How Do Forces Maintain Equilibrium in a Supported Shelf System?

[danago]

A container of mass 4kg on a shelf is supported by a strut as shown. The container is evenly loaded and it is centrally placed on the shelf. (Ignore the weight of the shelf)

http://img256.imageshack.us/img256/1038/7bq4tx9.gif

a) What are the three forces acting on the shelf?
b) What is the thrust from the strut, assuming it acts along its length?
c) What is the magnitude and direction of the force on the shelf where it touches the wall?

a) There is the weight force from the mass, the force from the strut, and the reaction force from the wall.

b) For part b, I am a little stuck. For a state of equilibrium, the vector sum of all forces must be zero. The container provides a force of 4000N downwards (using g=10ms^-2). Together, with the vertical components of the thrust from the strut, and the reaction from the wall, the net force in the vertical direction is zero.

The thrust (T) provided in the vertical direction by the strut is $$Tcos(60)N$$ upwards, the weight force is 4000N downwards. The angle and magnitude of the reaction from the wall is unknown, so I am not sure how to go about it.



Anyone able to help? Thanks in advance,
Dan.

 

[danago]

Hmm i just re-read the question (perhaps something i should have done before?), and realized it said the container is placed centrally on the shelf. Given this, i can show that the vertical component of the reaction force is equal to the vertical component of the thrust. Is this the path i should take in solving this problem?

 

[danago]

Ok i think I've done it. Assuming that what I've said above is correct, i can say:

$$2Tcos60=4000\therefore T=4000N$$

 

[Pyrrhus]

the strut and the shelf are pin joined right?, if so take moment about the joint to find the reaction forces of the shelf (wall and shelf union, i assume pin joined too), then find the force along the strut.