Moment-beam under bending momen?

[chandran]

A beam is under bending. Let us take a small part of a beam with length x. It has end A and end B. At end A the bending moment is M1 & shear force is S1 and at end B the bending moment is M2 & shear force is S2.
Let me take the moment equilibrium for this element about B.

M2-S2-M1+S1=0.

I need clarity in adding M1 in the above equation. Actually M1 acts with A as the centre. But why this is included while taking moment about B.

 

[Astronuc]

M is a moment or torque, which is not a force, but the effect of a force applied at some moment arm.

M has units of F-d (force - distance, e.g. N-m or ft-lbm).

In a static beam situation, the sum of the forces must = 0, and the sum of the moments = 0.

Here is a good reference on beam mechanics (statics) -
http://physics.uwstout.edu/StatStr/statics/Beams/beam41.htm#Topic 4.1 Shear Forces I

and

http://physics.uwstout.edu/StatStr/statics/

 

[charng]

Thank you for sharing this information about the bending moment and shear force of a beam. I can provide some clarification on the inclusion of M1 in the moment equilibrium equation for this specific element.

Firstly, it is important to understand that the moment equilibrium equation is used to determine the relationship between the forces and moments acting on a beam. In this case, the small element of the beam is being considered, so we need to take into account all the forces and moments acting on that specific element.

Now, when we take the moment equilibrium about point B, we are essentially looking at the balance of moments around that point. This means that all the forces and moments acting on the element at that point must be accounted for in the equation.

M1 is included in the equation because it is a moment acting on the element at point A, which is also a part of the element we are considering. So, in order to have a complete understanding of the forces and moments acting on the element at point B, we must also include M1 in the equation.

In summary, when taking the moment equilibrium about a specific point, we must consider all the forces and moments acting on the element at that point, even if they are not directly at that point. This allows us to have a complete understanding of the forces and moments acting on the element and helps us to accurately analyze its behavior under bending moment.