Name: Resultant Moment: Scalar Formulation
Uploaded: 2023-09-22T11:49:20
Description: Learn by watching this video about Resultant Moment: Scalar Formulation at JoVE.com

Consider a cantilever beam on which forces of 1000 N, 600 N, 750 N, and 500 N act at different points B, C, D, and E, respectively. The moment generated at point A by a particular force is the product of either of the forces with the corresponding perpendicular distance from the point of application of the force to the fixed-point A.
Here, the forces F1, F2, and F3 generate a moment in the clockwise direction, which is conventionally considered&#160; negative, while the moment produced by force F4 is positive considering the counterclockwise direction.
The resultant moment due to all four forces is calculated as the algebraic sum of all the moments generated by each force in the system.
Here, since the magnitude of the resultant moment is negative, it acts in the clockwise direction.
Now suppose the direction of force F3 is reversed. The resultant moment will be positive, indicating a counterclockwise moment about point A.&#160;

<ol>
	<li>Hibbeler, R.C. (2016). Engineering Mechanics &#8210; Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. Pp 122.</li>
</ol>

resultant moment: scalar formulation

When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to induce rotational motion about a fixed point. The scalar formulation of the resultant moment is a helpful tool in analyzing the equilibrium of structures subjected to multiple forces.
To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically counterclockwise since they are directed along the positive z-axis, while negative moments are clockwise. Each moment is given a sign based on its directional sense. To calculate the resultant moment due to all the forces, an algebraic sum of the products of each force and its respective perpendicular distance with respect to a given point A is taken.
<img alt="Equation 1" src="/files/ftp_upload/14252/14252_Equation_1v3.svg" style="text-align: center; height: 15px;" />
Sign conventions for moments are used in the calculation. After substituting the values of all the forces and their perpendicular distances in the above equation, if the numerical result of this equation is a positive scalar, the resultant moment will be counterclockwise. Conversely, the resultant moment will be clockwise if the result is negative.

Learn by watching this video about Resultant Moment: Scalar Formulation at JoVE.com

Resultant Moment: Scalar Formulation

When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to ...