Vakwerk_SB

Stelsel vergelijkingen (knoopevenwicht van een vakwerk)

import sympy as sp
Ah, Av, Bv, N1, N2, N3, N4, N5, F = sp.symbols('Ah Av Bv N1 N2 N3 N4 N5 F')

eq1 = sp.Eq(sp.nsimplify(Ah+N1+(1/sp.sqrt(5))*N2),0)
eq2 = sp.Eq(sp.nsimplify(Av+(2/sp.sqrt(5))*N2),0)
eq3 = sp.Eq(sp.nsimplify(-N1-(1/sp.sqrt(5))*N3+(1/sp.sqrt(5))*N4),0)
eq4 = sp.Eq(sp.nsimplify(Bv+(2/sp.sqrt(5))*N3+(2/sp.sqrt(5))*N4),0)
eq5 = sp.Eq(sp.nsimplify((-1/sp.sqrt(5))*N2+(1/sp.sqrt(5))*N3+N5),0)
eq6 = sp.Eq(sp.nsimplify((-2/sp.sqrt(5))*N2-(2/sp.sqrt(5))*N3),0)
eq7 = sp.Eq(sp.nsimplify((-1/sp.sqrt(5))*N4-N5+(3/5)*F),0)
eq8 = sp.Eq(sp.nsimplify((-2/sp.sqrt(5))*N4+(4/5)*F),0)
sol = sp.solve((eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8),(N1,N2,N3,N4,N5,Ah,Av,Bv))
display(sol)

{N1: F/2,
 N2: sqrt(5)*F/10,
 N3: -sqrt(5)*F/10,
 N4: 2*sqrt(5)*F/5,
 N5: F/5,
 Ah: -3*F/5,
 Av: -F/5,
 Bv: -3*F/5}

display(sol[N1].subs(F,50))
display(sol[N2].subs(F,50))
display(sol[N3].subs(F,50))
display(sol[N4].subs(F,50))
display(sol[N5].subs(F,50))
display(sol[Ah].subs(F,50))
display(sol[Av].subs(F,50))
display(sol[Bv].subs(F,50))

\[\displaystyle 25\]

\[\displaystyle 5 \sqrt{5}\]

\[\displaystyle - 5 \sqrt{5}\]

\[\displaystyle 20 \sqrt{5}\]

\[\displaystyle 10\]

\[\displaystyle -30\]

\[\displaystyle -10\]

\[\displaystyle -30\]