# Beam Bending Moment & Shear Force Calculator

Shear Force Diagram

Bending Moment Diagram

## Formulas Used:

**Support Reactions:**

R_{A} = \(\frac{{UDL \times L}}{2} + \frac{{Point Load \times (L - Point Load Position)}}{L}\)

R_{B} = UDL \times L + Point Load - R_{A}

**Shear Force:**

SF_{A} = R_{A}

SF just before Point Load = SF_{A} - UDL \times Point Load Position

SF just after Point Load = SF just before Point Load - Point Load

SF_{B} = SF just after Point Load - UDL \times (L - Point Load Position)

**Bending Moment:**

BM_{x} = R_{A} \times x - \(\frac{{UDL \times x^2}}{2}\) (for x <= Point Load Position)

BM_{x} = BM at Point Load Position - Point Load \times (x - Point Load Position) - \(\frac{{UDL \times (x - Point Load Position)^2}}{2}\) (for x > Point Load Position)

### Beam Bending Moment and Shear Force Calculator Tool

Understanding the behavior of beams under various loads is crucial in civil and structural engineering. To make this easier for professionals, students, and anyone interested in engineering, we’ve developed an intuitive **Beam Bending Moment and Shear Force Calculator Tool**. This tool is designed to simplify the process of calculating key parameters like shear force and bending moment for beams subjected to point loads and uniformly distributed loads (UDLs).

#### Key Features of the Tool

**User-Friendly Interface**: The calculator is easy to use with a clean and intuitive design. Simply input the beam’s length, the point load, its position, and the UDL value. After clicking the “Calculate” button, the tool provides immediate results.**Accurate Calculations**: The tool performs precise calculations for support reactions, shear forces, and bending moments. The results are based on standard formulas used in structural engineering, ensuring you get accurate and reliable data.**Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)**: The tool not only calculates the shear force and bending moment but also generates corresponding diagrams. These diagrams visually represent how the beam responds under the applied loads, making it easier to understand the stress distribution along the beam.**Formulas Used**: For those interested in the underlying mathematics, the tool displays the exact formulas used for calculations. This feature is particularly useful for students and professionals who want to understand the process step-by-step.

#### How the Beam Bending Moment and Shear Force Calculator Works

When you enter the beam’s length, the point load (in kN), the position of the point load along the beam, and the UDL (in kN/m), the calculator processes this information to determine the shear force and bending moment at key points along the beam.

**Support Reactions**: The tool first calculates the reactions at the supports, which are crucial for determining the shear force and bending moment.**Shear Force Calculation**: The shear force at different points along the beam is computed, particularly at the supports and just before and after the point load.**Bending Moment Calculation**: The bending moment is calculated at the supports and at the location of the point load, showing the maximum moment which is critical in design.**Diagrams**: The SFD and BMD diagrams provide a clear visual of how the beam reacts under the applied loads. These diagrams are essential for understanding the performance of the beam and are widely used in engineering analysis.

#### Why Use This Tool?

This **Beam Bending Moment and Shear Force Calculator** is ideal for students, educators, and engineers who need quick and accurate calculations. The tool eliminates the need for manual calculations and ensures that results are accurate and easy to understand. Whether you’re working on a structural analysis project or just learning the basics, this tool will save you time and help you grasp the core concepts of beam analysis.