Blanco

Semana 3 (problema #1)
Iy= 6495050

Ix= 1178175

COMPONENTE | AREA | X1m | Y1m | Ax1m3 | Ay1m3 | Ix | Iy | Iy+Ady2 |
1 | 1200 | 30 | 60 | 36000 | 72000 | 20000 | 45000 | 45000+1260750 = 1305750 |
2 | 450 | 30 | 42.5 | 13500 | 19125 | 84375 | 33750 | 33750+2700= 60750 |
3 | 600 | 30 | 30 | 18000 | 18000 | 2500 | 22500 | 22500+270750= 49550 |
4 | 450 | 30 | 17.5 | 13500 | 7875 |84375 | 33750 | 33750+1452000= 1485750 |
5 | 300 | 30 | 5 | 9000 | 1500 | 2500 | 22500 | 22500+3570750= 3593250 |
| 3000 | / | / | 90000 | 118500 | 84375 | 157500 | 6495050 |
X = Axi A 900003000=30
Y = Ayi A 1185003000=39.5

Ix=
30(20)312=20000

Iy=
(30)3 2012=45000

COMPONENTE | (dx)2 mm2 | Dy2 mm2 | Adx2 mm2 | A(dy)2 mm2 |
1 | 0 | 42025 | / | 1260750 |
2 | 0 | 9 |/ | 27000 |
3 | 0 | 9025 | / | 270750 |
4 | 0 | 484 | / | 1452000 |
5 | 0 | 119025 | / | 3570750 |
SUMATORIA | / | 219375 | / | 6581250 |

Ady2mm2
3000(420.25) = 1260750
3000(9) = 27000
300(9025) = 270250
3000(484) = 1452000
3000(1190.25) = 3570750

dx2 = (30-30)2 = 0
dx2 = (30-30)2 =0
dx2 = (30-30)2 =0
dx2= (30-30)2 =0
dx2= (30-30)2 =0

dy2= (39.5-60)2 =420.25
dy2 = (39.5-42.5)2 = 9
dy2 = (39.5-30)2 = 90.25
dy2= (39.5-42.5)2 = 484
dy2= (39.5-42.5)2 = 1190.25

Semana 3 (problema #2)

1.- Centroide particular 2.- Momentos de centroide
_
X1= 45/2 = 22.5 Y1= 10/2 = 5 X = ∑AXi / ∑A = 37687.5 / 1675 = 22.5 X2= 25/2 = 12.5 Y2= 40/2 = 20 _
X3= 45/2 = 22.5 Y3= 5/2 = 2.5 Y = ∑Ayi / ∑A = 48062.5 / 1675 = 28.69Centroide = 22.5, 28.69

Fig. 1
Iy = ½b3h = (.5) (45)3(10) = 455625
Ix = ½bh3 = (.5) (45) (10)3 = 22500

Fig. 2
Iy = ½b3h = (.5) (25)3(40) = 312500
Ix = ½bh3 = (.5) (25) (40)3 = 800000


Fig. 3
Iy = ½b3h = (.5) (45)3(5) = 227812.5
Ix = ½bh3 = (.5) (45) (5)3 = 2812.5

Semana 3 (problema #3)
105

1

30

110

2

3

20

40

Componente | Area | Xi | Yi | Axi | Ayi| Ix | Iy |
1 | 1950 | 32.5 | 95 | 63357 | 185250 | 146250 | 686562.5 |
2 | 4400 | 85 | 55 | 374000 | 242000 | 4436666.67 | 586666.67 |
3 | 1300 | 32.5 | 10 | 42250 | 13000 | 43333.3 | 4577083 |
Σ | 7650 | - | - | 479625 | 440250 | 4626249.97 | 1730937.47 |
1.- Centroide particular 2.- Momentos de centroide
_
X1= 65/2 = 32.5 Y1= 30/2 =15 X = ∑AXi / ∑A = 479625 / 7650 =62.69 X2= 40/2 = 20 Y2= 110/2 = 55 _
X3= 65/2 = 32.5 Y3= 20/2 = 10 Y = ∑Ayi / ∑A = 440250 / 7650 = 57.54

Centroide = 62.69, 57.54
Fig. 1
Ix = 1/12bh3 = (1/12) (65) (30)3 = 146250
Iy = 1/12b3h = (1/12) (65)3(30) = 686362.5
Fig. 2
Ix = 1/12bh3 = (1/12) (40) (10)3 = 4436666.7
Iy = 1/12b3h = (1/12) (40)3(10) = 586666.67
Fig. 3
Ix = 1/12bh3 = (1/12) (65)(20)3= 43333.3
Iy =1/12b3h = (1/12) (65)3(20) = 457708.3

Componente | dx²mm | dy²mm | A(dx²)mm⁴ | A(dy²)mm⁴ | Ix+adx²mm⁴ | Iy+ady²mm⁴ |
1 | 911.43 | 1403.25 | 6972439.5 | 10734862.5 | 7118689.5 | 11421425 |
2 | 497.73 | 6.45 | 3578134.5 | 49342.5 | 8014801.17 | 636009.17 |
3 | 911.43 | 2260.05 | 6972439.5 | 17289382.5 | 7015772.8 | 17747090.8 |
Σ | 2320.59 | 3669.75 | 17523013.5 | 28073587.5 | 22149263.47 |29804524.97 |
Semana 4 (problema #1)2223Kg
2170Kg
2100Kg

10237.5Kg
6325Kg
1.30m
1.50m

6
5
4
3
2
1
0
1000
3432.28
3432.28
7423.79
2359.82
7273.75
0
1520
3690.99
4392.99
5037.62
3444.88
5544.88
7299.88
6325
1.90m
8.75m
2.30m
B
A
W=1170kgm
W=2750kgm

∑MoA=(6325kgm)(1.15m)-(2100kg)(1.50m)-(10237.5kgm)(4.372m)-(2223kgm)(9.7m)-(2170kg)(9.35m)+(8.75)Rb=0
Rb= 82517.97/8.75
Rb=9430.618kgm

∑Fy=-6325kgm-2100kg-10237.5kgm+9430.618kgm-2223kgm-2170kg+Ra
Ra=13624.88 kgm

A1= bxh/2 = 2.30x6325/2 = -7273.75kgm
A2= B+bxh/2 = 7299.88+5544.88x1.50 = 9633.57 kgm
A3= 5063.97 kgm
A4= - 10856.0711kgm
A5= 2425.198 kgm
A6= 988.65 kgm








Semana 4 (problema #2)
3130kg
3.55m

W=4150 kg
W= 3130 kg
1100kg

2.45m...