Name: beam shear force diagram
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 27 s
Channel: JoVE

The shear diagram is a graphical representation of the distribution of the shear forces along the beam&#39;s length.
Consider a beam AB supported at two ends and subjected to perpendicular loads. Construct its shear diagram.
Draw the free-body diagram of the beam. Using the equilibrium equations of force and moment, the reaction forces at each support can be calculated.
Apply the method of section to the beam.
Next, consider an arbitrary distance from point A within the region AP. Draw a free-body diagram of the section. Under the equilibrium condition, the shear force in the section equals the reaction force at the support.
Similarly, consider an arbitrary point within the region PQ. By drawing the free-body diagram and using the equilibrium equation, the shear in the section can be determined.
Finally, the arbitrary point is considered within section QB. By drawing the free-body diagram and recalling the equilibrium equation, the shear in the section can be determined, which remains constant until the beam&#39;s end and ultimately goes to zero to maintain equilibrium.

shear diagram

In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
First, a free-body diagram of the beam is drawn, representing all the external forces and internal reactions acting on the beam. One can calculate the reaction forces at each support by employing the equilibrium equations of force and moment. The vertical component of the reaction forces at points A and B obtained for the given beam is  24 kN and 18 kN, respectively.
<img alt="Static equilibrium diagram; ΣFy=0, shear force analysis, 3-point load distribution, beam forces." src="/files/ftp_upload/14301/14301_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium diagram; beam with forces F1=30kN, F2=12kN; shear force distribution graph.">
A shear diagram is a graphical representation that illustrates the distribution of shear forces along the length of the beam. To create this diagram, the method of sections is applied to the beam. Next, an arbitrary distance from point A within the region AP is considered. A free-body diagram of this section is drawn to analyze the forces acting on it. Under the equilibrium condition, the shear force in the section is equal to the reaction force at the support, which is V1=24 kN.
Similarly, an arbitrary point within the region PQ is considered. By drawing a free-body diagram of this section and using the equilibrium equation, the shear force, V2, can be determined.
<img alt="Static equilibrium equation 24 kN - 30 kN - V₂ = 0, structural mechanics analysis." src="/files/ftp_upload/14301/14301_Equation_1v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation ΣFy=0 for force balance analysis, featuring 24 kN, 30 kN, V₂.">
Finally, an arbitrary point is considered within the section QB. A free-body diagram is drawn for this section, and the equilibrium equation is recalled to determine the shear force, V3, in the section.
<img alt="Static equilibrium equation ΣF=0 for force analysis, featuring forces in kilonewtons." src="/files/ftp_upload/14301/14301_Equation_2v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium equation, ΣFx=0, with forces in kilonewtons, illustrating balance conditions.">
This shear force remains constant until the end of the beam, ultimately going to zero to maintain equilibrium.

Shear Diagram

In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider ...

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beam shear force diagram

Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions.

The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24 kN and the vertical reaction at B is 18 kN. These values become the starting point for building the shear diagram.

To form the shear diagram, the method of sections is used. A point is chosen at an arbitrary distance from A in the region AP, and a free-body diagram of that section is drawn. From equilibrium, the shear force in that section is V1 = 24 kN.

The same process is repeated in the region PQ. An arbitrary point is selected, the section is isolated, and the equilibrium equation is applied to find V2. A third section is then taken in the region QB. Its free-body diagram gives V3, which stays constant until the end of the beam and then goes to zero so the beam remains in equilibrium.

Beam Shear Force Diagram

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Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions. The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24...

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key terms and concepts

Learn how to build a beam shear force diagram using free-body diagrams, reaction forces, and the method of sections for a supported beam.

Beam Shear Force Diagram | JoVE K12

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Beam Shear Force Diagram

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