Shear Force is the internal force that acts parallel to the cross-section of a beam[1]. It represents the algebraic sum of all vertical forces acting on either side of a section. Shear forces are maximum at supports and zero at points of maximum bending moment in simply supported beams.

Bending Moment is the internal moment that causes a beam to bend[7]. It is calculated as the algebraic sum of moments of all forces about a section. The maximum bending moment typically occurs where the shear force equals zero.

Simply Supported Beam with Point Load at Center:

Simply Supported Beam with UDL:

Cantilever Beam with Point Load at Free End:

Shear force and bending moment calculations are essential in structural engineering for designing safe and efficient beams[8]. These calculations help determine:

• Required beam size and material properties
• Maximum allowable loads and deflections
• Critical sections for reinforcement in concrete beams
• Optimal placement of supports and connections
• Safety factors and design margins

Engineers use these diagrams to identify critical points where maximum stresses occur, enabling optimal design of structural members while maintaining safety and economy[13].

Standard sign conventions for structural analysis:

• Shear Force: Positive when it tends to cause clockwise rotation of the left section
• Bending Moment: Positive when it causes compression in the top fiber (sagging)
• Deflection: Positive when downward from the original position

Common material properties for structural calculations:

• Steel: E = 200 GPa, Yield Strength = 250-400 MPa
• Concrete: E = 25-35 GPa, Compressive Strength = 20-40 MPa
• Timber: E = 10-15 GPa, Varies by species and grade
• Aluminum: E = 70 GPa, Yield Strength = 200-300 MPa