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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