Shear Moment Diagram Calculator
Free Shear moment diagram Calculator for statics. Enter variables to compute results with formulas and detailed steps.
Calculator
Adjust values & calculateShear Force Values (kN)
Bending Moment Values (kN-m)
Formula
The shear force at any section is the algebraic sum of all vertical forces to one side of that section. The bending moment is the algebraic sum of moments of all forces to one side. For a point load P at distance a: RA = Pb/L, RB = Pa/L. For UDL w: RA = RB = wL/2 (full span). Max moment occurs where shear equals zero.
Last reviewed: December 2025
Worked Examples
Example 1: Simply Supported Beam with Central Point Load
Example 2: Simply Supported Beam with Full UDL
Background & Theory
The Shear Moment Diagram Calculator applies the following established principles and formulas. Physics is the fundamental natural science concerned with matter, energy, and the interactions between them. Classical mechanics, founded on Newton's three laws of motion, provides the framework for analyzing the motion of objects. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: F = ma, where force equals mass times acceleration in SI units of newtons (N = kgยทm/sยฒ). The third law establishes that every action produces an equal and opposite reaction. Kinematics describes motion without reference to its causes. The four fundamental equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t: v = u + at, s = ut + ยฝatยฒ, vยฒ = uยฒ + 2as, and s = ยฝ(u + v)t. These assume constant acceleration and are foundational for solving projectile motion, free fall, and linear dynamics problems. Energy conservation underpins much of physics. Kinetic energy is KE = ยฝmvยฒ, where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g โ 9.81 m/sยฒ near Earth's surface and h is height in meters. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ฮKE. Electricity and circuits rely on Ohm's law: V = IR, where voltage V is in volts, current I in amperes, and resistance R in ohms. Electrical power is P = IV = IยฒR = Vยฒ/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength ฮป through f = v/ฮป, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/mยฒ). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(molยทK), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gmโmโ/rยฒ, where G = 6.674ร10โปยนยน Nยทmยฒ/kgยฒ is the gravitational constant.
History
The history behind the Shear Moment Diagram Calculator traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384โ322 BCE) proposed that all matter consisted of four elements and that objects moved toward their natural place, with heavier objects falling faster than lighter ones. While largely incorrect, his systematic approach to explaining nature dominated Western thought for nearly 2,000 years. The Scientific Revolution overturned Aristotelian physics. Galileo Galilei (1564โ1642) performed groundbreaking experiments on inclined planes and falling bodies, demonstrating that all objects fall with the same acceleration regardless of mass, and established the principle of inertia. His use of mathematics to describe motion was revolutionary. Isaac Newton synthesized these developments in his landmark Principia Mathematica (1687), laying out the three laws of motion and the law of universal gravitation. Newton's framework unified terrestrial and celestial mechanics, explaining planetary orbits with the same equations governing a falling apple. His calculus provided the mathematical language for expressing rates of change. The 19th century brought two major theoretical achievements. James Clerk Maxwell formulated his equations of electromagnetism between 1861 and 1862, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves traveling at the speed of light. Thermodynamics was developed by Carnot, Clausius, and Kelvin, establishing the laws governing heat, work, and entropy. The 20th century produced two revolutions that fundamentally altered the classical picture. Albert Einstein published the special theory of relativity in 1905, showing that space and time are not absolute but relative to the observer, and that mass and energy are equivalent via E = mcยฒ. His general theory of relativity in 1915 reinterpreted gravity as the curvature of spacetime. Simultaneously, quantum mechanics emerged from the work of Planck, Bohr, Heisenberg, and Schrรถdinger, revealing that at atomic scales energy is quantized and particles exhibit wave-particle duality. These developments culminated in the Standard Model of particle physics, which describes all known fundamental particles and three of the four fundamental forces.
Frequently Asked Questions
Formula
V(x) = RA - Sum of loads to left of x | M(x) = Integral of V(x) dx
The shear force at any section is the algebraic sum of all vertical forces to one side of that section. The bending moment is the algebraic sum of moments of all forces to one side. For a point load P at distance a: RA = Pb/L, RB = Pa/L. For UDL w: RA = RB = wL/2 (full span). Max moment occurs where shear equals zero.
Worked Examples
Example 1: Simply Supported Beam with Central Point Load
Problem: A 6 m simply supported beam carries a 10 kN point load at the center (3 m from each support). Determine the reactions, maximum shear, and maximum bending moment.
Solution: Reactions: RA = RB = P/2 = 10/2 = 5 kN (symmetric loading)\nShear: V = +5 kN from left support to load, V = -5 kN from load to right support\nMax Shear = 5 kN (at supports)\nMax Moment = PL/4 = 10 x 6/4 = 15 kN-m (at center)\nZero shear occurs at x = 3 m (load point)
Result: RA = RB = 5 kN | Max Shear: 5 kN | Max Moment: 15 kN-m at center
Example 2: Simply Supported Beam with Full UDL
Problem: A 6 m beam carries a uniformly distributed load of 5 kN/m over its entire length. Find the maximum shear and moment.
Solution: Total load = 5 x 6 = 30 kN\nReactions: RA = RB = 30/2 = 15 kN\nMax Shear = wL/2 = 5 x 6/2 = 15 kN (at supports)\nMax Moment = wL^2/8 = 5 x 36/8 = 22.5 kN-m (at midspan)\nShear is zero at midspan (x = 3 m)
Result: RA = RB = 15 kN | Max Shear: 15 kN | Max Moment: 22.5 kN-m at midspan
Frequently Asked Questions
What are shear force and bending moment diagrams used for in structural analysis?
Shear force diagrams (SFD) and bending moment diagrams (BMD) are fundamental tools in structural engineering that graphically represent the internal forces and moments acting along the length of a beam. The shear force diagram shows how the internal vertical force varies at each cross-section, which is critical for designing against shear failure and determining required web thickness in steel beams or stirrup spacing in reinforced concrete. The bending moment diagram reveals the internal moment distribution, which determines the maximum bending stress and governs the required section modulus or reinforcement for the beam. Together, these diagrams enable engineers to identify critical sections, size structural members, and verify that designs meet safety requirements.
What is the relationship between shear force and bending moment?
Shear force and bending moment are mathematically related through calculus. The bending moment at any point is the integral (area under the curve) of the shear force diagram up to that point. Conversely, the shear force is the derivative (rate of change) of the bending moment. This means the bending moment reaches its maximum or minimum value where the shear force equals zero or changes sign. The distributed load intensity equals the negative derivative of the shear force. These relationships provide important shortcuts: the change in moment between two points equals the area under the shear diagram between those points, and the slope of the moment diagram at any point equals the shear force at that point.
Can I use Shear Moment Diagram Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
References
Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy