Cantilever with load. Shear Force, bending-moment?

Question

A cantilever, 1.5m long has a weight of 3kN and carries concentrated loads of 4kN at the free-end and 5kN at a distance of 0.5m from the free-end. Determine:

a) The shear force at each load and at the support
b)The bending moment at each load
c)The maximum bending-moment and its location on the beam.

This is the question. I've been spending hours just staring at this now and am no wiser (but more fed up) if someone can please explain to me how this would be done I would appreciate it so much. I've got another bunch of these types of questions. If i could understand how to do this then I will tackle the rest.

Thank you.

Answer 1

For Part a)

 

We must use the static equilibrium equations:

 

∑M _{fixed point}=0

∑F_y=0

 

where M is the moment and F_y is the force in the y direction.

 

These two equations will allow you to calculate the reaction at the fixed point.  You will then use the calculated reaction in addition to the initial forces to find your shear force in the beam. 

 

For Part b)

 

Draw the moment diagram using your results from Part a.

 

Refer to your engineering textbook to obtain moment formulas of a cantilever beam.