Use this calculator to estimate basic parameters for structural footings and simply supported beams. This tool provides preliminary calculations for required footing area based on applied load and soil bearing capacity, and for maximum bending moment and shear force in a beam under various loads.
Footing Design (Basic Area)
Calculate the required area for a shallow footing based on the applied axial load and the soil's allowable bearing capacity.
Square
Circular
Beam Analysis (Simply Supported)
Determine the maximum bending moment and shear force for a simply supported beam under uniformly distributed and/or point loads.
Examples
Footing Example:
A column carries an axial load of 150 kN. The allowable soil bearing capacity is 100 kPa. If a square footing is used:
Required Footing Area = 150 kN / 100 kPa = 1.5 m²
Footing Side = sqrt(1.5) ≈ 1.22 m
If a circular footing is used:
Required Footing Area = 1.5 m²
Footing Diameter = 2 * sqrt(1.5 / π) ≈ 1.38 m
Beam Example:
A simply supported beam has a span of 6 meters. It carries a uniformly distributed load of 10 kN/m and a point load of 20 kN at 3 meters from the left support.
Max Bending Moment (from uniform load) = (10 kN/m * (6 m)²) / 8 = 45 kNm
Max Bending Moment (from point load) = (20 kN * 3 m * (6 m – 3 m)) / 6 m = 30 kNm
Total Max Bending Moment ≈ 45 kNm + 30 kNm = 75 kNm (Note: This is a simplified sum; actual max moment location may vary)
Max Shear Force (from uniform load) = (10 kN/m * 6 m) / 2 = 30 kN
Max Shear Force (from point load) = 20 kN (at supports, or just the reaction)
Total Max Shear Force ≈ 30 kN + 20 kN = 50 kN (at supports)
Understanding Footings and Beams in Structural Design
Footings and beams are fundamental components of almost any structure, from residential homes to towering skyscrapers. They play critical roles in transferring loads safely to the ground and distributing forces throughout the building frame.
What is a Footing?
A footing is the lowest part of a structure, typically made of concrete, that directly contacts the soil. Its primary purpose is to transfer the loads from the columns or walls of a structure to the underlying soil over a larger area. This distribution reduces the pressure on the soil to a level that the soil can safely support without excessive settlement or shear failure. Without proper footings, concentrated loads could cause the soil to yield, leading to structural instability and damage.
Key considerations for footing design include:
Applied Axial Load: The total vertical force coming down from the structure above.
Allowable Soil Bearing Capacity: The maximum pressure the soil can safely withstand without failure. This is determined through geotechnical investigations.
Footing Shape and Size: Determined by the load, soil capacity, and practical construction considerations (e.g., square, rectangular, circular).
Depth of Footing: Influenced by frost line, soil strata, and potential for scour.
Reinforcement: Steel rebar is used to resist bending moments and shear forces within the footing itself.
Our calculator focuses on the basic required area, which is the first step in footing design.
What is a Beam?
A beam is a horizontal structural element that primarily resists loads applied perpendicular to its longitudinal axis. These loads cause bending moments and shear forces within the beam, which it must be designed to withstand. Beams are essential for supporting floors, roofs, and walls, transferring their loads to columns or other supporting elements.
Common types of beams include:
Simply Supported Beam: Supported at both ends, allowing rotation but preventing vertical movement. This is the most basic type and is used in our calculator.
Cantilever Beam: Supported at one end and free at the other.
Fixed Beam: Supported at both ends with no rotation allowed.
Continuous Beam: Supported at more than two points.
Key considerations for beam design include:
Span Length: The distance between supports.
Applied Loads: Can be uniformly distributed (e.g., weight of a floor slab), concentrated point loads (e.g., a column resting on the beam), or varying loads.
Material Properties: Such as concrete compressive strength (f'c) and steel yield strength (Fy) for reinforced concrete beams, or material properties for steel or timber beams.
Cross-sectional Dimensions: The width and depth of the beam, which influence its stiffness and strength.
Bending Moment: A measure of the internal forces that cause the beam to bend. Maximum bending moment is critical for determining the required amount of longitudinal reinforcement.
Shear Force: A measure of the internal forces that cause the beam to shear or slide apart. Maximum shear force is critical for determining the required shear reinforcement (stirrups).
Our beam calculator helps you find the maximum bending moment and shear force, which are crucial values for the subsequent detailed design of the beam's cross-section and reinforcement.
Limitations of This Calculator
This calculator provides simplified, preliminary estimates. Actual structural design requires a comprehensive understanding of structural mechanics, material properties, building codes, and site-specific conditions. Factors not considered here include:
Self-weight of the footing or beam.
Detailed soil-structure interaction.
Punching shear, one-way shear, and bending reinforcement for footings.
Deflection, torsion, and stability for beams.
Specific building code requirements (e.g., ACI, Eurocode, ASCE).