```python
from sympy import *

F, l = var("F, l")
q = F/l
R = q*l

# Reactions:
MA, Ah, Av, Gh, Gv, Bv = var("MA, Ah, Av, Gh, Gv, Bv")

eq1 = Eq(Ah + Gh)
eq2 = Eq(Av + Gv - 2*R)
eq3 = Eq(MA + 2*l*Gv - l*2*R)

eq4 = Eq(- Gh - F - F)
eq5 = Eq(- Gv - R - F - F + Bv)
eq6 = Eq(- R/2 - F - 2*F + 3*Bv)

eqns = [eq1, eq2, eq3, eq4, eq5, eq6]
unks = [MA, Ah, Av, Gh, Gv, Bv]

sol = solve(eqns, unks)
pprint(sol)

# Sections:
x = var("x")
MA,Ah,Av,Gh,Gv,Bv = \
    sol[MA],sol[Ah],sol[Av],sol[Gh],sol[Gv],sol[Bv]

# Region 1:
N = - Ah
Q = - q*x + Av
M = - MA - q*x*x/2 + Av*x

pprint("\nN, Q, M:")
S = Matrix([N, Q, M])
pprint(S)
pprint("\nAt x = 0:")
pprint(S.subs(x,0))
pprint("\nAt x = 3l:")
pprint(S.subs(x,3*l))

# ⎧             23⋅F      7⋅F                -11⋅F       17⋅F⋅l⎫
# ⎨Ah: 2⋅F, Av: ────, Bv: ───, Gh: -2⋅F, Gv: ──────, MA: ──────⎬
# ⎩              6         6                   6           3   ⎭
#
# N, Q, M:
# ⎡          -2⋅F          ⎤
# ⎢                        ⎥
# ⎢       23⋅F   F⋅x       ⎥
# ⎢       ──── - ───       ⎥
# ⎢        6      l        ⎥
# ⎢                        ⎥
# ⎢                       2⎥
# ⎢  17⋅F⋅l   23⋅F⋅x   F⋅x ⎥
# ⎢- ────── + ────── - ────⎥
# ⎣    3        6      2⋅l ⎦
#
# At x = 0:
# ⎡  -2⋅F  ⎤
# ⎢        ⎥
# ⎢  23⋅F  ⎥
# ⎢  ────  ⎥
# ⎢   6    ⎥
# ⎢        ⎥
# ⎢-17⋅F⋅l ⎥
# ⎢────────⎥
# ⎣   3    ⎦
#
# At x = 3l:
# ⎡-2⋅F ⎤
# ⎢     ⎥
# ⎢ 5⋅F ⎥
# ⎢ ─── ⎥
# ⎢  6  ⎥
# ⎢     ⎥
# ⎢4⋅F⋅l⎥
# ⎢─────⎥
# ⎣  3  ⎦

```

c9a99a735e6d933314997370c0366bd57b153da6
ipynb
Jupyter Notebook
ipynb/TEM-Exam/2017-3/a1.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
ipynb/TEM-Exam/2017-3/a1.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
ipynb/TEM-Exam/2017-3/a1.ipynb
kassbohm/wb-snippets
f1ac5194e9f60a9260d096ba5ed1ce40b844a3fe
MIT
Qwen/Qwen-72B
1. YES
2. YES