Forces in Beams (vector mechanics)

[crashdirty86]

Homework Statement

For the Beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
Beam ACDB (left to right) has a downward Force of 24 kN acting at A and a linear distributed downward force of 8 kN/m acting from C to D. There is a roller connection at C and a fulcrum connection at B. The separation distance between AC = CD = DB = 3m.

Homework Equations

ƩF=0 and ƩM=0

The Attempt at a Solution

Initially, I started off the problem by finding the values of the reaction force considering the entire system as the FBD. Then, by sectioning the beam, I began to find the internal shear force and bending moments through out the beam itself. I have attached a picture of the work that I have done so far, if anyone can assist me in aiming that my work is correct I would be very grateful.

 

[SteamKing]

Your image is too small to review your work without going blind. Can you repost a larger image?

 

[crashdirty86]

one moment.

 

[crashdirty86]

Here is the new image as requested.

 

[pongo38]

Your expression for Mz must be wrong because when you put x=0 you should get 72. You are asking our help to check your work, but this problem is statically determinate, and so you have the means to check it yourself. For example, when you had found the reactions, you should have checked them by taking moments about any point not so far used, say point A. Similarly, when determining the internal actions with a free body diagram, as you have done, you can always check it yourself by checking the three equilibrium equations are satisfied, using an equation as yet unused. In your first diagram, where does the blue 12 kN come from? Finally, when you draw the diagrams for shear force and bending moment, there is a check using the differential integral relationships between them. You really don't need us to check it for you!

 

[crashdirty86]

In your first diagram, where does the blue 12 kN come from? Finally, when you draw the diagrams for shear force and bending moment, there is a check using the differential integral relationships between them. You really don't need us to check it for you!

The 12 kN comes from concentrating the linearly distributed load at it's centroid location along the beam. As far as the check goes, I was just struggling with finding my equations to draw the diagrams. This was because of the multiple forces compiling altogether through out the beam. Not a problem anymore, I moved on from this problem and began practice on some other problems and have resolved my momentary lapse of reason. Thanks for the help though.

 

[pongo38]

OK. You have moved on. But, for the record 3 x 8 = 24 not 12.
These problems are of interest because there are two definitions of shear force (and bending moment). One definition can be proved from the other, and vice versa. The first is that the shear force at a section is the algebraic sum of the forces parallel to the section and on one side of it; or the other side. That gives you one check. Similarly with moments. The differential relationship between V and M is an alternative approach that gives you a checking opportunity at the end. And believe me, you need these checks, especially if you can't multiply 3 by 8!

 

[crashdirty86]

Look dude, its called a learning process. I'm not here for you to try and talk down to me. I asked for help, not a smartass. Simple mistakes are made in everything a person intially unfolds to create a roadmap to success,but I guess for you that would be impossible since your Mr. Perfection.