Equivalent Systems

For the following questions, set F₁ and F₂ such that they only have components in the -y and -x directions, respectively. If F₁ is translated 2 units to the left (the -x direction), what will happen to the magnitude of F_r?

Translating F₁ 2 units to the left (the -x direction) will have what effect on the location of F_r?

Translating F₁ 2 units to the right (the +x direction) will have what effect on the location of F_r?

Translating F₂ 2 units toward support A (the -y direction) will have what effect on the location of F_r?

If F₁ is translated 2 units to the right (the +x direction), what will happen to θ_r?

If F₁ and F₂ only have components in the -y and -x directions, respectively, the correct expression for the magnitude of the resultant force F_r on member CD will be,

The correct expression for the angle θ_r measured from the horizontal to F_r is,

Given the above information, what is the correct expression for the location of F_r on member CD from point C?

Where, along member CD, should F₁ be located for F_r to be located at a distance of +4 m in the +x direction from C?

Given the above information, what is the correct expression for the location of F_r on member AB from point A?

Where, along member AB, should F₂ be located for F_r to be located at a distance of +2 m in the +y direction from A?

Moving the location of couple moment M₁ from point C to B has what effect on the location of F_r?

Moving the location of couple moment M₂ from point A to B has what effect on the location of F_r?

If M₁ is the only couple moment acting on the frame, what effect will an increase in M₁ have on the location of F_r along member CD?

If M₁ is the only couple moment acting on the frame, what effect will a decrease in M₁ have on the location of F_r along member CD?

If M2 is the only couple moment acting on the frame, what effect will an increase in M₂ have on the location of F_r along member CD?

If M2 is the only couple moment acting on the frame, what effect will a decrease in M₂ have on the location of F_r along member CD?

Which of the following is the correct expression for the sum of moments about point C?

If d is the distance of F_r from point C along member CD, what is the correct expression for the sum of moments about point C due to F_r?

Using the above information, what is most nearly the correct value for d?