Test: Simplification of a Force and Couple System - Civil Engineering (CE) MCQ

Principle of transmissibility states that the force acting on the body is a sliding vector. That is it can be applied at any point of the body. It will give the same effect as if applied at any point other than the specific point. Thus the answer.

Calculating Horizontal Forces:

- Section AB:
- The horizontal force at section AB is 100 N to the right.

- Section BC:
- The horizontal force at section BC is 150 N to the left.

- Section CD:
- The horizontal force at section CD is 200 N to the right.

- Section DE:
- The horizontal force at section DE is 250 N to the left.

Calculating Total Resultant Force:
- Total resultant force = (100 N to the right) + (150 N to the left) + (200 N to the right) + (250 N to the left)
- Total resultant force = 100 N - 150 N + 200 N - 250 N
- Total resultant force = 50 N + 200 N
- Total resultant force = 250 N to the right

Therefore, the total resultant force acting horizontally in the given figure is 250 N to the right. So, the correct answer is option C: 250 N.

The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

A particular system of the rules is followed that is if the upward direction is taken as positive then the downward direction is taken as negative. This is the same as done with the couple in the 2D. That is the forces can be easily simplified. If taken in the vector form then the task is even easier.

Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

Couple: When the pair of equal parallel forces that are opposite in direction applied on a body then it rotates of tries to rotate about a point or axis is called a couple. ​

Moment of a couple or couple (C) = P × a
Characteristics of a couple: A couple (whether clockwise or anticlockwise) has the following characteristics: 

• The algebraic sum of the forces, constituting the couple, is zero. 
• The algebraic sum of the moments of the forces, constituting the couple, about any point is the same, and equal to the moment of the couple itself.
• A couple cannot be balanced by a single force. But it can be balanced only by a couple of opposite sense. 
• Any no. of co-planer couples can be reduced to a single couple, whose magnitude will be equal to the algebraic sum of the moments of all the couples.

Torque (τ): It is a physical quantity, similar to force that causes the rotational motion. It is the cross product of the force with the perpendicular distance between the axis of rotation and the point of application of the force with the force.
⇒ τ = r × F = r F sin θ
Where r = distance from point of application of force (in meter), f = force (in Newton), and θ = angle between 
Also, Torque (τ) = r × f = r ×  F
Where r = component of the distance in the direction perpendicular to the 
F = component of the force in the direction perpendicular to 

Moment of a Couple:
A couple is defined as two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance “d".
The moment of a couple is defined as M_o = F.d (using a scalar analysis) or as M_o = r × F (using a vector analysis).
Here r is any position vector from the line of action of F to the line of action of F

• The net external effect of a couple is that the net force equals zero and the magnitude of the net moment equals F × d.
• Since the moment of a couple depends only on the distance between the forces, the moment of a couple is a free vector. It can be moved anywhere on the body and have the same external effect on the body.
• Moments due to couples can be added together using the same rules as adding any vectors.