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Angle Beam

Angle Beam

Angle Beam

(OP)
I have to calculate maximum shear for an angle beam of 44W steel.

The setup goes that its actually a sliding bender applying a "moment" onto my beam. The bender has a "Travel" distance I'm trying to find the worst case scenarios where the tension would create the largest stress on it.

Anyone have a few tips of how to start this, thanks.


Mat

RE: Angle Beam

A sketch would help. I can't figure out what you're talking about. But there are smarter people than me on this board.

RE: Angle Beam

Yes - sketch please

RE: Angle Beam

Yes, a sketch would be good.

BA

RE: Angle Beam

(OP)
Making one at the moment!

RE: Angle Beam

(OP)
Just a little insight on me, I'm currently working for a company as a student they give me little projects but don't have much time to help me with them I'm a little stuck on this one help would be very appreciated.

Ok so this is the "real setup" on the sketch, the pulley has a travel distance it slides on the beam, the beam which it slides on is the one I'm analysing, basically I want to start by analysing it completely horizontal (neglecting the fact its at an angle in reality)

I understand the "sliding" strap bender generates a moment because there is a force going up and a force going down.

I will post another hand made sketch of how I want to start by analysing it to have a basic understanding before going anywhere specific

Thanks guys!

RE: Angle Beam

you're looking at the pieces with the red X on them ?

or the two little angles that attach the slider to this beam ?

that looks like a motor, belt driven ?, sitting on the "slider" (which might function at a belt tensioner ?) ?

RE: Angle Beam

(OP)
Hi Rb1957,

No I'm analysing the angle beam just above the one with red Xs!

RE: Angle Beam

(OP)
And no it is not a motor sitting on it, yes the assembly is a belt tensioner but it is just a pulley, the drive assembly is separate, this part adjusts the tension on the belt by moving the pulley up and downwards a little like some bend pulley's in vehicule driven accessories.

RE: Angle Beam

the 1st thing to do is to draw a free body diagram (wiki that if you have to) showing all the belt forces for one position, and calc the reactions at the ends of your beam.

then do some more positions, look at the two extreme positions and one in the middle, to see how the reactions change.

at each position the loads will be applied to the beam at a different place on the beam, yes?

now you'll have several free bodies, calculate the bending moment, etc in the angle beam for each position, to arrive at the maximums.

are there two of these beams supporting the belt tensioner ass'y ? are they going to be equally loaded ?

RE: Angle Beam

(OP)
What were trying to find out in our scenario is the maximum tension this beam will allow before failing. Basically I don't have a value for the tension available, but we need to rate the maximum allowable tension for this ass'y on the plans sent to the company using it.

There are two beams yes, but I'm analyzing one side. So how do I go about finding the worst case scenario on the beams.

RE: Angle Beam

The beam in the sketch is not "fixed at both ends". The only corner visible on the right appears to be hinged. The left hand boundary conditions are unclear.

The belt force puts a moment on the beam. Is there also a vertical load from the conveyor?

The statics are not too difficult if all of the applied forces are known. Are there two inverted "V" beams, one at each side of the conveyor belt?

BA

RE: Angle Beam

(OP)
@BAretired,

The beam IS fixed at both ends it was hard to represent it as so but the "V" beam or angle beam is bolted onto the beam under it, which is bolted into concrete, the values as I said are for now unknown as the goal is to determine structurally, the maximum load this beam can allow to remain undamaged.

RE: Angle Beam

Plastickmat, you have a different definition of "fixed" than I do. Fixed means the beam is not free to move laterally, vertically and is not free to rotate. I doubt that your beam is prevented from rotating.

BA

RE: Angle Beam

(OP)
I might have a bad conception, and please correct me if I do, but the beam is "bolted" onto the lower beam, which I realise is not the same as 'FIXED' in structural terms.

RE: Angle Beam

In any event, it is conservative to consider the beam hinged at one end with a roller at the other. Then calculate reactions and find maximum shear and bending moment.

BA

RE: Angle Beam

(OP)
After putting some thought (as this is new to me) I agree on the conservative nature of such an approach. But I'm still stuck at the same step, what are the first steps involved in this when you want to work backwards? (Knowing the maximum force the beam can take at anypoint)

RE: Angle Beam

(OP)
I did a simple calculation to find a proportion of the moment transfered to the beam with respect to the tension felt ( Set as 1 ) which is why I consider it a proportion.

So when I find the maximum "momentum" that can be applied at different points I can know how much that means in tension. (Correct or no ? )

Still looking for some starts on calculating the angle beam's resistance. Looking at some cases in diffrent books of beam loads. Unsure how to apply them correctly.

Thanks

RE: Angle Beam

why not use a unit tension, 1000 lbs ? 100 lbs ??, and calc a bending stress in the angle.

if the angle is stable in compression (thick flanges) then your limit belt tension is (fcy/calc'd stress)*(unit tension)/SF,
SF = Safety Factor

RE: Angle Beam

if your pic is right, then your problem is easier ... the maxiomum moment in the angle is 1/2 the applied moment.

yes, unit tension = 1kN, max moment in angle = 130kN.mm, reaction = 0.44kN.

ok, good, now wiki "bending stress in beam" or something like, or find a strength of materials text. you're looking for something like stress = My/I.

something to consider is that your applied moment isn't along a principal axis of the section, you should be able to find that too (wiki or texts).
you should be able to determine the principal axes of your angle cross-section (the quick answer is the minor (weak) axis is through the mid pts of the two legs of the angle, the major (strong) axis is normal to this, thru the elbow of the angle (this includes several simplifying assumptions). You applied moment will be broken into two components acting along the principal axes and resultant stress = M1*y1/I1 + M2*y2/I2.

good luck !

RE: Angle Beam

(OP)
Why is your max moment 130kN.mm?

I understand what you mean with the component moments and having the angle in this position was one of the challenges I realised.

Since we're using a unit tension, where does it come together that I have the official 'max value' if my calculations are based on arbitrary values.

Thanks

RE: Angle Beam

If T = 1 kN, the applied moment is 0.261 kN-m. The reactions at each end are 0.437 kN as shown on the sketch, one up and one down. Force F is 0.261/b, one up and one down where b is the distance between them.

Beam moment varies linearly from 0 to -Ra to Rc to 0 at left support, first F, second F and right support respectively. In the above, a is distance from left support to first F and c is distance from second F to right support.

This is elementary statics which you should know if you are making these calculations. I think your employer will require the services of a structural engineer if the results are to be sent out to customers.

BA

RE: Angle Beam

trying to find the maximum tension allowed, you're using a unit tension load to develop the critical internal stresses (= key design limitations).

and you know your maximum allowable stress (fty, fcy) and the SF you want in the design.

so you can factor the unit tension up untill the internal stress calculated equals the maximum allowable ... T = Tu*(allowable/stress)/SF

you can calc the maximum moment on the beam, draw a moment diagram. you'll see it starts at zero (pinned ends), increases to a maxmimum, drops where your external moment is applied, and increases again. 1/2ing the external value applies when the load is introduced at the mid-length of the beam; different positions will produce a higher beam moment.

RE: Angle Beam

(OP)
Many thanks guys,

Ya basic statics I am still learning, I see it becomes very elementary for guys like you which is nice to see. All of you have been very helpful I'll be crunching up some more with your help!

Thanks a lot
Mat

RE: Angle Beam

get a strength of materials textbook, look up online reference's MIT's opencourseware is a good resource.

RE: Angle Beam

(OP)
Just realised something don't know if it makes a difference to your understanding,


The sketch including moment calculations only represents the "sliding part" on top of the main beam. Basic statics I guess again, but is it more logical to represent the reactions calculated on the top part in two forces on the main beam or is it "ok" to represent the same moment on the beam as another ponit moment.?

Basically what makes the setup easier to analyse, because on the slider it generates a moment on the "center point" for rotation, but on the main beam the slider's position creates a punctual moment in different points.

Thanks

RE: Angle Beam

yes, the slider is probably not applied a moment to the angle beam (it would do if it was clamped over it, like a sleeve on a tube) ... a couple is more reasonable.

it should actually slightly reduce the peak moment, ie using the moment is conservative for the beam bending moment.

RE: Angle Beam


Quote (Plastickmat)

The sketch including moment calculations only represents the "sliding part" on top of the main beam. Basic statics I guess again, but is it more logical to represent the reactions calculated on the top part in two forces on the main beam or is it "ok" to represent the same moment on the beam as another ponit moment.?
To calculate end reactions on the beam, it makes no difference whether you consider a "point" moment or a force couple. You must use a couple if you want to draw the beam moment diagram correctly.

Quote (Plastickmat)

Basically what makes the setup easier to analyse, because on the slider it generates a moment on the "center point" for rotation, but on the main beam the slider's position creates a punctual moment in different points.

What is a "punctual" moment? A moment which is on time? So far as end reactions are concerned, the position of the point moment (or couple) makes no difference to the end reactions of the beam but changes the shape of the bending moment diagram.

By the way, you should draw the shear force and bending moment diagrams of the beam for a clearer understanding of the problem.

BA

RE: Angle Beam

(OP)
A punctual moment is a moment that is on time, yes. ;)

Think I've got it nailed down a little better now, thanks for the support guys!

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