Question

Statics question, The Jib crane is supported by a pin at C and rod AB. If the load has a mass of 2 Mg with its center of mass located at G, determine the horizontal and vertical components of reaction at the pin C and the force developed in rod ab on the crane when x=5m

Answer 1

Do you have a diagram?

Answer 2

Yes I do sorry someone jacked my previous thread so I posted a new one and forgot to post the diagram.

Answer 3

Let's set-up our EOM for the system around point C.

We will have the following\[\sum F_{C,x} = 0 \]\[\sum F_{C,y} = 0\]\[\sum M_C = 0\]
Our coordinate system will have upwards as positive y (from C to A). Left as positive y (from C to B). and Clockwise as positive moment.

You should get a FBD that looks like the attached image.

We see that the only two forces in the x-direction are the x-component of tension in cable AB and the reaction at C. Therefore, \[X: -T_{AB} {4 \over 5.122} + F_{C,X} = 0\]
Tension in cable AB also has a vertical (y) component. We also have the weight of D. We will ignore the mass of the boom from which mass D hangs. There is again the vertical reaction at C. Therefore, \[Y: T_{AB} {3.2 \over 5.122} + F_{C,Y} - m_D \times g = 0\]

I count three unknowns at this point, therefore we need to develop the moment equation. This is\[M: -T_{AB} \left( {3.2 \over 5.122} \right) (4) - T_{AB} \left({4 \over 5.122} \right)(0.2)+ m_D (g) (5) = 0\]Recall that because C is a pin connection, it has no reaction moment.

Now, we have three equations and three unknowns. Our system is fully defined. We can solve the system of equations for all unknowns.

Answer 4

Great answer! Thanks for the help this was a very well explained answer.