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Assume that the points of application of the major forces acting on the tall cra

ID: 3162550 • Letter: A

Question

Assume that the points of application of the major forces acting on the tall crane modeled in figure below are coplanar. Force F on the right is normally vertical, but it may make an angle up to 5 with the vertical. The other major loads, are the counterweight P at the top left and the weight W of the vertical column whose centerline is the y-axis. Determine the equivalent force-couple system acting at the base O of the column tor a given height L of the crane with: F making a 5 degree angle with the vertical and acting in the xy plane. F making a 5 degree angle with the vertical and acting in the yz plane.

Explanation / Answer

Forces acting on the system are

1. Load P   - arm length 0.45 m

2. Force F - making an angle 5 deg with the verticle

3. Weight of the column W passing through the point O

as force W is passing through the point O its moment about O = 0

Taking the moments of P and W about O ( we take CW moments as -ve and CCW moments as +ve

we resolve F along the verticle ( F Cos(5) and FSin(5) along the horizontal

Net moment about O in x-y plane

   = FCos(5) *0.9L + FSin(5) *L - P*0.45

= 0.984L* F -0.45P

2. when F is acting in y-z plane

the verticle component is agian F Cos(5) = 0.996F

The horizontal component is parallel to z-axis and will not produce any momentum in x-y plane

Net momentum about O in x-y plane

= 0.996F *0.9L - 0.45 P

= 0.897L F - 0.45P

The horizontal component of F in YZ plane will produce a moment about y-axis i.e in y-z plane

= FSin(5) * 0.9L

= 0.078L F

    

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