Structural Engineering Specialist & Technical Consultant
Calculate beam reactions and shear force distributions instantly. This tool helps engineers and students visualize the internal forces of a simply supported beam under a concentrated point load, providing precise values for structural analysis.
Shear Force Diagram Calculator
Shear Force Diagram Calculator Formula:
Reaction A (Left): $R_A = \frac{P \times (L – a)}{L}$
Reaction B (Right): $R_B = \frac{P \times a}{L}$
Shear Force ($V$): $V(x) = R_A$ (if $0 < x < a$); $V(x) = -R_B$ (if $a < x < L$)
Source: ScienceDirect Engineering Reference
Variables:
- P (Load): The concentrated vertical force applied to the beam.
- L (Length): The total distance between the two supports.
- a (Position): The distance from the left support (A) to the point of load application.
- V (Shear Force): The internal force acting perpendicular to the beam’s longitudinal axis.
Related Calculators:
What is a Shear Force Diagram Calculator?
A Shear Force Diagram (SFD) calculator is a specialized tool used in structural engineering to determine how internal vertical forces vary along the length of a beam. It identifies points of maximum shear, which are critical for designing the shear reinforcement (stirrups) in concrete or checking the web capacity in steel beams.
Understanding the SFD is the first step in structural analysis. By knowing where the shear force changes magnitude or direction, engineers can ensure that the beam structure will not fail due to sliding or “cutting” forces under its design load.
How to Calculate Shear Force (Example):
- Identify the point load (e.g., $P = 20\text{ kN}$).
- Measure total beam length (e.g., $L = 10\text{ m}$) and load position (e.g., $a = 4\text{ m}$).
- Calculate $R_A$: $20 \times (10 – 4) / 10 = 12\text{ kN}$.
- Calculate $R_B$: $20 \times 4 / 10 = 8\text{ kN}$.
- The shear is $+12\text{ kN}$ from $0$ to $4\text{m}$, and $-8\text{ kN}$ from $4\text{m}$ to $10\text{m}$.
Frequently Asked Questions (FAQ):
What is the unit of shear force? In the SI system, it is typically measured in Newtons (N) or KiloNewtons (kN).
Why is shear force negative? The sign convention (positive or negative) depends on whether the force tends to rotate the beam segment clockwise or counter-clockwise.
Does self-weight affect the SFD? Yes. This simple calculator focuses on point loads; a uniform distributed load (UDL) would create a sloped line in the diagram.
What happens at the point of load? There is a sudden “jump” or discontinuity in the shear force value equal to the magnitude of the load $P$.