Name: beam forces: tension, shear, and bending
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

When a beam is subjected to a load, it experiences internal forces that can be categorized as normal, shear, and bending moments.
Internal forces can be determined by using the method of sections. A special sign convention is applied as they occur in pairs, and their direction depends on which side of the section is to be analyzed.
The normal force is assumed to be positive if it creates tension, whereas it is considered negative if it generates compression in the object.
Suppose the forces acting tangentially to the cross-section are directed downwards and upwards on the left and right sides of the section, respectively. In that case, the shear force is regarded as positive, resulting in a clockwise rotation.
Similarly, if the direction of the forces on each side is reversed, a negative shear is produced, resulting in an anti-clockwise rotation.
When an external force acts on the beam, it experiences a bending moment, forming an upward or downward concave curvature. The bending moment is positive for upward curvature and negative for downward curvature.

sign convention

When analyzing a beam subjected to various loads, it is crucial to understand the internal forces and moments generated within the structure. These internal forces can be broadly classified into normal forces, shear forces, and bending moments. To determine these forces and moments, we use the method of sections and apply a specific sign convention based on their direction and the side of the section being analyzed.
The normal force acts perpendicular to the beam&#39;s cross-section and can cause tension or compression within the object. When the normal force creates tension, it is assumed to be positive, whereas when it generates compression, it is considered negative.
Shear force refers to the forces acting tangentially to the cross-section of the beam. These forces typically occur in pairs, with one force acting on the left side of the section and the other on the right side. If the force on the left side is directed downward and the force on the right side is directed upward, the shear force is considered positive, resulting in a clockwise rotation. Conversely, if the direction of the forces on each side is reversed, a negative shear force is produced, leading to a counterclockwise rotation.
The bending moment is the rotational effect caused by an external force acting on the beam. When subjected to such a force, the beam experiences a curvature, which can either be upward (concave) or downward (convex). The sign convention for bending moments dictates that a positive bending moment corresponds to an upward (concave) curvature, while a negative bending moment corresponds to a downward (convex) curvature. This convention plays a vital role in understanding the deformation pattern of the beam and designing appropriate structural elements to resist bending.
In summary, the sign conventions for normal force, shear force, and bending moment are essential tools in structural analysis. They help engineers and designers understand the behavior of structures under various loads, predict potential failure modes, and design robust and efficient structural elements.

Sign Convention

When analyzing a beam subjected to various loads, it is crucial to understand the internal forces and moments generated within the structure. These ...

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Internal Forces

KEY TERMS AND CONCEPTS

beam forces: tension, shear, and bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative.

Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it easier to read and compare force results during structural analysis.

Shear force acts tangentially along the cross-section of the beam. It often appears as a pair of forces, with one side of the cut carrying the left-side force and the other side carrying the right-side force. A downward force on the left side and an upward force on the right side represent positive shear and a clockwise rotation. If the directions are reversed, the shear force is negative and the rotation is counterclockwise.

Bending moment describes the turning effect created by an external force on a beam. It changes the beam’s shape into either an upward, concave curve or a downward, convex curve. A positive bending moment gives upward, concave curvature. A negative bending moment gives downward, convex curvature. These conventions help predict how beams deform under load and support better structural design.

Beam Forces: Tension, Shear, and Bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative. Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it...

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key terms and concepts

Learn how normal force, shear force, and bending moment use sign conventions in beam analysis, and how tension, compression, and curvature are labeled.

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JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Beam Forces: Tension, Shear, and Bending

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