bu soruları resimli bir şekilde ,serbest cisim diy...

python
doc = fitz.open('/mnt/data/STATİK bütünleme.pdf')
page = doc.load_page(0)
pix = page.get_pixmap(dpi=150)
img_path = '/mnt/data/page1.png'
pix.save(img_path)
img_path

'/mnt/data/page1.png'

python
from IPython.display import display
display(Image.open(img_path))

python
# crop approximate truss region
import numpy as np
img = Image.open(img_path)
w,h = img.size
# For center region maybe half width
crop = img.crop((w*0.4, h*0.2, w*0.9, h*0.7))
display(crop)

python
crop2 = img.crop((w*0.5, h*0.2, w*0.9, h*0.55))
display(crop2)

python
# zoom right support area
crop3 = img.crop((w*0.6, h*0.35, w*0.9, h*0.7))
display(crop3)

python
# zoom top left area
crop4 = img.crop((w*0.45, h*0.15, w*0.85, h*0.3))
display(crop4)

python
crop5 = img.crop((w*0.35, h*0.25, w*0.6, h*0.55))
display(crop5)

python
# bigger crop for full truss
cropbig = img.crop((w*0.2, h*0.1, w*1.0, h*0.7))
display(cropbig)

python
# zoom mid interior
crop6 = img.crop((w*0.55, h*0.23, w*0.7, h*0.5))
display(crop6)

python
crop7 = img.crop((w*0.55, h*0.25, w*0.8, h*0.55))
display(crop7)

python
crop8 = img.crop((w*0.45, h*0.3, w*0.6, h*0.6))
display(crop8)

python
crop9 = img.crop((w*0.55, h*0.35, w*0.7, h*0.55))
display(crop9)

python
# Let's display with different scale
import matplotlib.pyplot as plt
plt.figure(figsize=(5,3))
plt.imshow(cropbig)
plt.axis('off')

(-0.5, 992.5, 1052.5, -0.5)

python
truss = cropbig.crop((0,0,475,475))
plt.imshow(truss)
plt.axis('off')

(-0.5, 474.5, 474.5, -0.5)

python
# load second page image
page2 = doc.load_page(1)
pix2 = page2.get_pixmap(dpi=150)
img2_path = '/mnt/data/page2.png'
pix2.save(img2_path)
display(Image.open(img2_path).crop((0,0,768,768)))

python
display(Image.open(img2_path).crop((600,0,1100,1100)))

python
# zoom top part section dimension
sec = Image.open(img2_path).crop((600,100,1100,600))
plt.figure(figsize=(3,6))
plt.imshow(sec)
plt.axis('off')

(-0.5, 499.5, 499.5, -0.5)

python
# define coordinates
coords = {'A': sp.Point(0,0),
          'B': sp.Point(3,3),
          'C': sp.Point(6,3),
          'D': sp.Point(9,3),
          'E': sp.Point(6,0),
          'F': sp.Point(3,1.5)}
# define edges list
edges = [('A','B'),
         ('B','F'),
         ('A','F'),
         ('F','C'),
         ('C','E'),
         ('D','E'),
         ('A','E'),
         ('B','C'),
         ('C','D')]
# unknown forces along each: tension positive from first to second node
F_vars = sp.symbols('F1:'+str(len(edges)+1))
# unknown reactions Ax, Ay at A; Ey at E (roller vertical), Ex maybe horizontal 0 (if roller)
Ax, Ay, Ex, Ey = sp.symbols('Ax Ay Ex Ey')
# external loads: 5 kN down at A; 4 kN down at B.
# Build equilibrium eqns for each node.

eqs = []
for node in coords:
    # sum of forces x and y
    sumx = 0
    sumy = 0
    # external
    if node == 'A':
        sumx += Ax
        sumy += Ay - 5  # 5 kN downward negative y
    elif node == 'B':
        sumy -= 4
    elif node == 'E':
        sumx += Ex
        sumy += Ey
    # contributions from members
    for idx,(n1,n2) in enumerate(edges):
        if node == n1 or node == n2:
            # direction vector from n1 to n2
            p1 = coords[n1]
            p2 = coords[n2]
            dx = p2.x - p1.x
            dy = p2.y - p1.y
            L = sp.sqrt(dx**2 + dy**2)
            ux = dx/L
            uy = dy/L
            if node == n1:
                # force acts on node along member toward n1->n2 (tension pulls away from node)
                sumx += -F_vars[idx]*ux
                sumy += -F_vars[idx]*uy
            else:
                # node == n2
                sumx += F_vars[idx]*ux
                sumy += F_vars[idx]*uy
    eqs.extend([sumx, sumy])

eqs_solved = sp.solve(eqs, list(F_vars) + [Ax, Ay, Ex, Ey])
eqs_solved

{F1: 4*sqrt(2),
 F2: 0,
 F3: -2*sqrt(5),
 F4: -2*sqrt(5),
 F5: 2,
 F6: 0,
 F7: -Ex,
 F8: 4,
 F9: 0,
 Ax: -Ex,
 Ay: 7,
 Ey: 2}

python
page3 = doc.load_page(2)
pix3 = page3.get_pixmap(dpi=150)
img3_path = '/mnt/data/page3.png'
pix3.save(img3_path)
display(Image.open(img3_path).crop((500,0,1100,800)))

python
display(Image.open(img3_path).crop((0,0,600,400)))

python
import matplotlib.pyplot as plt

# Coordinates for approximate truss (m)
coords = {'A': (0, 0),
          'B': (3, 3),
          'C': (6, 3),
          'D': (9, 3),
          'E': (6, 0),
          'F': (3, 1.5)}

members = [('A','B'),
           ('B','F'),
           ('F','A'),
           ('F','C'),
           ('C','E'),
           ('E','D'),
           ('A','E'),
           ('B','C'),
           ('C','D')]

# Member force results from quick joint‑equilibrium (kN)
forces = {('A','B'): 5.66,   # tension  +  (blue)
          ('B','F'): 0.0,
          ('F','A'): -4.47,  # compression (red)
          ('F','C'): -4.47,  # compression
          ('C','E'): 2.0,
          ('E','D'): 0.0,
          ('A','E'): 0.0,
          ('B','C'): 4.0,
          ('C','D'): 0.0}

fig, ax = plt.subplots(figsize=(6,4))
# draw members
for (n1,n2) in members:
    x1,y1 = coords[n1]
    x2,y2 = coords[n2]
    f_val = forces[(n1,n2)]
    color = 'blue' if f_val>0 else ('red' if f_val<0 else 'black')
    ax.plot([x1,x2],[y1,y2],lw=3,color=color,alpha=0.7)

# plot joints
for n,(x,y) in coords.items():
    ax.plot(x,y,'ko')
    ax.text(x,y+0.2,n,ha='center')

# external loads
ax.arrow(coords['A'][0],coords['A'][1]+0.3,0,-1,head_width=0.2,head_length=0.3,color='green')
ax.text(coords['A'][0]-0.3,coords['A'][1]-1.2,'5 kN ↓',color='green')

ax.arrow(coords['B'][0],coords['B'][1]+0.3,0,-1,head_width=0.2,head_length=0.3,color='green')
ax.text(coords['B'][0]-0.3,coords['B'][1]-1.2,'4 kN ↓',color='green')

# supports (simple symbols)
# pin at A
ax.plot(coords['A'][0]-0.4,coords['A'][1]-0.2,'k^')
# roller at E
ax.plot(coords['E'][0],coords['E'][1]-0.2,'ks')

ax.set_aspect('equal')
ax.axis('off')
ax.set_title('Q1 – Truss Free‑Body Diagram\nBlue: Tension, Red: Compression')
plt.show()