Shear Force (SF):

• Shear force at a section is the algebraic sum of all the vertical forces acting either to the left or to the right of the section.
• It represents the internal force within the beam that resists the tendency of one part of the beam to slide or shear relative to the other part.
• A shear force diagram plots the variation of this shear force along the length of the beam.

Bending Moment (BM):

• Bending moment at a section is the algebraic sum of the moments of all the forces acting either to the left or to the right of the section about that section.
• It represents the internal moment within the beam that resists the bending caused by the applied loads.
• A bending moment diagram plots the variation of this bending moment along the length of the beam.

Purpose and Use:

• Determining Internal Forces: SFBMDs help determine the magnitude and location of maximum shear force and bending moment, which are critical for structural design.
• Structural Design: Engineers use these diagrams to select appropriate beam sizes and materials to ensure the structure can withstand the internal forces and moments without failure.
• Identifying Critical Points: They help identify points of maximum stress and deflection, which are important for ensuring the structural integrity and serviceability of the beam.
• Understanding Beam Behavior: SFBMDs provide a visual representation of how the beam responds to different loading conditions, aiding in understanding its overall structural behavior.

How to Create:

• Calculate Support Reactions: Determine the reactions at the supports of the beam.
• Establish Sections: Divide the beam into sections based on the locations of applied loads and supports.
• Calculate Shear Force and Bending Moment Equations: For each section, derive equations for shear force and bending moment as a function of the distance along the beam.
• Plot the Diagrams: Plot the shear force and bending moment equations on a graph, with the beam's length on the x-axis and the shear force/bending moment on the y-axis.

Sign Conventions:

• Shear Force: A common convention is to consider upward forces to the left of the section as positive and downward forces to the right of the section as positive.
• Bending Moment: A common convention is to consider moments that cause compression in the upper fibers of the beam (sagging) as positive and moments that cause tension in the upper fibers (hogging) as negative.