Sistemas estructurales 111

METODO DE COEFICIENTES
1.-
MOMENTOS
Mmax =1400 KG (9.5)²8
Mmax= 15,793.75 = 15,794 KG
CORTANTES +
V1=1400 KG (9.5)2= 6,650 KG

V2=1400 KG (9.5)2=6,650 KG

PERFIL
h = L/15 = 9.50/15 = 0.65 m
b = h/2 = 0.65/2 = 0.32 = 0.35 m
A= b x h= 0.2275 m = 22.75 cm²
INERCIA
Ixx= 1/12 bh³ + A1D1²
Ixx= 1/12 (35cm)(65cm)³ + (22.75 cm²)(0)²=
Ixx = 800,989.5833
MODULO DE SECCION
Sxx= I total / C
C= h / 2
C = 65/2 = 32.5
C= 800,989.5833 cm4/ 32.5cm
Sxx= 24,645.8333 cm³

REVISION A CORTE
Q= R max / h (tw)
Q= 6650 k/ (65) (35)
Q= 3580.76
ESFUERZO A FLEXION
σ FLEXION = M max (100)(C) / Ixx
σ FLEXION = 15794 kg(100)(32.5) / 800989.58
σ FLEXION = 64.08385487

METODO DE COEFICIENTES
3.-
CORTANTES +
V1=1800 KG (7.2)2= 6480 KG
V3=1800 KG (6.3)2= 5670 KG
V5=1.15 (1300)(6.5)2= 4859 KG

CORTANTES -
V2=1.15(1800)(7.2)2= 7452 KG
V4=1800 KG (6.3)2= 5670 KG
V6=1300 KG (6.5)2= 4225 KG
MOMENTOS +
M1 = (1800 k/ml)(7.2m)2 /11
M1 = 8483 k/ml
M2= (1800 k/ml)(6.3m)2 /16
M2 = 4466 k/ml
M3= (1300 k/ml)(6.5m)2 /11
M3= 4994 k/ml
MOMENTOS -
M1 = (1800kg) ((7.2 + 6.3)2 /2)) / 10
M1 = 19283
M2 = ((1800kg+ 1300kg)/2) (6.3 + 6.5)2 /2)) / 10
M2 = 22345

PERFIL
h = L/15 = 7.2/15 = 0.48 m
b = h/2 = 0.48/2 = 0.24 m
A= b x h=(24)(48) = 1152 cm²
INERCIA
Ixx= 1/12 bh³ + A1D1²
Ixx= 1/12 (24cm)(48cm)³ + (1152 cm²)(0)²=
Ixx = 221184 cm4
MODULO DE SECCION
Sxx= I total / C
C= h / 2
C = 24 /2 = 32.5
Sxx= 221184 cm4/ 12cm
Sxx= 18432 cm³
REVISION A CORTE
Q= R max / h (tw)
Q= 18432 k/ (48) (24)
Q= 9216 cm
ESFUERZO A FLEXION
σ FLEXION = M max (100)(C) / Ixx
σ FLEXION = 22345 kg(100)(12 cm) / 18432 cm3
σ FLEXION = 1455

METODODE COEFICIENTES
5.-
CONDICION
MENOR DE 1.20
POR LO TANTO SI CUMPLE

6.5 / 5.8 = 1.12
5.8 / 5 = 1.16
5 / 4.5 = 1.11
5.3 / 4.5 = 1.17

CORTANTES +
V1=2400 KG (6.5)2= 7800 KG
V3=2400 KG (5.8)2= 6960 KG
V5=2400 KG(5)2= 6000 KG
V7=2400 KG (4.5)2= 5400 KG
V9=1.15 (2400 KG)(5.3)2= 7314 KG

CORTANTES -
V2=1.15 (2400)(6.5)2= 8970 KG
V4=2400 KG (5.8)2= 6960 KG
V6=2400 KG (5.8)2= 6000 KG
V8=2400 KG (4.5)2=5400 KG
V10=2400 KG (5.3)2= 6360 KG

MOMENTOS +
M1 = (2400 k/ml)(6.5 m)2 /11
M1 = 9219 k/ml
M2= (2400 k/ml)(5.8 m)2 /16
M2 = 5046 k/ml
M3= (2400 k/ml)(5 m)2 /16
M3= 3750 k/ml
M4= (2400 k/ml)(4.5 m)2 /16
M4 = 3038 k/ml
M5= (2400 k/ml)(5.3 m)2 /11
M5= 6129 k/ml
MOMENTOS -
M1 = (2400 kg) ((6.5 + 5.8)2 /2)) / 10
M1 = 21207
M2 = (2400 kg) ((5.8 + 5)2 /2)) / 11
M2 = 15031
M3 = (2400 kg) ((5 + 4.5)2/2)) / 11
M3 = 11469
M4 = (2400 kg) ((4.5 + 5.3 )2 /2)) / 10
M4 = 12270
PERFIL
h = L/15 = 6.5 /15 = 0.45 m
b = h/2 = 0.45 /2 = 0.25 m
A= b x h= (45)(25) = 1125 cm²

INERCIA
Ixx= 1/12 bh³ + A1D1²
Ixx= 1/12 (25 cm)(45 cm)³ + (1152 cm²)(0)²=
Ixx = 189843.75 cm4
MODULO DE SECCION
Sxx= I total / C
C= h / 2
C = 45 /2 = 25
Sxx= 189943 cm4/ 25 cm
Sxx= 7593.75 cm³
REVISION A CORTE
Q= R max / h (tw)
Q= 8970k/ (45) (25)
Q= 4983.3333 cm
ESFUERZO A FLEXION
σ FLEXION = M max (100)(C) / Ixx
σ FLEXION = 21207 kg(100)(25 cm) / 189843.75 cm4
σ FLEXION = 279.26913

METODO DE COEFICIENTES
6.-
CONDICION
MENOR DE 1.20
POR LO TANTO SI CUMPLE

9 / 8.5 = 1.05
9 / 8.5 = 1.05
9 / 7.5 = 1.2
8 / 7.5 = 1.05
9.2 / 8 = 1.15

CORTANTES +
V1=3400 KG (9)2= 15300 KG
V3=3400 KG (8.5)2= 14450 KG
V5=3400 KG(9)2= 15300 KGV7=2100 KG (7.5)2= 7875 KG
V9=(2100 KG)(8)2= 8400 KG
V11=1.15 (2100 KG)(9.2)2= 11100 KG
CORTANTES -
V2=1.15 (3400)(9)2= 17595 KG
V4=3400 KG (8.5)2= 14450 KG
V6=3400 KG (9)2= 15300 KG
V8=2100 KG (7.5)2= 7875 KG
V10=2100 KG (8)2= 8400 KG
V12=2100 KG (9.2)2= 9660 KG
MOMENTOS +
M1 = (3400 k/ml)(9 m)2 /11
M1 = 25037 k/ml
M2= (3400 k/ml)(8.5 m)2 /16
M2 = 15354 k/ml
M3= (3400 k/ml)(9 m)2 /16
M3= 17213 k/mlM4= (2100 k/ml)(7.5 m)2 /16
M4 = 7383 k/ml
M5= (2100 k/ml)(8 m)2 /16
M5= 8400 k/ml
M6= (2100 k/ml)(9.2 m)2 /11
M6= 16159 k/ml

MOMENTOS -
M1 = (3400 kg) ((9 + 8.52 /2)) / 10
M1 = 59692
M2 = (3400 kg) ((8.5 + 9)2 /2)) / 11
M2 = 52237
M3 = (3400 kg + 2100 kg)/2) ((9 + 7.5)2 /2)) / 11
M3 = 65764
M4 = (2100 kg) ((7.5 + 8 )2 /2)) / 11
M4 = 25248
M5 = (2100 kg) ((8 + 9.22 /2)) / 10
M5 = 33340

PERFIL...