What is bending moment (BM) & Shear force (SF) – Explain

Bending moment (BM) and shear force (SF) are two fundamental concepts in structural engineering that describe the behavior of a structural element, such as a beam or a column, under loads.

1. Bending Moment (BM): Bending moment is a measure of the internal force or moment that exists within a structural element when an external force is applied perpendicular to its longitudinal axis, causing the element to bend. It is a function of the applied force, the distance from the force to a particular point on the element (known as the moment arm), and the angle of the force relative to the element.
   • Mathematically, bending moment (M) at any point along the length of a beam is given by the product of the applied force and the perpendicular distance from the force to the point of interest. Mathematically,
   • it can be expressed as: 
     $M=F\times d$ where:
     $M$ = Bending Moment,
     $F$ = Applied force (load),
     $d$ = Perpendicular distance from the point to the line of action of the force.
   • Units: Bending moment is typically measured in units of force multiplied by distance, such as Newton-meters (Nm) or pound-feet (lbf-ft).
   • Effects: Bending moment causes the beam to bend or deform. It is crucial in determining the stress and deflection of the structural member, which are essential considerations in structural design.
2. Shear Force (SF): Shear force is the internal force that acts parallel to the cross-section of a structural element when external forces are applied perpendicular to its longitudinal axis. It tends to cause one part of the material to slide or deform relative to an adjacent part. Shear force is experienced in all materials and is particularly important in elements like beams, where it can lead to shear failure if not adequately considered in design.
   • Mathematically, shear force (V) at any point along the length of a beam is equal to the algebraic sum of the external forces acting on one side of the section. Mathematically, it can be expressed as: V=∑F
   •  where: $V$ = Shear Force, $\sum F$ = Sum of all external forces acting on one side of the section.
   • Units: Shear force is typically measured in units of force, such as Newtons (N) or pounds (lb).
   • Effects: Shear force leads to the deformation of the material along the plane of the cross-section. Excessive shear force can cause structural failure, especially in elements like beams where it can lead to shear buckling or tearing.

In summary, bending moment and shear force are both critical factors in the analysis and design of structural elements, particularly beams. Understanding their distribution along the length of a structural member is essential for ensuring its stability, safety, and optimal performance under various loading conditions.