7.6:
Shear Diagram
The shear diagram is a graphical representation of the distribution of the shear forces along the beam'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's end and ultimately goes to zero to maintain equilibrium.
7.6:
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.
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.
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.
This shear force remains constant until the end of the beam, ultimately going to zero to maintain equilibrium.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. pp 361.
- Beer, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. and Self, B.P.(2019). Vector Mechanics for Engineers ‒ Statics and Dynamics. New York: McGraw-Hill. Pp 381.