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

[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.

 

[Valerie Park]

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.