2.1.D.sagews

from sympy import *
from sympy import N as Num

F, l, EA        = var('F, l, EA')

# Unknowns:
S1, S2 = var('S_1 S_2')
Dl1, Dl2, phi = var('Delta_l1, Delta_l2, varphi')

unknowns = [S1, S2, Dl1, Dl2, phi]

sq = sqrt(2)/2
eqns = [
    Eq(0, S1/2-F+sq*S2),
    Eq(Dl1, l/2*phi),
    Eq(Dl2, sq*l*phi),
    Eq(Dl1, S1*l/2/EA),
    Eq(Dl2, S2*sq*l/EA),
    ]

# Solve equations:
sol = solve(eqns, unknowns)
pprint(sol)

phi=sol[phi]

v2 = l*phi

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

# derived units:
N = kg*m/s/s
Pa = N/m/m
GPa = 1000000000*Pa
mm = m/1000

pprint(v2)
subs={}
subs[EA] = 210*GPa * 2*mm*2*mm
subs[l] = 2*m
subs[F] = 1000*N
v2_in_mm = v2.subs(subs)/mm
pprint(Num(v2_in_mm,3))

___ \/ 2 *F*l 2*F*l ___ {Delta_l1: --------------, Delta_l2: --------------, S_1: -2*F + 2*\/ 2 *F, S_ / ___ \ / ___ \ EA*\\/ 2 + 2/ EA*\\/ 2 + 2/ ___ ___ 2*\/ 2 *F 2: -2*F + 2*\/ 2 *F, varphi: --------------} / ___ \ EA*\\/ 2 + 2/ ___ 2*\/ 2 *F*l -------------- / ___ \ EA*\\/ 2 + 2/ 1.97