What I feel is that :
Since you are considering concentrated load of 6 N at the middle only and
both the ends are fixed then only the following part of the code would
suffice the solution-
In [81]: b5 = Beam(4, E, I)
In [82]: b5.bc_deflection = [(0, 0), (4, 0)]
In [83]: b5.apply_load(-R1, 0, -1)
In [84]: b5.apply_load(-R2, 4, -1)
In [85]: b5.apply_load(6, 2, -1)
In [86]: b5.solve_for_reaction_loads(R1, R2)
In [87]: b5.reaction_loads
Out[87]: {R2: 3, R1: 3}
Jason, Can you please verify if I am applying correct logic?
Regards
Sampad Kumar Saha
Mathematics and Computing
I.I.T. Kharagpur
On Thu, Jan 12, 2017 at 7:40 PM, SAMPAD SAHA <[email protected]> wrote:
>
>
> ---------- Forwarded message ----------
> From: Durve Sanjiv (External) <[email protected]>
> Date: Thu, Jan 12, 2017 at 6:40 PM
> Subject: RE: SingularityFunction in sympy.physics.continuum_mechanics.beam
> To: SAMPAD SAHA <[email protected]>
>
>
> Sampad,
>
>
>
> Thanks for your reply and interest. You can add Sympy group in this thread
> – I have no problem just send me a link.
>
>
>
> I think my question was not very clear. I am sorry about that.
>
>
>
> My problem is a beam fixed at both ends with a concentrated load of 6
> units in the center. Theoretical answer for M1 and M2 is 6*4/8 = 3.
>
>
>
> When I run the following script,
>
>
>
> from sympy.physics.continuum_mechanics.beam import Beam
>
> from sympy.functions import SingularityFunction
>
> from sympy import symbols, Piecewise, plot
>
> E, I, x = symbols('E, I, x')
>
> R1, R2 = symbols('R1, R2')
>
> M1, M2 = symbols('M1, M2')
>
> b = Beam(4, E, I)
>
> b.apply_load(R1, 0, -1)
>
> b.apply_load(6, 2, -1)
>
> b.apply_load(R2, 4, -1)
>
> b.apply_load(M1, 0, -1)
>
> b.apply_load(M2, 4, -1)
>
> b.bc_deflection = [(0, 0), (4, 0)]
>
> b.bc_slope = [(0, 0), (4, 0)]
>
> print b.boundary_conditions
>
> #b.solve_for_reaction_loads(R1, R2)
>
> b.solve_for_reaction_loads(R1, R2,M1,M2)
>
> print b.load
>
> print b.shear_force()
>
> print b.bending_moment()
>
> print b.slope().subs({E:1,I:1})
>
> print b.deflection().subs({E:1,I:1})
>
>
>
>
>
> I get following output
>
>
>
>
>
>
>
> In [*2*]: runfile('C:/UserApps/Python27/Lib/site-packages/xy/problem01.py',
> wdir='C:/UserApps/Python27/Lib/site-packages/xy')
>
> {'slope': [(0, 0), (4, 0)], 'deflection': [(0, 0), (4, 0)]}
>
> M1*SingularityFunction(x, 0, -1) + M2*SingularityFunction(x, 4, -1) + (-M1
> - 3)*SingularityFunction(x, 0, -1) + (-M2 - 3)*SingularityFunction(x, 4,
> -1) + 6*SingularityFunction(x, 2, -1)
>
> M1*SingularityFunction(x, 0, 0) + M2*SingularityFunction(x, 4, 0) + (-M1 -
> 3)*SingularityFunction(x, 0, 0) + (-M2 - 3)*SingularityFunction(x, 4, 0) +
> 6*SingularityFunction(x, 2, 0)
>
> M1*SingularityFunction(x, 0, 1) + M2*SingularityFunction(x, 4, 1) + (-M1 -
> 3)*SingularityFunction(x, 0, 1) + (-M2 - 3)*SingularityFunction(x, 4, 1) +
> 6*SingularityFunction(x, 2, 1)
>
> Traceback (most recent call last):
>
>
>
> File "<ipython-input-2-febc462b31fc>", line 1, in <module>
>
> runfile('C:/UserApps/Python27/Lib/site-packages/xy/problem01.py',
> wdir='C:/UserApps/Python27/Lib/site-packages/xy')
>
>
>
> File "C:\UserApps\Python27\lib\site-packages\spyderlib\widgets\
> externalshell\sitecustomize.py", line 685, in runfile
>
> execfile(filename, namespace)
>
>
>
> File "C:\UserApps\Python27\lib\site-packages\spyderlib\widgets\
> externalshell\sitecustomize.py", line 71, in execfile
>
> exec(compile(scripttext, filename, 'exec'), glob, loc)
>
>
>
> File "C:/UserApps/Python27/Lib/site-packages/xy/problem01.py", line 28,
> in <module>
>
> print b.slope().subs({E:1,I:1})
>
>
>
> File "C:\UserApps\Python27\lib\site-packages\sympy-1.0.1.dev0-
> py2.7.egg\sympy\physics\continuum_mechanics\beam.py", line 455, in slope
>
> slope_curve = slope_curve.subs({C3: constants[0][0]})
>
>
>
> IndexError: list index out of range
>
>
>
> In [*3*]: b.reaction_loads
>
> Out[*3*]: {M2: M2, M1: M1, R2: -M2 - 3, R1: -M1 - 3}
>
> I expect to get something like {R2:-3,R1:-3,M1:3, M1:3}
>
> I can understand that the problem I am trying to solve has indeterminacy
> of 2 and that is why my script is missing some additional statements.
>
> Once this appears in the thread, I will pursue this because it is an
> intersting problem for a hobbyist like me.
>
> Thanks for the help.
>
>
>
> Regards,
>
> Sanjiv Durve
>
> Ex- I I T Kanpur (1976)
>
>
>
> *From:* SAMPAD SAHA [mailto:[email protected]]
> *Sent:* 12 January 2017 12:34
> *To:* Durve Sanjiv (External)
> *Subject:* Re: SingularityFunction in sympy.physics.continuum_mechan
> ics.beam
>
>
>
> Sorry for the late reply.
>
>
>
> I tried it in my system. I am getting {R2: -3, R1: -3} as output for the
> reaction forces.
>
> Can you please share us your outputs and also the problem statement which
> you are trying to solve?
>
>
>
> And one more thing, it is absolutely fine contacting me directly at my
> gmail but still it is more preferrable that you post these queries into
> the Sympy group and CC other developers. This way you don't have to wait
> for long and can get very quick response as there are many active
> developers working on Sympy currently.
>
>
>
> If you don't mind Can I add Sympy Group in this thread?
>
>
>
>
> Regards
>
> Sampad Kumar Saha
>
> Mathematics and Computing
>
> I.I.T. Kharagpur
>
>
>
> On Tue, Jan 10, 2017 at 10:29 PM, Durve Sanjiv (External) <
> [email protected]> wrote:
>
> Hello Sampad,
>
>
>
> I have been trying to solve a fixed beam problem with concentrated load at
> the center of the beam using sympy. You seem to have done a wonderful job
> of implementing SingularityFunction. I hope you don’t mind me contacting
> you directly at your gmail.
>
>
>
> I have the following code which does not give the correct bending moment
> at the fixed ends. The line * b.bc_slope = [(0, 0), (4, 0)] *seems
> to have no effect
>
>
>
> Is there a quick fix or let me know if I am missing something. I also
> tried introducing M1, M2 and then commented out (shown in bold lines)
>
>
>
> Your help would be appreciated.
>
>
>
>
>
> from sympy.physics.continuum_mechanics.beam import Beam
>
> from sympy.functions import SingularityFunction
>
> from sympy import symbols, Piecewise, plot
>
> E, I, x = symbols('E, I, x')
>
> R1, R2 = symbols('R1, R2')
>
> M1, M2 = symbols('M1, M2')
>
> b = Beam(4, E, I)
>
> b.apply_load(R1, 0, -1)
>
> b.apply_load(6, 2, -1)
>
> b.apply_load(R2, 4, -1)
>
> *#b.apply_load(M1, 0, -1)*
>
> *#b.apply_load(M2, 4, -1)*
>
> b.bc_deflection = [(0, 0), (4, 0)]
>
> b.bc_slope = [(0, 0), (4, 0)]
>
> print b.boundary_conditions
>
> b.solve_for_reaction_loads(R1, R2)
>
> *#b.solve_for_reaction_loads(R1, R2,M1,M2)*
>
> print b.load
>
> print b.shear_force()
>
> print b.bending_moment()
>
> print b.slope().subs({E:1,I:1})
>
> print b.deflection().subs({E:1,I:1})
>
>
>
> p2 = plot(b.shear_force(),(x,0,4))
>
> p3 = plot(b.bending_moment(),(x,0,4))
>
> p1 = plot(b.slope().subs({E:1,I:1}),(x,0,4))
>
> p4 = plot(b.deflection().subs({E:1,I:1}),(x,0,4))
>
> Regards,
>
> Sanjiv Durve
>
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