Figuring out ROARK's methods on beams 1

[jimmyH155]

I am trying to teach myself how to calculate stresses and moments etc. I refer to Roark 7th edition. I thought I would follow through a worked example. In Section 8.7 is an example of a beam simply supported with uniformly dist load , concentrated lateral load and axial compressive load.
Answer a) I can just understand, b) starting to get lost, but hanging on there interpolating coefficients. Then in part c) they say to use Table 8.8 cases 1e and 2e.
When they come to calculating Max Moment M8, they use terms with theta in them, but neither case 1e or 2e has any equation with theta in it for the moments. Also in the moment calc they use the reaction Ra, which is nowhere in the written down equations in the tables. Am I missing something? Do I have to assume an already considerable knowledge of these things? I am a pumping engineer, and have been asked to do some calcs on beams at a pump station so am out of my depth.
I thought you simply looked up the Max M for example and then plugged in the stress formula and that was that??

 

[israelkk]

Look at case 2, you will see the meaning of RA, RB and theta A and theta B. Those are the reactions and the beam deflection slopes respectively.

 

[prex]

Try the first site below, under Beams -> Bending + compression -> Simply supported
Note however that analyzing a beam with bending + compressive forces generally requires the existence of special conditions to be justified. As an example a beam with one sliding support where a spring applies the compression would be a good representation of the situation; if, by contrast, the axial compression is contributed by the constraint of adjacent structures, you could be required to analyze more in depth to determine the actual value of the compressive force. And of course, don't forget to check buckling.

prex

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[desertfox]

Hi jimmyH155

What beams are you doing calculations for? is a frame to sit the pump on or to lift the pump in place.
we may be able to help further if you can elaborate on what your trying to do.
Here is a site which may help:-

http://www.roymech.co.uk/Useful_Tables/Form/Stress_Strain.html

desertfox

 

[Twoballcane]

Just a question, once you get the stresses, do you understand and know the failure theories? Because, you can not compare yield and ultimate stress with normal and bending stresses, so be careful. And, since you are working with pumps, you may have to do some dynamic calculations to see if the vibration from the pumps may couple into the beam which may be worst than just static weight.

Tobalcane
"If you avoid failure, you also avoid success."

 

[jimmyH155]

Thanks for that, guys. What I was really after was an explanation of that worked example in Roark section 8.7. I haven't actually got a real problem yet - I was studying for the time when I will have a real problem!!

 

[rb1957]

i'm not so sure that roark is the place i'd start to learn stress analysis ... his (excellent) book is not alot more than a compendium of results. look into a strength of materials text book to learn the fundamentals. if you did this, you'd appreciate the difference between laterally loade beams and axailly loaded beam-columns.

good luck