elemento resorte
DESCRIPTION
Elemento resorteTRANSCRIPT
FACULTAD DE INGENIERÍA
ESCUELA DE INGENIERÍA INDUSTRIAL
“ELEMENTO RESORTE”
DOCENTE
ING. ALEJANDRO SEGUNDO VERA LAZARO
CURSO
MECÁNICA DE MATERIALES
INTEGRANTES
BRAYAN VÁSQUEZ SANCHEZ
CARLOS ORDERIQUE MEDINA
IRVIN FRANSHESCO SOLIS ZAPATA
MARCOS ANTONIO RAMOS PEJERREY
RODRIGO GÓMEZ HERNÁNDEZ
CICLO ACADÉMICO
2016-I
CHICLAYO, ABRIL 2016
k1 = k3= k5=2500 N/mm k2 = k4= k6 = 4000 N/mm k7=6000 N/mm P=2000 N Q=1500 N R=6000 N
>> ke1=(k2*k3) /(k2+k3)
ke1 = 1.5385e+03
>> ke2=(k4*k5) /(k4+k5)
ke2 =1.5385e+03
>> ke3=ke1+ke2
ke3 =3.0769e+03
>> a= [k1 -k1 0 0 0; -k1 k1 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> b= [0 0 0 0 0 ;0 ke3 -ke3 0 0 ;0 -ke3 ke3 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> c= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 k6 -k6 0 ;0 0 -k6 k6 0 ;0 0 0 0 0]
>> d= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 k7 -k7 ;0 0 0 -k7 k7]
>> m=a+b+c+d
m = 1.0e+04 *
0.2500 -0.2500 0 0 0
-0.2500 0.5577 -0.3077 0 0
0 -0.3077 0.7077 -0.4000 0
0 0 -0.4000 1.0000 -0.6000
0 0 0 -0.6000 0.6000
1
>> r= [k1+ke3 -ke3 0 0; -ke3 ke3+k6 -k6 0 ;0 -k6 k6+k7 -k7 ;0 0 -k7 k7]
r =1.0e+04 *
0.5577 -0.3077 0 0
-0.3077 0.7077 -0.4000 0
0 -0.4000 1.0000 -0.6000
0 0 -0.6000 0.6000
>> y= [6000; -1500;0;2000]
y =
6000
-1500
0
2000
>> x=inv(r)*y
x =
u2= 2.6000
u3= 2.7625
u4= 3.2625
u5= 3.5958
k1 = k2= k4 = 2800 N/mm k3 = k5= k6 = 3500 N/mm k7=5000 N/mm P=8000 N Q=2000 N R=10 000 N S=12 000 N
>> ke1=((k4*k5) /(k4+k5)) +(k6)
ke1 =5.0556e+03
>> a= [k1 -k1 0 0 0 0; -k1 k1 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]
>> b= [0 0 0 0 0 0;0 k2 -k2 0 0 0;0 -k2 k2 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0]
>> c= [0 0 0 0 0 0;0 0 0 0 0 0;0 0 k3 -k3 0 0;0 0 -k3 k3 0 0;0 0 0 0 0 0;0 0 0 0 0 0]
>> d= [0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 0 0 0;0 0 0 ke1 -ke1 0;0 0 0 -ke1 ke1 0;0 0 0 0 0 0]
>> e= [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 k7 -k7;0 0 0 0 -k7 k7]
>> m=a+b+c+d+e
m =1.0e+04 *
0.2800 -0.2800 0 0 0 0
-0.2800 0.5600 -0.2800 0 0 0
0 -0.2800 0.6300 -0.3500 0 0
0 0 -0.3500 0.8556 -0.5056 0
0 0 0 -0.5056 1.0056 -0.5000
0 0 0 0 -0.5000 0.5000
>> r= [k1+k2 -k2 0 0 0; -k2 k2+k3 -k3 0 0;0 -k3 k3+ke1 -ke1 0;0 0 -ke1 ke1+k7 -k7;0 0 0 -k7 k7]
2
r = 1.0e+04 *
0.5600 -0.2800 0 0 0
-0.2800 0.6300 -0.3500 0 0
0 -0.3500 0.8556 -0.5056 0
0 0 -0.5056 1.0056 -0.5000
0 0 0 -0.5000 0.5000
>> y= [-12000; -10000;0; -2000;8000]
y =
-12000
-10000
0
-2000
8000
>> x=inv(r)*y
x =
u2= -5.7143
u3= -7.1429
u4= -5.4286
u5 = -4.2418
u6 = -2.6418
k1 = k2= k4 = k7= 5000 N/mm k3 = k5= k6 = 4000 N/mm k8=4000 N/mm P=15 000 N Q=8000 N R=10 000 N S=12 000 N
>> ke1=k1+k2
ke1 =10000
>> ke2=(k3*k4) /(k3+k4)
ke2 =2.2222e+03
>> ke3=(k5) +((k6*k7) /(k6+k7))
ke3 =6.2222e+03
>> a= [ke1 -ke1 0 0 0; -ke1 ke1 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> b= [0 0 0 0 0 ;0 ke2 -ke2 0 0 ;0 -ke2 ke2 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> c= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 ke3 -ke3 0 ;0 0 -ke3 ke3 0 ;0 0 0 0 0]
>> d= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 k8 -k8 ;0 0 0 -k8 k8]
>> m=a+b+c+d
m = 1.0e+04 *
3
1.0000 -1.0000 0 0 0
-1.0000 1.2222 -0.2222 0 0
0 -0.2222 0.8444 -0.6222 0
0 0 -0.6222 1.0222 -0.4000
0 0 0 -0.4000 0.4000
>> r= [ke1+ke2 -ke2 0 0; -ke2 ke2+ke3 -ke3 0 ;0 -ke3 ke3+k8 -k8 ;0 0 -k8 k8]
r = 1.0e+04 *
1.2222 -0.2222 0 0
-0.2222 0.8444 -0.6222 0
0 -0.6222 1.0222 -0.4000
0 0 -0.4000 0.4000
>> y= [12000; -8000;10000;15000]
y =
12000
-8000
10000
15000
>> x=inv(r)*y
x =
u2= 2.9000
u3=10.5500
u4= 14.5679
u5=18.3179
k1 = k2= k3 = 2500 N/mm k4 = k5= k6 = 3000 N/mm k7=4000 N/mm P=8000 N Q=10 000 N R=5000 N S=6000 N
>> ke1=((k2*k3) /(k2+k3)) +((k4*k5) /(k4+k5))
ke1 =2750
>> a= [k1 -k1 0 0 0; -k1 k1 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> b= [0 0 0 0 0 ;0 ke1 -ke1 0 0 ;0 -ke1 ke1 0 0 ;0 0 0 0 0 ;0 0 0 0 0]
>> c= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 k6 -k6 0 ;0 0 -k6 k6 0 ;0 0 0 0 0]
>> d= [0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 0 0 ;0 0 0 k7 -k7 ;0 0 0 -k7 k7]
>> m=a+b+c+d
m =
2500 -2500 0 0 0
-2500 5250 -2750 0 0
0 -2750 5750 -3000 0
0 0 -3000 7000 -4000
0 0 0 -4000 4000
4
>> r= [k1+ke1 -ke1 0 0; -ke1 ke1+k6 -k6 0 ;0 -k6 k6+k7 -k7 ;0 0 -k7 k7]
r =
5250 -2750 0 0
-2750 5750 -3000 0
0 -3000 7000 -4000
0 0 -4000 4000
>> y= [-6000; -5000;10000;8000]
y =
-6000
-5000
10000
8000
>> x=inv(r)*y
x =
u2=2.8000
u3=7.5273
u4= 13.5273
u5= 15.5273
k2 = k4= k6 = 4000 N/mm k1 = k3 k5 = 6000 N/mm P=2000 N Q=10 000 N R=6000 N
>> ke1=((k1*k2) /(k1+k2)) +(k3)
ke1 =8400
>> ke2=(k5*k6) /(k5+k6)
ke2 =2400
>> a= [ke1 -ke1 0 0; -ke1 ke1 0 0;0 0 0 0;0 0 0 0]
>> b= [0 0 0 0;0 k4 -k4 0;0 -k4 k4 0;0 0 0 0]
>> c= [0 0 0 0;0 0 0 0;0 0 ke2 -ke2;0 0 -ke2 ke2]
>> m=a+b+c
m =
8400 -8400 0 0
-8400 12400 -4000 0
0 -4000 6400 -2400
0 0 -2400 2400
>> r= [ke1+k4 -k4 0; -k4 k4+ke2 -ke2;0 -ke2 ke2]
5
r =
12400 -4000 0
-4000 6400 -2400
0 -2400 2400
>> y= [-6000; -10000;2000]
y =
-6000
-10000
2000
>> x=inv(r)*y
x =
u2= -1.6667
u3= -3.6667
u4= -2.8333