Ejercicios Resueltos Con Matlab De Resistencia De Materiales

EJERCICIO 01

* Del triangulo se deduce que por ser ángulos conocidos de 30°, 60° y 90°

10m = a√3 2(a)=2(5.77m)=11.54m
5.77m = a

| | BARRA | ANGULO | COSENO | SENO | COSENO ² | SENO ² | C*S |
| K1 | 1 - 2 | 30 | 0.87 | 0.5 | 0.75 | 0.25 | 0.44 |
| K2 | 2 - 3 | 180 | -1 | 0 | 1 | 0 | 0 |
| K3 | 1 - 3 | 90 | 0 | 1 | 0 | 1 | 0 |

K1=E1A1L1=300X109Nm2(8X10-4m2)11.54m=20797KNm

K2=E1A1L1=300X109Nm2( 8X10-4m2)10m=24000KNm

K3=E1A1L1=300X109Nm2( 8X10-4m2)5.77m=41594KNm

>> K1=20797*[0.75 0.44 -0.75 -0.44 0 0; 0.44 0.25 -0.44 -0.25 0 0; -0.75 -0.44 0.75 0.44 0 0; -0.44 -0.25 0.44 0.25 0 0; 0 0 0 0 0 0; 0 0 0 0 0 0]

K1 =

1.0e+004 *

1.5598 0.9151 -1.5598 -0.9151 0 0
0.9151 0.5199 -0.9151-0.5199 0 0
-1.5598 -0.9151 1.5598 0.9151 0 0
-0.9151 -0.5199 0.9151 0.5199 0 0
0 0 0 0 0 0
0 0 0 0 0 0

>> K2=24000*[0 0 0 0 0 0; 0 0 0 0 0 0; 0 0 1 0 -1 0; 0 0 0 0 0 0; 0 0 -1 01 0; 0 0 0 0 0 0]

K2 =

0 0 0 0 0 0
0 0 0 0 0 0
0 0 24000 0 -24000 0
0 0 0 0 0 0
0 0 -24000 0 24000 0
00 0 0 0 0

>> K3=41594*[0 0 0 0 0 0; 0 1 0 0 0 -1; 0 0 0 0 0 0; 0 0 0 0 0 0; 0 0 0 0 0 0; 0 -1 0 0 0 1]

K3 =

0 0 0 0 0 0
0 41594 0 0 0 -41594
0 0 0 0 0 0
00 0 0 0 0
0 0 0 0 0 0
0 -41594 0 0 0 41594

>> KT=K1+K2+K3

KT =

1.0e+004 *

1.5598 0.9151 -1.5598 -0.9151 0 0
0.9151 4.6793 -0.9151 -0.5199 0 -4.1594
-1.5598-0.9151 3.9598 0.9151 -2.4000 0
-0.9151 -0.5199 0.9151 0.5199 0 0
0 0 -2.4000 0 2.4000 0
0 -4.1594 0 0 0 4.1594

>> KRT=[3.9598 0.9151; 0.9151 0.5199]

KRT =

3.9598 0.9151
0.9151 0.5199

>> F=[8000;-5000]

F =

8000
-5000

>> U=inv (KRT)*F

U =

1.0e+004 *

Ux2= 0.7152
Uy2=-2.2206

>> E1=26000000*[-1 1]*[0.87 0.50 0 0; 0 0 0.87 0.50]*[0; 0; 0.7152; -2.2206]

E1 = -1.2690e+007

>> E2=30000000*[-1 1]*[-1 0 0 0; 0 0 -1 0]* [0.7152; -2.2206; 0; 0]

E2 = 21456000

>> E3=52000000*[-1 1]*[0 1 0 0; 0 0 0 1]*[0; 0; 0; 0]

E3 = 0EJERCICIO 02

* Del triangulo se deduce que por ser ángulos conocidos de 45°, 45° y 90°

25m = a a√2=25m√2=35.36m


| | NODOS | ANGULO | COSENO | SENO | COSENO ² | SENO ² | C*S |
| K1 | 1 - 2 | 0 | 1 | 0 | 1 | 0 | 0 |
| K2 | 1 - 4 | 270 | 0 | -1 | 0 | 1 | 0 |
| K3 | 2 - 3 | 270 | 0 | -1 | 0 | 1 | 0 |
| K4 |  2 - 4 | 225 | -0.71 | -0.71 | 0.5 |0.5 | 0.5 |
| K5 | 3 - 4 | 180 | -1 | 0 | 1 | 0 | 0 |


K1=E1A1L1=200X109Nm2( 5X10-4m2)25m=4000KNm =k2 =k3 =k5

K4=E1A1L1=200X109Nm2( 5X10-4m2)35.36m=2828KNm

>> K1=4000*[1 0 -1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; -1 0 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0; 0 0 0 0...