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Greg: Good idea. I have read about McCaulay but have not worked with it at all so I would have to do some work with it. I had thought of using multiple point loads but thought if I could integrate the semicircle it would be easier to model. I will probable work on the point load idea. This...

Rb1957: I am not sure what you are referring to above. I am trying to solve this by hand, Any direction you could give me would be appreciated.

Gentlemen: First of all I want to thank you all for your help with solving my problem above. I was not understanding how to apply the beam deflection formulas and you have taught me how for which I am grateful. I now have the calculations worked out and we are applying them to our product...

BAretired: One word: Elegant. I had all the pieces the first time I looked at this but could not see the forest for the trees. Thank you.

rb1957: Unit load is not something I have come across in my Elements of Strength of Materials Textbook I am working through. And I have no experience with structural engineering. I posted to this site with two goals. First to find a solution to the statically indeterminant triangular load...

Doug: For the full sinusoidal load applied from 6" to 68" I get Reactions of 1,634.37 lb. and deflection at 6" of .2529" from my elastic line equations. So we agree. As far as your second part, I am not familiar with the term unit load. What do you mean by that? And how is it applied in...

To all: The total length of the shaft is 74". The sine load is only applied between supports B & C which are 62" apart. The total force applied to the 62" diameter round blade is F = 30 "H20 x 0.03609 lb/In^2/"H20 x PI (62"/2)^2 = 3,268.75 Lb. W = 3,268.75 lb * PI / 62" / 2 = 82.815 lb/in...

BAretired: I noticed that and thought something was amiss but checking page 5 a 2" round cross section is shown. Thanks,

4 support beam deflection reporthttps://files.engineering.com/getfile.aspx?folder=40159615-6d44-4106-b843-c2f870928dab&file=Beam_Analysis_4_Supports.pdf

2 support beam deflection reporthttps://files.engineering.com/getfile.aspx?folder=408fb971-d9dc-4df0-8b66-f200b8c1790a&file=Beam_Analysis_2_Supports.pdf

BAretired: I worked through the information contained in your most recent post and have attached your diagram with my notes. I used your equation for theta 0 due to Ra and Rb and added q0 from the applied load. Solving for Ra resulted in 1,711 lb. which does not equal the result of 3,214 lb...

BAretired: Attached is the derivation of the beam formulas for the simply supported beam with the sine load. From this theta is equal to W*L^3/π^3.https://files.engineering.com/getfile.aspx?folder=c9f90554-7f2f-47c8-8ef1-1f1363a5aa18&file=Beam_Freely_Supported_at_Ends_-_Sine_Wave_Load_20240923.pdf

BAretired: Thank you for your response above. To answer your questions: 1) Too short to be considered a beam. A and B together make one fixed support. Same with C and D - I'm not sure what you mean here. The real world example is a shaft for a valve. The support locations, from left to right...

Gentlemen: I thought I had this. I understand how to solve my original problem with the VDL using superposition setting angles equal to each other. After working it out it seemed simple. But I am now trying to apply this to a real world problem where I know what the answers are but am unable...

Doug: I may have not been clear. The two outside supports are rigid (bearings). The two interior supports are shaft seals that have some flexibility. We originally thought that the shaft seals were rigid enough to be considered fixed supports but we now believe that they may flex enough to...

OP has not abandoned ship. I have been following this discussion closely and have enjoyed both the philosophical and technical responses. The two most recent posts have been most helpful. I had been unable to see the forest on this problem and now have two ways of solving the problem that I...

Gentlemen: Thank you for your responses above. I am still not able to get to the finish line on this problem using your input. I have attached a word document showing what I have done so far. If one of you could take a look and show me the steps to get to the answers, I would appreciate it...

I am trying to solve the following problem which is in the method of superposition section of my Strength of Materials textbook. I am stuck and am wondering if anyone could point me in the right direction. A beam of length 3L is supported by four supports, A, B, C, and D from left to right...

Going back to strength of materials book to refresh after many years. Working through problems. Looking for help solving the following problem: 2. A cantilever beam is composed of two 6x6-in timbers held together by bolts and connector rings. The beam is 3 1/2 feet long as has a concentrated...