Final answer:
The calculus-based method helps to simplify calculations when analyzing the relationships between shear force and bending moments in structural engineering, utilizing shear modulus and static equilibrium principles.
Step-by-step explanation:
The calculus-based method discussed is used to relate shear load to bending moments primarily because it simplifies the calculations involved in determining the internal forces and moments in structural elements. Understanding the relationship between shear force and bending moments is crucial in the field of structural engineering, where we use concepts such as shear modulus, elastic modulus for shear stress, and shear strain to analyze and predict how structures will behave under various loads.
The relationship can be described by differential equations, where the derivative of the shear force with respect to the length of the beam equals the load, and the derivative of the bending moment with respect to the length equals the shear force. This mathematical relationship holds true in the absence of distributed loads, providing engineers with a powerful tool for structural analysis. Moreover, when analyzing the static equilibrium of a system, it is imperative to account for all forces and moments to ensure that the body remains at rest or moves with constant velocity in our selected frame of reference.