V-M diagram for a hinged beam (probably an easy question)

[NoobieAKP]

I'm still very much a newbie and would really like some help. I've looked through my old Strength of Materials textbook but couldn't find an example of how to draw V-M diagrams for a hinged beam.

My goal is to calculate the stress at the slot. Not sure if I'm looking at solving this correctly (I've written out my thought process on the attached file) or if I even need a V-M diagram (though it would be nice to see how the shear and bending change throughout the beam).

Question 2 is where could I find the theoretical stress concentration factor for a slot? I've seen the graphs for beams in bending with a hole but not for a slot...could you please help with that also?

 

[NoobieAKP]

Is it correct to draw the V-M diagram based on the very bottom FBD that I created in the attached file?

 

[desertfox]

NoobieAKP

Where is the external force on the beam? and wheres it acting? which end of the beam is pivoting as it appears you have pivots at both ends.
I assume you mean a bending moment and shear force diagram when you say V-M diagram.
My only comment at present in your resolving of forces is in the vertical or Y plane the force w is unaccounted for.
With a bit more detail we might be able to help further.

desertfox

 

[NoobieAKP]

Sorry about the lack of info...

Fy and Fx are externally applied forces acting on arm 1. All of the forces are known except for Rx and Ry which are easily solved using the static equilibrium equations.

The arm is similar to a cantilever beam. It pivots about the pin where Ry and Rx act. Fx and Fy prevent this rotation. The pivot point at the opposite end is where another set of externally applied loads act due to the weight of an attachment and some horizontal forces.

I'm assuming that Fy and Fx act at the centroid of the cross section of arm 1 and Fy,eq, Fx, eq, and Meq act at the centroid of the cross section of arm 2.

Yes, I mean shear and bending diagrams.

Very true, I realized that I forgot to add W to my FBD and forgot to update my equations.

 

[desertfox]

Hi NoobieAKP

Okay thanks for clearing that up.
If I understand correctly, then arm 2 wants to rotate clockwise under the force of Fy eq and w which is resisted by Fx and Fy at arm 1, Fx eq only gives a thrust load in arm 2 and therefore doesn't add anything to the rotation of arm 2.
Now that being the case the pin between arm 1 and arm 2 is in torsion under the action of those forces again you make no mention of that.
I am unsure what Meq does to arm 2 if the other end is a pivot point then I cannot see Meq having any affect on arm 2 so please clarify. Finally Fy on arm 1 appears to me to be acting in the wrong direction if its preventing rotation of arm 2 in the manner I have described.
It might be easier if you provide a sketch with the physical items shown on the link rather than what you think the reactions are of those items.

desertfox

 

[NoobieAKP]

Yes, that's correct. The pin, arm 1, and arm 2 are all welded together so they rotate together as one piece.

Yes, I understand that the pin is under torsion and that should be a fairly easy calculation but my main goal is to cut a section through the pin (looking at the front view) and calculating the stress at a point where the slot is. Afterward, I will look at the pin.

The equivalent loads at the right side pivot of arm 2 are due to the wind loads (Fx,eq) and weights (Fy,eq) of a person inside a platform. So, I just created an equivalent force-couple system so that I could apply the forces and moment directly to the end of the arm and analyze it as a beam problem.

Fy on arm 1 is very small, in fact the resultant force is less than 5 deg relative to the horizontal. It is mainly a force in the x-direction. The resultant force is from a hydraulic cylinder.

I didn't include any values because 1.) I left the new values at my desk and 2.) I just needed to learn how to analyze this correctly...didn't want ppl to think that I'm just trying to get my problem solved for me. So, any arbitrary numbers will do because I'm just looking to understand the procedure for analyzing a beam with a hinged support. However, if you really need numerical values to be able to assist me with this I can get them.

Thanks for all the help so far desertfox

 

[desertfox]

Hi NoobieAKP
Your welcome.
I didn't want the values, what I was requesting was a drawing showing the very things your now talking about ie the platform for the person and the position and orientation of the hydraulic cylinder.
From what your describing now it might be that arm 2 is not in bending, I need to see and understand where your getting your Fx eq and Fy eq and finally M eq.
Put another way, all I can see is your drawing of arm 2 with what you consider to be the loads and reactions, then your asking if that is correct, well I can't answer that till I see the hydraulic cylinder and platform, because I don't know if your reaction forces that you show are appropriate for the situation your modeling.

desertfox

 

[NoobieAKP]

Arm 2 is in bending due to the platform weight and wind load and it's own weight. It bends about the pivot point on the left side.

Again, I'm only interested in the front view so that I can either draw a shear and bending moment diagram or so I can cut a section at the hinge (pivot point on the left side) so that I can find the internal bending moment, internal axial force, and internal shear force so that I can calculate the stresses at the stress concentration which is the slot shown in the top view.

Once I find the stresses I need to find the theoretical stress concentration factor for a slot. I do not know where to find that or what it is. I only have tables for a member in bending with a hole in it...not a slot.

 

[NoobieAKP]

here's a new dwg

 

[desertfox]

Hi NoobieAKP

Okay your going on the right lines, now if the platform is rigid ie cannot pivot independently about arm 2 then your beam will have a constant bending moment on it all along its length equal to :- windforce * vert distance between arm 2 centroid and platform centre of gravity where wind force acts.If the platform pivots independently on arm 2 then all you will have is Fx eq and Fy eq.
Not sure all your reactions on your free body are going in the right direction however if you draw yourself a little X and Y axis like a graph then assume anything acting in the same direction as the X and Y axis you have drawn is positive anything in the other direction is negative, then the reactions should all drop out correctly.
Incidently your cylinder resultant force and the wind force on the platform are actually generating a anti-clockwise moment on arm 2 and are not in oposition to each other, I am assuming a rigid connection between platform and arm 2.
look at this site for beam diagrams:-

http://www.roymech.co.uk/Useful_Tables/Beams/Beam_Index.html

here for freebody diagrams:-

http://www.roymech.co.uk/Useful_Tables/Mechanics/Statics.html

 

[desertfox]

Hi NoobieAKP

My previous post was a bit rushed as I was getting ready for work,I'll try this evening to post some sketches which might help you.

Regards

desertfox

 

[rb1957]

it looks to me as how the hydraulic cyclinder in pic 2 changes things significantly ... that this determines the line of action of the force in arm1, which (from the pic) greatly reduces the arm for reacting the moment from the forces on arm2.

as drawn i don't think it can work, i think the pin needs to be supported ??