Analyse a beam
"Modernised"
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closed account (48T7M4Gy)
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+++ ACTIONS ALONG BEAM +++
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LOAD TAG: Pt load (Pt load at centre, P = 30000)
BEAM TAG: CPP2, E = 1e+14, I = 1.8, L = 20000, dx = 1000
END REACTIONS: Ra = 15000 Rb = 15000
END MOMENTS: Ma = 0 Mb = 0
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PT X V BM Slope Defl'n
____^_________^_________^______________^______________^______________^
0 0 15000 0 -0.00416667 0
1 1000 15000 1.5e+07 -0.004125 -4.15278
2 2000 15000 3e+07 -0.004 -8.22222
3 3000 15000 4.5e+07 -0.00379167 -12.125
4 4000 15000 6e+07 -0.0035 -15.7778
5 5000 15000 7.5e+07 -0.003125 -19.0972
6 6000 15000 9e+07 -0.00266667 -22
7 7000 15000 1.05e+08 -0.002125 -24.4028
8 8000 15000 1.2e+08 -0.0015 -26.2222
9 9000 15000 1.35e+08 -0.000791667 -27.375
10 10000 15000 1.5e+08 0 -27.7778
11 11000 -15000 1.35e+08 0.000791667 -27.375
12 12000 -15000 1.2e+08 0.0015 -26.2222
13 13000 -15000 1.05e+08 0.002125 -24.4028
14 14000 -15000 9e+07 0.00266667 -22
15 15000 -15000 7.5e+07 0.003125 -19.0972
16 16000 -15000 6e+07 0.0035 -15.7778
17 17000 -15000 4.5e+07 0.00379167 -12.125
18 18000 -15000 3e+07 0.004 -8.22222
19 19000 -15000 1.5e+07 0.004125 -4.15278
20 20000 -15000 0 0.00416667 0
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@lastchance As you no doubt expected there is essentially total agreement again.
I now see your earlier point about shear force at the RH end being zero as a check. That was the only difference I could see. It is another interesting artifact at the limit of the discontinuity and forces a decision on whether the design shear is -15000 (+15000) or 0 at the support. Given it is a beam segment I think it is 15000, keeping in mind if my program spat out 0 I probably wouldn't have objected ...
Just a thought, but you probably realise that your 'Macaulay integrator' plus end fixity and restraint matrix solver has the advantage of making the problem completely general. ie any load function f(x) can be applied to the beam, so separate load types are not needed if you have a system of writing and parsing f(x) whereby the load constructor is more or less just an equation.
Hi @kemort, thanks for taking the time to try this out.
Yes, I had noted this. However, I steered clear of it here because most structural load conditions are usually given in terms of point loads and piecewise linear ones (effectively, UDL + triangle). Also, I would still have to integrate it analytically several times, so the only realistic combinations would be simple functions like polynomials, exponentials or the trig functions. The only cases where I encounter much more complicated distributions are on aerodynamic shapes like airfoils or wind loading on "vertical beams" (e.g. wind-turbine monopiles).
A more complicated, but still tractable problem, is where the beam sectional properties (especially I) change with distance - for example, wind loading on tapered monopiles.
My original code also had point moments in (e.g. from side connections) but, as you will see from the almost complete dearth of comments in my code, I was really struggling to make it fit into the allowable post size, so I dropped them.
It's been a good learning exercise, but I hope the original poster doesn't think I'm a structural engineer! My first degree is in maths - I'm just supposed to understand things like beam loading when working in an engineering department.
| any load function f(x) can be applied to the beam, so separate load types are not needed if you have a system of writing and parsing f(x) whereby the load constructor is more or less just an equation. |
Yes, I had noted this. However, I steered clear of it here because most structural load conditions are usually given in terms of point loads and piecewise linear ones (effectively, UDL + triangle). Also, I would still have to integrate it analytically several times, so the only realistic combinations would be simple functions like polynomials, exponentials or the trig functions. The only cases where I encounter much more complicated distributions are on aerodynamic shapes like airfoils or wind loading on "vertical beams" (e.g. wind-turbine monopiles).
A more complicated, but still tractable problem, is where the beam sectional properties (especially I) change with distance - for example, wind loading on tapered monopiles.
My original code also had point moments in (e.g. from side connections) but, as you will see from the almost complete dearth of comments in my code, I was really struggling to make it fit into the allowable post size, so I dropped them.
It's been a good learning exercise, but I hope the original poster doesn't think I'm a structural engineer! My first degree is in maths - I'm just supposed to understand things like beam loading when working in an engineering department.
@lastchance
I won't hold it against you!
It's been an interesting discussion and I've learned quite a bit. However, with my lack of knowledge of C++ it's going to be some time before I write code to the same level as you (if ever). At the moment I'm sticking to the simple mechanics of a simply supported beam, with no frills like applied moments, torsion etc. That should get me through structs, functions and possibly OOP.
Thanks very much for your help.
I won't hold it against you!
It's been an interesting discussion and I've learned quite a bit. However, with my lack of knowledge of C++ it's going to be some time before I write code to the same level as you (if ever). At the moment I'm sticking to the simple mechanics of a simply supported beam, with no frills like applied moments, torsion etc. That should get me through structs, functions and possibly OOP.
Thanks very much for your help.
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