Example Extension week 1 strain energy#

import sympy as sp

q, L, x, F, N, EA = sp.symbols('q L x F N EA')

N = q * (L-x) + F
eps = N  / EA
Ps = sp.integrate(EA*eps**2/2,(x,0,L))
display(sp.simplify(Ps))
Ps = sp.integrate(1/EA*N**2/2,(x,0,L))
display(sp.simplify(Ps))
sp.plot(N.subs([(L,10),(F,25e3),(q,5e3),(EA,2500e3)]),(x,0,10),title="Normal force $N(x)$ in N")
display(Ps.subs([(L,10),(F,25e3),(q,5e3),(EA,2500e3)]).evalf())

\[\displaystyle \frac{L \left(3 F^{2} + 3 F L q + L^{2} q^{2}\right)}{6 EA}\]

\[\displaystyle \frac{L \left(3 F^{2} + 3 F L q + L^{2} q^{2}\right)}{6 EA}\]

\[\displaystyle 5416.66666666667\]