Understanding the Impact of an Internal Hinge on Bending Moment and Shear Force Diagrams for Simply Supported Beams

In structural engineering, an internal hinge within a simply supported beam introduces a point of rotation, which significantly affects the bending moment and shear force diagrams. This article delves into the details of these impacts, with specific emphasis on the location of the hinge, effects on bending moments, and influences on shear forces.

Effects of an Internal Hinge in Simply Supported Beams

When an internal hinge is incorporated into a simply supported beam, it divides the beam into two segments, each of which can rotate independently about the hinge, leading to significant changes in the distribution of forces and moments.

Location of the Hinge

The installation of an internal hinge affects the distribution of bending moments and shear forces. The existence of the hinge allows the beam segments to rotate independently, leading to unique characteristics in the bending and shear force diagrams.

Bending Moment

At the Hinge: The bending moment at the exact location of the internal hinge is zero. This is due to the hinge's characteristic of not resisting bending at that point. Instead, it allows for rotation, which means there is no resistance to moments.

Segments: For the segments on either side of the hinge, the bending moment diagrams show the application of loads to each segment, with a sharp decrease in bending moment to zero at the hinge. This discontinuity in the bending moment diagram is a clear indication of the hinge's effect on the beam's structural behavior.

Shear Force

Continuity across the Hinge: The shear force remains continuous across the hinge. However, the magnitude of shear force can change depending on the loads applied to each segment of the beam. This is because the internal hinge allows for rotation, which redistributes forces in a way that impacts the shear force diagram.

Evaluating Bending and Shear Forces with Example Analysis

To accurately analyze the effects of an internal hinge, the first step is to create a free body diagram (FBD) for each segment of the beam. Each segment should be subjected to the equations of equilibrium, such as ΣFy 0 (sum of vertical forces equals zero) and ΣM 0 (sum of moments equals zero).

Once these equilibrium equations are applied, it becomes possible to calculate the shear forces and bending moments at key points, including the supports and the hinge. These values are then plotted to produce shear force and bending moment diagrams.

Shear Force Diagram: The shear force diagram may display a change in slope at the hinge, indicating a change in shear force magnitude. This is a clear visual representation of the effect of the internal hinge on the shear force distribution.

Bending Moment Diagram: The bending moment diagram will show a clear drop to zero at the hinge, reflecting the zero bending moment at that point. This drop is a direct result of the hinge's functionality to allow rotation without resistance.

Conclusion

In summary, an internal hinge in a simply supported beam results in the following:

Understanding these effects is crucial for accurately designing and analyzing beam structures in engineering applications.