Analyzing Beam Deflection in Complex Loader Arm Structures

[grandnat_6]

Hi,

I haven't done beam deflection before. My textbook shows the usual simple beams with a perpendicular force acting on it. This one is a lot more complicated. I'm pretty sure the forces acting in the horizontal direction have to be added into this some how.

Can someone look at the attached file and give me some pointers on what I did right and wrong?

point E, D, C, and B are all pin connections. Point B hooks to the bucket, Point C is a hydraulic cylinder that connects to the bucket for tilting. Point D is a hydraulic cylinder that rasies and lowers the arm. Point E is a pin connection to the tractor.

The moment of inera has been calculated by the beams cross section the force goes though.

Thank you.

 

[OldEngr63]

In general, every force contributes either a transverse or an axial force component, or both at each point in the beam. It is the transverse component that creates a bending moment and leads to significant bending displacement. Thus your first task is to express the transverse component of each force at each point along the beam so that you can then write the bending moment due to that force at each point.

 

[grandnat_6]

Hi OldEngr63,

Thanks for replying.

The attached is my shear moment diagram.

What do I do next?

Thank you.

 

[OldEngr63]

Did you simply straighten the entire beam out? I'm not sure that is a legitimate approach. I would deal with it in two segments, keeping a fixed angle between the two.

Did you include the loads due to the hydraulic cylinder and the load on the bucket? They have to be included also, and it does not look like you have done so?

To talk about a beam deflection, you will need to establish a reference line somewhere that you will take as the undeflected form. Have you considered what makes sense for this?

 

[grandnat_6]

I have not straighted the beam out. I thought this would have been done from the beginning but was told to keep it as is. I've had help up to this point so far. This is from the thread: Help with statics and material strengths from not too long ago.

We kept the beam the same length. We used a 350# lifting load, the rest of the 500#'s on the bucket is the weight of the bucket and also some of the weight of the rams. The 850# force on the bucket is what the tractor can produce. The forces for the rams were figured by using the 500# and 850#. in three different positions.

As far as the reference line? Would it be straight or bent? I'd say bent following the center lines of the two beams. I feel between pins E and D the beam will bow upward and between pin D and B it will bow downward and to the left.

 

[OldEngr63]

Your moment & shear diagrams were plotted along a straight line; that is why I asked if you had straightened out the beam. I don't know how to interpret them as they appear. If you are comfortable with them, then carry on to the integrations to get y' and y.

 

[grandnat_6]

Sorry, The shear/moment diagram is as long as the horizontal distace from Pin E to Pin B. 57.8547". I'll work on the y' and y. later this weekend.

Thanks.

 

[grandnat_6]

attached are the traverse loading deflections.