Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) play a crucial role in designing any structure. The essence of SFD and BMD lies in the fact that they translate the external force system into an internal force system. These internal forces are then translated to Internal Stresses. Finally, the internal stresses may be compared with the strength of the material to evaluate whether the structure is safe or not.
The cantilever beam is a beam supported on one end by fixed support. This fixed support offers complete rigidity by producing 03 reactions in the form of Vertical force reaction, Horizontal Force reaction, and Moment reaction.
In a beam system, however, we consider the force system to be Coplanar-Parallel i.e. there is no component of external force in the Horizontal axis direction. This reduces the reactions to 02 in number.
Solving any beam is a simple 04 step process:
Finding the Degree of Structural Indeterminacy
In order to find the Degree of Structural Indeterminacy, you can check out my previous video on the topic here: https://youtu.be/acx_55ZcpZg In the case of a cantilever beam, the Degree of Indeterminacy is Zero. Hence, the structure is Determinate and hence all the reactions and internal forces can be evaluated by just using the equations of static equilibrium
Free Body Diagram
Free Body diagram is a diagram of the structure wherein all the supports have been replaced by an unknown reaction force. FBD is hence a schematic display of the structure where only the forces on the structure are shown and no supports or restraints.
Finding the Reactions
Reactions for a cantilever beam can be simply evaluated by using the equations of Static Equilibrium. The Free Body Diagram is checked for equilibrium for No vertical, horizontal, or rotational movement. This is achieved by equating the Summation of all forces in the X direction and Y Direction as zero as well as all moments about the XY plane or Z direction as zero
Finding Shear Forces and Shear Force Diagram (SFD) & Bending Moments and Bending Moment Diagram (BMD)
Shear force and bending moments inside the body are obtained by cutting a section at a distance of x from either side and exposing the internal unknown forces in the form of Horizontal and Vertical force as well as Moment. These sections are again passed through the framework of static equilibrium and internal forces are calculated as a function of x. This is later used to find the Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)