Simply Supported Beam: Shear and Moment Diagrams

This app calculates and plots the shear force and bending moment diagrams for a simply supported beam subjected to:

• A uniformly distributed load (UDL) of intensity w (in kN/m) over the entire span
• A concentrated load P (in kN) applied at the midspan

Inputs

• Beam Span (L): The total length of the beam, in meters.
• Uniform Load (w): The intensity of the distributed load, in kN/m.
• Concentrated Load (P): The magnitude of the point load at midspan, in kN.

Calculation Method

The beam is simply supported at both ends. The reactions at the supports are calculated as:

• Reaction at each support: $\frac{wL}{2} + \frac{P}{2}$

The shear force and bending moment at any position x (from the left support) are given by:

• For x < midspan:
• $V(x) = R_1 - w x$
• $M(x) = R_1 x - \frac{w x^2}{2}$
• For x ≥ midspan:
• $V(x) = R_1 - w x - P$
• $M(x) = R_1 x - \frac{w x^2}{2} - P(x - a)$, where $a = \frac{L}{2}$

Diagrams

• Shear Force Diagram: Shows the variation of shear force along the beam. The diagram has a jump at the midspan due to the concentrated load.
• Bending Moment Diagram: Shows the variation of bending moment along the beam. The maximum moment typically occurs at midspan.

Key Points

The app calculates and displays the shear and moment values at:

• Left support (A, x=0)
• Quarter span (B, x=L/4)
• Just before midspan (C-, x=a-)
• Just after midspan (C+, x=a+)
• Three-quarter span (D, x=3L/4)
• Right support (E, x=L)

How to Use

1. Enter the beam span, uniform load, and concentrated load values.
2. View the interactive diagrams. Hover over the plots to see values at any point.
3. Check the table for exact values at key locations.