Shear Force Calculator
Estimate shear force for your project with our free calculator. Get accurate material quantities, costs, and specifications.
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Adjust values & calculateAnalysis Summary
Formula
For a simply supported beam with uniform distributed load w over span L, the maximum shear force equals wL/2 at each support and the maximum bending moment is wL squared over 8 at midspan. For a point load P at distance a from the left support, the reactions are Pa/L and Pb/L where b is the distance from the right support.
Last reviewed: December 2025
Worked Examples
Example 1: Simply Supported Beam with UDL
Example 2: Point Load at Third Point
Background & Theory
The Shear Force Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Shear Force Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Key Features
- Solves all four kinematic equations for displacement, velocity, acceleration, and time given any two known variables, making it easy to analyze linear motion problems.
- Applies Newton's second law to compute net force, mass, or acceleration directly from entered values, supporting multiple force components in two dimensions.
- Calculates kinetic energy, gravitational potential energy, and verifies work-energy conservation so users can quickly check energy transformations in mechanical systems.
- Computes wave frequency, wavelength, period, and wave speed from any combination of known wave properties, covering both sound and electromagnetic waves.
- Determines electric field strength and electrostatic force between point charges using Coulomb's law, with support for multi-charge configurations along a line.
- Analyzes Ohm's law relationships and solves series, parallel, and mixed resistor networks for equivalent resistance, current, and voltage drops across each element.
- Calculates projectile range, maximum height, and total time of flight from launch angle and initial speed, with optional air resistance adjustments.
- Applies special relativity formulas to compute time dilation, length contraction, and mass-energy equivalence via E=mcยฒ, useful for high-velocity and nuclear energy problems.
Frequently Asked Questions
Formula
Simply Supported UDL: Vmax = wL/2, Mmax = wL^2/8 | Point Load: Ra = Pb/L, Rb = Pa/L
For a simply supported beam with uniform distributed load w over span L, the maximum shear force equals wL/2 at each support and the maximum bending moment is wL squared over 8 at midspan. For a point load P at distance a from the left support, the reactions are Pa/L and Pb/L where b is the distance from the right support.
Worked Examples
Example 1: Simply Supported Beam with UDL
Problem: Find the maximum shear force for a 6m simply supported beam carrying 20 kN/m uniformly distributed load.
Solution: Total load = 20 * 6 = 120 kN\nRa = Rb = wL/2 = 20*6/2 = 60 kN\nVmax = 60 kN (at supports)\nMmax = wL^2/8 = 20*36/8 = 90 kN-m
Result: Maximum shear force = 60 kN at both supports
Example 2: Point Load at Third Point
Problem: Find reactions and shear for a 9m beam with a 45 kN point load at 3m from the left support.
Solution: Ra = P*b/L = 45*6/9 = 30 kN\nRb = P*a/L = 45*3/9 = 15 kN\nVmax = 30 kN\nMmax = P*a*b/L = 45*3*6/9 = 90 kN-m
Result: Ra = 30 kN, Rb = 15 kN, Vmax = 30 kN
Frequently Asked Questions
What is shear force in a beam?
Shear force at any cross-section of a beam is the algebraic sum of all transverse forces acting on either side of that section. It represents the internal force that resists sliding of one part of the beam relative to the other. Shear force is typically maximum at the supports for simply supported beams and at the fixed end for cantilevers. It is measured in kilonewtons (kN) or pounds (lbs).
How do shear force and bending moment relate to each other?
The shear force at any point along a beam equals the rate of change of bending moment at that point, expressed mathematically as V = dM/dx. This means that where the shear force is zero, the bending moment reaches a maximum or minimum value. Engineers use shear force diagrams and bending moment diagrams together to understand the complete internal force distribution along a beam.
What is the difference between positive and negative shear force?
By the standard beam sign convention, positive shear force causes a clockwise rotation of the beam element, meaning the left face moves upward relative to the right face. Negative shear causes counterclockwise rotation. In a simply supported beam with a downward uniform load, the shear force is positive at the left support and transitions to negative at the right support, passing through zero at midspan.
Why is shear force important for structural design?
Shear force determines the required shear reinforcement (stirrups) in concrete beams and governs the web thickness of steel beams. Shear failures in concrete are sudden and brittle, which is why building codes require a minimum level of shear reinforcement even when calculated shear stresses are low. For short, deep beams, shear capacity often controls the design rather than flexural capacity.
Where does maximum shear force occur?
For simply supported beams with uniform loads, maximum shear occurs at the supports and equals half the total load. For point loads, the maximum shear is at the support nearest to the concentrated load. In cantilever beams, the maximum shear force is always at the fixed support and equals the total applied load. Fixed-fixed beams also have their maximum shear at the supports.
How do you draw a shear force diagram step by step?
To draw a shear force diagram, first calculate all support reactions using equilibrium equations. Start from the left end of the beam and move rightward, plotting the shear value at each point. At each support reaction, the shear jumps up by the reaction magnitude. At each downward point load, the shear drops by the load magnitude. Under a uniformly distributed load, the shear changes linearly with a slope equal to the negative load intensity. Mark the zero-shear crossing point because this is where the bending moment reaches its maximum. The diagram should close back to zero at the right end if all forces are accounted for correctly.
References
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