Help with Statics and Strengths of Materials

[grandnat_6]

Attached is the reworked alternative upright beam. How does this look?

In my mind I had it since the distance was shorter it would be the worst case senario, Now I see the actual extreme fiber is the worst case senario.

nvn,

Just so we are on the same page, in the lower right corner of the drawing in a purple box; pin connection F shows how the hole can be elongated in the upright. In post 90 the factors of safety will apply to the elongation of the holes?

Thank you.

 

[nvn]

grandnat_6: Yes, hole elongation involves the beam material. For the beam material, you can currently use a yield factor of safety of 3.

Your file in post 91 now looks correct, except 3.49 is wrong. Parameter h = cross-sectional depth = 2.69, not 3.49.

 

[grandnat_6]

moving on the the upright position 2 I encounterd a problem, and noticed I made the mistake in position 1.

My dimensions show pin g is offset by 1" by the rest of the pins.

I was able to balance out the forces. Next I rotated the beam to make the shear and moment diagrams, but in my final M29 shows I have a positive moment of 556.799. My work is attached.

Can someone tell me where I went wrong? I've been working with it for the past 6 hours and can't get it to come out.

nvn, re-reading in the past I see in post 77 it was mentioned h= 2*distance from centroid to extreme fiber, but in post 78 it was mentioned it is the cross sectional depth. So I should just be using the total distance from one end of the cross section to the other end parallel to the shearing plane?

Thank you,

 

[nvn]

grandnat_6: Yes, h is the total height (depth) of a cross section.

You moved holes F and h closer to a vertical line passing through point g, but it currently appears you did not update your perpendicular distances from point g to force vectors Ff and Fh, when you moved the holes.

 

[grandnat_6]

Doh! That was the problem, I think I have it now. Thank you nvn.

I have updated the fix.

I also atempted to work on upright Position 2, I made sure the distances did not change. I trasfered over the forces on pin E, and Pin F, along with the angle of the cylinder for position 2. I balanced out the forces and then checked for shear and it works out. I went ahead and went straight to checking M29 for balance, but it did not. I went back and checked the perpendicular distance and everything comes out correctly. Again I'm at a lost and don't know where I messed up. Where did I go wrong this time?

Thank you,

 

[nvn]

grandnat_6: In your first attached file in post 95, M23.2592+ is now wrong.

In your second attached file, you failed to copy force Ff correctly from the top of the page to the bottom of the page. Remember to always proofread what you write or type.

After you make this correction, then to check the moment balance, you can compute M_29.0000+. Moment M_29.0000 should be nonzero, whereas M_29.0000+ should be approximately zero.

 

[grandnat_6]

AH! I did not realize I needed a M29.0000+. It took me a little bit, but it makes sense. The horizonal force is 1" above the line of action. Thank you nvn for pointing this out to me.

Sorry, I do proof read my work, I think because I work on it so long it all looks good, I try to be carefull with my work but sometimes i jump around and should not.

Attached I have the math and shear/moment forces for P1, P2, P3.

I feel confident P1, and P3 are correct. P2 I am unsure because my value at M29.0000+ is about 11lbs. This might be high, It appears I have everything right.

How do these look?

Thank you.

 

[nvn]

grandnat_6: Your p1 file in post 97 looks correct. In your p3 file in post 97, M_23.2592 and M_23.2592+ are erroneously labeled as negative on the moment diagram.

In your p2 file in post 97, you failed to copy force Ff correctly from the top of the page to the bottom of the page, which I mentioned in post 96. Remember to always proofread what you write or type.

 

[grandnat_6]

I see my mistakes now.

The attached are corrected.

In P3 the moment diagram crosses the zero line. Where it crosses, is it proper to check the shear in those area's by using the -411.636#'s? Or does it not matter where the moment diagram crosses the zero line, or is it just the shear diagram crossing the zero line that matters and should be checked?


Going backwards a bit. The arm.pdf. We made the cross section for beam 1 by using the maximium moment at point G and then using shear to find point E. I mentioned since beam 2 is very close to the maximium bending moment of beam 1, that I'll just make beam 2 exactly like beam 1. I'm pretty sure I was wrong on this, since B has a different shear force. I should use my shear diagrams for all three positions and find the maximium shear and calculate the size beam at point B.

As I have it drawn, I would like to cut out some solid steel with a radi on them and weld them to the ends of the beams. For beam 1 and beam 2, would I just dimension my moment diagrams in all three positions and find the maximium moment and size the end of the beam to the measured moment where my weld will be to join the radius and the beam together?

Thanks.

 

[grandnat_6]

I've been reviewing the plate in post 66. besides the holes, there must be something else that needs to be done to size up the plate. Do I add the force vectors tip to tail to get a resultant and use that to find the yield and shear strength of the material?

Thanks.

 

[nvn]

grandnat_6: Generally, check a beam where the moment diagram is maximum, which is often where the shear diagram is zero. And/or check at any cross section(s) of interest. If you have textbooks that explain this, follow the guidance therein.

In general, you can check the axial stress, bending stress, and shear stress at each cross section you want to design.

 

[grandnat_6]

Did some calcuations on beam 1 and beam 2. Found out the shear stress is more than the maximum tension and compression stress.

At this point with beam 1, beam 2, and the uprights. Should anything else be checked like defection, buckling, ect. or is it ok to make production drawings of these?

nvn, for the textbook I have a fourth edition Statics and Strength of Materials by Bassin, Brodsky, and Wolkoff, copy right 1988.

My instructor back then said it's an old book but is the best he has found. I know myself and a lot of other students found it rather hard to follow without instructor guidence. If you have a suggestion for a textbook please let me know the title, author, or ISBN # and I'll will gladly pick it up somewhere.

 

[nvn]

grandnat_6: Yes, there are other things to check. At the moment, I have exceeded the amount of time I can currently afford for one thread. Perhaps others may choose to answer.

 

[grandnat_6]

alright nvn, Thank you for all the help this far. I've learned a lot!