
Calculate Reinforcement Areas
Main reinforcement
The main reinforcement area is determined through a specific mathematical calculation. This calculation involves using an expression that takes into account various factors and variables. The resulting value from this expression serves as the main reinforcement area, which is a critical component in certain processes or systems. The expression is formulated based on specific criteria or requirements, and it may involve complex mathematical equations, algorithms, or formulas. Accurate computation of the main reinforcement area is crucial in ensuring the effectiveness and reliability of the overall process or system where it is applied. It is essential to understand and properly utilize the given expression in order to determine the correct main reinforcement area for the intended application.
In the given context, we are dealing with the main reinforcement area, denoted as “As”. The ultimate moment, denoted as “Mu”, is obtained from equation 1. The strength reduction factor, denoted as “Phi”, is assumed to be equal to 0.9. The yield strength of steel is denoted as “fy”. The effective depth, denoted as “d”, is calculated by subtracting the concrete cover of 75mm from the total depth. The depth of the rectangular stress block, denoted as “a”, is assumed based on equation 5, and is determined through trial and error. It is recommended to start with a trial value of 0.2 times the footing depth for “a”, and three trials are suggested to arrive at the final value.
Minimum Reinforcement
The minimum reinforcement is calculated using the following formulas: For steel grades lower than 420:
Steel grade 420 is a type of steel that is widely used in various applications due to its unique properties. This grade of steel is known for its high tensile strength, good ductility, and excellent corrosion resistance. It is commonly used in industries such as automotive, aerospace, and manufacturing, where strength and durability are critical requirements.
The tensile strength of steel grade 420 is significantly higher than that of other types of steel, making it ideal for applications that require materials to withstand heavy loads and extreme conditions. Its high tensile strength also makes it suitable for use in structural components such as beams, columns, and bridges, where structural integrity is of utmost importance.
In addition to its strength, steel grade 420 also exhibits good ductility, which means it can be easily shaped and formed without losing its mechanical properties. This makes it suitable for manufacturing processes such as welding, bending, and machining, allowing for versatile applications in various industries.
One of the notable features of steel grade 420 is its excellent corrosion resistance. This makes it suitable for use in environments where the material may be exposed to corrosive substances, such as chemical processing plants or marine applications. Its resistance to corrosion helps prolong the lifespan of components made from steel grade 420, reducing maintenance costs and improving overall performance.
Overall, steel grade 420 is a reliable and versatile material that is widely used in various industries due to its high tensile strength, good ductility, and excellent corrosion resistance. Its unique properties make it suitable for a wide range of applications where strength, durability, and resistance to corrosion are critical factors.
missing figure
The distributed reinforcement area for the wall footing is determined by equation 7, where the variables b and h represent the width and depth of the footing, respectively. This equation calculates the amount of distributed reinforcement that is required for the wall footing.
Bar Spacing/ Placement
The computation of the reinforcement area from equation 5 involves dividing it by the area of one bar (Ab), resulting in an estimate of the number of bars (n). This number of bars is then used to calculate the spacing for the main reinforcement using the provided expression.
Main bar spacing:
Distributed bar spacing:
The number of distributed bars in a construction project can be calculated by dividing the total area of steel reinforcement, as specified in equation 7, by the area of a single bar that will be used for distributed reinforcement. This calculation helps determine the quantity of bars needed for reinforcing the structure in a distributed manner.
Once the number of distributed bars is determined, the spacing between these bars can be calculated by dividing the width of the footing by the previously calculated number of distributed bars. This spacing calculation ensures that the bars are evenly distributed across the width of the footing, following the project specifications and design requirements.
Maximum Spacing:
The maximum spacing for steel bars should not exceed the smaller value between 3 times the bar diameter (3h) or 450mm. This means that the spacing between steel bars should be kept within this limit to ensure proper reinforcement. Exceeding this value may compromise the structural integrity and strength of the construction element being reinforced, and therefore should be avoided. Adhering to this maximum spacing requirement is crucial to ensure the desired performance and durability of the reinforced structure.
The concrete shear strength, denoted as Vc, is calculated using various parameters. One such parameter is the strength reduction factor, denoted as Phi, which has a value of 0.75. Another parameter is Lamda, which is equal to 1 for normal strength concrete. The concrete compressive strength, denoted as fc’, is another important parameter and should not be less than 17 MPa. Additionally, the width of the footing, denoted as b, and the effective depth of the footing, denoted as d, are also used in the calculation of Vc.
Fig. 2: Detail of Reinforcements
Summery of Design Procedure
The given task involves multiple calculations and design specifications for a footing. The first step is to estimate the thickness of the footing, denoted by h, which must meet the shear requirement and provide a minimum effective depth of 150mm. Once this is determined, the weight of both the fill and the footing should be calculated.
The effective bearing capacity, qe, must then be computed, followed by an estimation of the required area, denoted by Areq. The design pressure, qu, on the base of the footing (Areq) due to factored loads can then be calculated.
Next, the shear force and design shear strength of the concrete must be determined in order to check the shear requirements. The maximum moment can then be calculated, followed by an estimation of the required reinforcement area.
The minimum reinforcement and maximum spacing must be computed in order to ensure the structural integrity of the footing. This includes estimating the main and distributed bars spacing.
Finally, a design draft should be created to illustrate the calculated specifications and to serve as a reference for the construction process.