Beam with a rope - type of problem (Statics)

[goodOrBad]

Homework Statement

In the image there is a beam I had to solve (reaction forces and moments in the points), I solved it but I do not know if the work is good so I need someone to check it.

Relevant Equations

Fx=0 -> +
Fy=0 ^ +
Given: 6kN at point A at 30deg, M=3000Nm but I changed the direction to make it easier so M=-3000Nm
the whole beam is 19m long.
Anyway I got
FD=3733.737 N
FBx=3056.360 N
FBy=-5400 N

 

[kuruman]

Hi @goodOrBad and welcome to PF.



I cannot evaluate your work as either good Or Bad because I cannot read what you have posted. Maybe it's because of my tired old eyes, maybe it's because of the small characters maybe it's the poor contrast. Please consider that if you want people to help you, you need to make it easy for them to do so.

 

[haruspex]

Your answers all look correct, except that you quote too many significant figures. As a result, you got 26.99... kNm for the moment about B, when it should be 27kNm exactly (6 kN sin(30) x 9m).

 

[goodOrBad]

Yeah I will keep that in mind, thanks

 

[Lnewqban]

... Please consider that if you want people to help you, you need to make it easy for them to do so.

Welcome, goodOfBad

Are you studying Structural engineering?
I ask because the choice you made for the moment’s diagram, where moments look all negative.
The normal convention used in most engineering applications (other than for concrete structures) for a positive bending moment is to warp the element into a smile shape (compression at the top of the beam and tension on the bottom).

The way you assigned negative numbers to the distances in the summation of moments equation seems confusing (unless you have been taught that method).
I prefer assigning the sign to each moment according to the direction of rotation of each force-distance combination.

All your numerical results look good to me, except the moment diagram at the point moment.
It seems to me that, moving left to right, the moment should change from 27 000 N-m at point B to 17400 N-m at point C, where it should drop to 14 400 N-m and then reach a value of zero at point D.

 

[goodOrBad]

Thank you for the feedback.

It is Mechatronics so there are some elements of Structural engineering, we have this class called Statics, and yes, you are right, it first goes to -17400 Nm then to -15000Nm I only spotted that some time after.

Since I like to watch everything from left to right and I use that the left from right as + when it comes to the x direction forces, I also like to go from point to point when I do moments in that direction.

I found the negative distance thing much better than flipping the drawing or thinking about directions the smaller the possibility of something going wrong the better.

 

[Lnewqban]

You are welcome.

It seems that your personal system works for you.
I learned a different method many years ago; therefore, newer approaches confuse me some.
Best