Houses in Astrology Calculator

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Reviewed by David Chen, PE (Civil Engineering) • Expert in Structural Analysis and Mechanical Design.

Calculate the reaction forces, maximum shear force, and maximum bending moment for a simply supported beam with a single point load instantly with our engineering-grade calculator.

Shear Force and Bending Moment Calculator

Maximum Results:

Shear Force and Bending Moment Calculator Formula:

Reactions:
Ra = P * (L – a) / L
Rb = P * a / L

Max Shear (V_max):
V_max = max(Ra, Rb)

Max Bending Moment (M_max):
M_max = (P * a * (L – a)) / L
Reference: Beam Bending Formulas – EngineersEdge Tutorial: SFD and BMD Analysis – SkyCiv

Variables:

  • Beam Length (L): The total span of the beam from support to support.
  • Point Load (P): The magnitude of the concentrated force acting downward.
  • Distance (a): The distance from the left-most support to where the load is applied.

Related Calculators:

What is a Shear Force and Bending Moment Calculator?

A Shear Force and Bending Moment Calculator is a specialized engineering tool used to determine the internal forces within a structural element. When a beam is subjected to external loads, it experiences internal shear forces that attempt to “slide” parts of the beam against each other, and bending moments that cause the beam to curve.

This calculator specifically models a “Simply Supported Beam,” which is the fundamental unit in structural engineering. It is pinned at one end and has a roller at the other, ensuring that it is statically determinate and stable for static load analysis.

How to Calculate Shear Force and Bending Moment (Example):

  1. Identify the Beam Length (L = 10m), Load (P = 20kN), and Distance (a = 5m).
  2. Calculate Reaction Ra: 20 * (10 – 5) / 10 = 10kN.
  3. Calculate Reaction Rb: 20 * 5 / 10 = 10kN.
  4. Determine Max Shear Force: In this symmetrical case, V_max = 10kN.
  5. Calculate Max Bending Moment at Point a: (20 * 5 * 5) / 10 = 50 kNm.

Frequently Asked Questions (FAQ):

What is the difference between SF and BM? Shear Force represents the vertical internal resistance, while Bending Moment represents the internal rotational resistance.

Where does the maximum bending moment occur? For a single point load on a simply supported beam, the maximum moment always occurs directly under the point of load application.

Can distance ‘a’ be greater than length ‘L’? No, the point of load must be within the span of the beam for this standard calculation.

What units should I use? You can use any consistent units (e.g., meters and kiloNewtons), but ensure the results are interpreted in the same unit system (e.g., kNm for moment).

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