# How to Determine the Restraining Couple Moment for a Twisting System?

• mattypatty000
In summary, to restrain the twisting action of this system about an axis going from r1 = 6i+3j+2k ft to r2 = 10i-2j+3k ft while giving a moment of 100 lb-ft about the x-axis and 50 lb-ft about the y-axis, a final couple moment of C = 100i + 50j + 38.9k lb-ft is required.
mattypatty000
Given the following couple moments:

C1=100i+30j+82k lb-ft
C2=-16i+42j lb-ft
C3=15k lb-ft

what couple will restrain the twisting action of this system about an axis going from

r1=6i+3j+2k ft to r2=10i-2j+3k ft
while giving a moment of 100 lb-ft about the x-axis and 50 lb-ft about the yaxis?

I understand that because of the given information the final couple moment will be C = 100i +50j +?k, but I am unsure as to how you compute the value for the k component of the vector. I don't think i can use the axis given to find the force in the other couples because they arent on the same axis. Please advise.

Thank you!To solve this problem, you need to determine the magnitude of the couple moment required to restrain the twisting action. In this case, the twisting action is about an axis passing from r1 = 6i+3j+2k ft to r2 = 10i-2j+3k ft. To do so, you can use the cross product of vectors r1 and r2: r1 x r2 = (6i+3j+2k) x (10i-2j+3k) = (30i+36j-12k) ft The magnitude of the couple moment required to restrain the twisting action is then given by: C = |r1 x r2| = √(30^2 + 36^2 +(-12)^2) = 38.9 lb-ft Therefore, the final couple moment to give a moment of 100 lb-ft about the x-axis and 50 lb-ft about the y-axis is C = 100i + 50j + 38.9k lb-ft.

## 1. What is a restraining couple in terms of vectors?

A restraining couple is a pair of forces that act on an object in such a way that they produce a torque, or rotational force, that prevents the object from moving or rotating freely. In other words, the forces are equal in magnitude and opposite in direction, creating a net torque of zero.

## 2. How are restraining couples represented by vectors?

Restraining couples are typically represented by two vectors, with each vector representing one of the forces in the couple. The vectors are drawn from the point of application of the force to the pivot point or axis of rotation.

## 3. What is the purpose of using restraining couples?

The purpose of using restraining couples is to stabilize an object and prevent it from moving or rotating. This is particularly useful in engineering and construction, where stability is crucial for the safety and functionality of structures.

## 4. How do you calculate the magnitude of a restraining couple?

The magnitude of a restraining couple can be calculated by multiplying the distance between the two forces by either force. The distance is measured perpendicular to the line of action of the forces. Mathematically, the equation is T = F x d, where T is the torque, F is the magnitude of either force, and d is the distance between the two forces.

## 5. Can restraining couples only be applied in two dimensions?

No, restraining couples can be applied in three dimensions as well. In three-dimensional cases, the two forces in the couple act on different planes and are not necessarily parallel. The same principles of equal and opposite forces creating a net torque of zero still apply.

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