ANALISIS ESTRUCTURAL II

EJERCICIOS DE APLICACIÓN

TEMA: ARMADURAS PLANAS

DOCENTE: ING. CHILON MUÑOZ CARMEN

ESTUDIANTE: FERNANDEZ HEREDIA KEYMER YODAN

FACULTAD DE INGENIERÍA, ARQUITECTURA Y URBANISMO

ESCUELA PROFESIONAL DE INGENIERÍA CIVIL

ANALISIS ESTRUCTURAL II

EJERCICIOS DE APLICACIÓN

FACULTAD DE INGENIERÍA, ARQUITECTURA Y URBANISMO

ESCUELA PROFESIONAL DE INGENIERÍA CIVIL

PROBLEMA 1

DATOS:

E = 240 KN/mm2

Resolución

1.-PASO 1 [a] y [k]

Cálculo de [a]

1 0 0 B1 [a] = 0 0 -1 B2

0.707 -0.707 0 B3X1 Y1 Y2

NUDO 1 NUDO 2

Cálculo [k]

Sabemos que:

BRRAS E A EA/L1 240 2000 2402 240 2000 2403 240 2828 240

240 0 0 [k]= 0 240 0

0 0 240

2.-PASO 2

k = (Ei)(Ai)/(Li)

1 0 0.707 240 0[K]= 0 0 -0.707 X 0 240

0 -1 0 0 0

240 0 169.68 1 0[K]= 0 0 -169.68 X 0 0

0 -240 0 0.707 -0.707

359.96 -119.96 0.00[K]= -119.96 119.96 0.00

0.00 0.00 240.00

3.-PASO 3

Calculamos [F]

40[F]= -50

0

0.004 0.004 0.000 40[u]= 0.004 0.013 0.000 x -50

0.000 0.000 0.004 0

-0.04[u]= -0.46 (mm)

0.00

4.-paso 4 [e] = [a] [u]

1 0 0 -0.04[e]= 0 0 -1 x -0.46

0.707 -0.707 0 0.00

-0.04[e]= 0.00 (mm)

0.29

5.-paso 5 [s] = [k] [e]

240 0 0 -0.04 [s]= 0 240 0 x 0.00

0 0 240 0.29

-10.00 [s]= 0.00 (KN)

70.72

6.-paso 6

1 0 0.707 -10.00[F]= 0 0 -0.707 x 0.00

0 -1 0 70.72

40[F]= -50 (KN)

0

0 1 0 00 X 0 0 -1

240 0.707 -0.707 0

0-10

PROBLEMA 2

Resolución

1.-PASO 1 [a] y [k]

Cálculo de [a]

-1 0 1 0 00 1 0 0 00 0 -1 0 10 0 0 1 0

[a] = 0 0 0.8 0.6 00 0 0 0 0.80 0 0 0 00 0 0 0 00 0 0 0 0

X1 Y1 X2 Y2 X3NUDO1 NUDO2 NUDO3

Cálculo [k]

Sabemos que:

E A EA/L2040 120 6122040 140 9522040 120 6122040 140 9522040 140 571.22040 140 571.2

k = (Ei)(Ai)/(Li)

2040 140 9522040 120 6122040 120 612

612 0 0 0 00 952 0 0 00 0 612 0 00 0 0 952 0

[k]= 0 0 0 0 571.20 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

2.-PASO 2

-1 0 0 0 00 1 0 0 01 0 -1 0 0.80 0 0 1 0.6

[K]= 0 0 1 0 00 0 0 0 00 0 0 0 00 0 0 -1 00 0 0 0 0

-612 0 0 0 00 952 0 0 0

612 0 -612 0 4570 0 0 952 343

[K]= 0 0 612 0 00 0 0 0 00 0 0 0 00 0 0 -952 00 0 0 0 0

612.00 0.00 -612.00 0.00 0.000.00 952.00 0.00 0.00 0.00

-612.00 0.00 1589.57 274.18 -612.000.00 0.00 274.18 1157.63 0.00

[K]= 0.00 0.00 -612.00 0.00 977.570.00 0.00 0.00 0.00 274.180.00 0.00 0.00 0.00 -365.57

0.00 0.00 0.00 -952.00 -274.180.00 0.00 0.00 0.00 0.00

3.-PASO 3

Calculamos [F]0000

[F]= 0 (KN)00

-500

0.00411 0.00000 0.00248 -0.00148 0.001660.00000 0.00105 0.00000 0.00000 0.000000.00248 0.00000 0.00248 -0.00148 0.00166-0.00148 0.00000 -0.00148 0.00441 -0.00039

[u]= 0.00166 0.00000 0.00166 -0.00039 0.00248-0.00039 0.00000 -0.00039 0.00053 -0.000390.00082 0.00000 0.00082 -0.00109 0.00082-0.00109 0.00000 -0.00109 0.00388 0.00000

0.000816993 0 0.000816993 0.00 0.00

0.050.000.05-0.19

[u]= 0.00 (mm)-0.030.05-0.220.05

4.-paso 4 [e] = [a] [u]

-1 0 1 0 00 1 0 0 00 0 -1 0 10 0 0 1 0

[e]= 0 0 0.8 0.6 0

0 0 0 0 0.80 0 0 0 00 0 0 0 00 0 0 0 0

0.0000.000-0.0540.026

[e]= -0.073 (mm)0.073-0.0260.0000.054

5.-paso 5 [s] = [k] [e]

612 0 0 0 00 952 0 0 00 0 612 0 00 0 0 952 0

[s]= 0 0 0 0 571.20 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

0.000.00

-33.3325.00

[s]= -41.67 (KN)41.67-25.000.00

33.33

6.-paso 6

-1 0 0 0 00 1 0 0 01 0 -1 0 0.80 0 0 1 0.6

[F]= 0 0 1 0 00 0 0 0 00 0 0 0 00 0 0 -1 00 0 0 0 0

0.000.000.000.00

[F]= 0.00 (KN)0.000.00

-50.000.00

DATOS:

BARRA Area (cm2) E = 2040 Tn/cm21 1->2 1202 6->1 1403 2->3 1204 4->2 1405 6->2 1406 4->3 1407 5->3 1408 4->5 1209 6->4 120

0 0 0 0 B10 0 0 0 B20 0 0 0 B30 0 -1 0 B40 0 0 0 B5

0.6 -0.8 -0.6 0 B61 0 0 0 B70 -1 0 1 B80 1 0 0 B9

Y3 X4 Y4 X5NUDO3 NUDO4 NUDO5

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

571.2 0 0 00 952 0 00 0 612 00 0 0 612

0 0 0 0 612 00 0 0 0 0 9520 0 0 0 0 00 0 0 0 0 0

0.8 0 0 0 X 0 00.6 1 0 0 0 0-0.8 0 -1 1 0 0-0.6 0 0 0 0 0

0 0 1 0 0 0

0 0 0 0 -1 00 0 0 0 0 10 0 0 0 0 00 0 0 0 0 0

457 0 0 0 X 0 0343 952 0 0 0 0-457 0 -612 612 0 0-343 0 0 0 0 0

0 0 612 0 0 0

0.00 0.00 0.00 0.000.00 0.00 0.00 0.000.00 0.00 0.00 0.000.00 0.00 -952.00 0.00

274.18 -365.57 -274.18 0.001157.63 -274.18 -205.63 0.00-274.18 1589.57 274.18 -612.00

-205.63 274.18 1157.63 0.000.00 -612.00 0.00 612.00

-0.00039 0.00082 -0.00109 0.00082 00.00000 0.00000 0.00000 0.00000 0-0.00039 0.00082 -0.00109 0.00082 00.00053 -0.00109 0.00388 -0.00109 0-0.00039 0.00082 0.00000 0.00082 x 00.00105 0.00000 0.00053 0.00000 00.00000 0.00163 -0.00109 0.00163 00.00053 -0.00109 0.00441 -0.00109 -50

0.00 0.00 0.00 0.00 0

0 0 0 0 0.050 0 0 0 0.000 0 0 0 0.050 0 -1 0 -0.190 0 0 0 x 0.00

0.6 -0.8 -0.6 0 -0.031 0 0 0 0.050 -1 0 1 -0.220 1 0 0 0.05

0 0 0 0 0.00000 0 0 0 0.00000 0 0 0 -0.05450 0 0 0 0.02630 0 0 0 x -0.0729

571.2 0 0 0 0.07290 952 0 0 -0.02630 0 612 0 0.00000 0 0 612 0.0545

0 0 0 0 0.000 0 0 0 0.000 0 0 0 -33.330 0 0 0 25.00

0.8 0 0 0 x -41.670.6 1 0 0 41.67-0.8 0 -1 1 -25.00-0.6 0 0 0 0.00

0 0 1 0 33.33

0 0 0 0 0 0 00 0 0 0 0 0 0

612 0 0 0 0 0 00 952 0 0 0 0 00 0 571.2 0 0 0 00 0 0 571.2 0 0 00 0 0 0 952 0 00 0 0 0 0 612 00 0 0 0 0 0 612

1 0 0 0 0 0 00 0 0 0 0 0 0-1 0 1 0 0 0 00 1 0 0 0 -1 0

0.8 0.6 0 0 0 0 00 0 0.8 0.6 -0.8 -0.6 00 0 0 1 0 0 00 0 0 0 -1 0 10 0 0 0 1 0 0

-1 0 1 0 0 00 1 0 0 0 00 0 -1 0 1 00 0 0 1 0 0

X 0 0 0.8 0.6 0 00 0 0 0 0.8 0.60 0 0 0 0 10 0 0 0 0 00 0 0 0 0 0

0 0 00 0 00 0 00 1 00 0 0

-0.8 -0.6 00 0 0-1 0 11 0 0

PROBLEMA 3

DATOS:

E =

BARRA1 2->12 3->13 1->44 2->35 5->26 3->47 5->3

Resolución

1.-PASO 1 [a] y [k]

Cálculo de [a]

0.707 0.707 -0.707 -0.707 00 1 0 0 0

-0.707 0.707 0 0 0[a] = 0 0 -1 0 1

0 0 0 1 00 0 0 0 -10 0 0 0 0.514x1 y1 x2 y2 x3

nudo1 nudo2 nudo3

Cálculo [k]

Sabemos que: k = (Ei)(Ai)/(Li)

E A EA/L300.0 15000.0 1060.7 barra1300.0 15000.0 1500.0 barra2300.0 15000.0 1060.7 barra3300.0 16000.0 1600.0 barra4300.0 16000.0 960.0 barra5300.0 16000.0 1600.0 barra6300.0 16000.0 823.2 barra7

1060.7 0 0 0 00 1500.0 0 0 00 0 1060.7 0 0

[k]= 0 0 0 1600 00 0 0 0 9600 0 0 0 00 0 0 0 0

2.-PASO 2

0.707 0 -0.707 0 00.707 1 0.707 0 0-0.707 0 0 -1 0

[K]= -0.707 0 0 0 10 0 0 1 00 -1 0 0 00 0 0.707 0 0

749.89 0.00 -749.89 0.00 0.00749.89 1500.00 749.89 0.00 0.00-749.89 0.00 0.00 -1600.00 0.00

[K]= -749.89 0.00 0.00 0.00 960.000.00 0.00 0.00 1600.00 0.000.00 -1500.00 0.00 0.00 0.000.00 0.00 749.89 0.00 0.00

1060.34 0.00 -530.17 -530.17 0.000.00 2560.34 -530.17 -530.17 0.00

-530.17 -530.17 2130.17 530.17 -1600.00[K]= -530.17 -530.17 530.17 1490.17 0.00

0.00 0.00 -1600.00 0.00 3417.480.00 -1500.00 0.00 0.00 362.61

-530.17 530.17 0.00 0.00 -1600.00

3.-PASO 3

Calculamos [F]-300

00

[F]= 0 (KN)0

-4000

0.0113 -0.0023 0.0100 -0.0003 0.0102-0.0023 0.0015 -0.0022 0.0005 -0.00250.0100 -0.0022 0.0102 -0.0009 0.0101

[u]= -0.0003 0.0005 -0.0009 0.0010 -0.00090.0102 -0.0025 0.0101 -0.0009 0.0107-0.0034 0.0015 -0.0033 0.0005 -0.00360.0111 -0.0028 0.0107 -0.0009 0.0112

-2.040.07-1.68

[u]= -0.10 (mm)-1.610.14-1.74

4.-paso 4 [e] = [a] [u]

0.707 0.707 -0.707 -0.707 00 1 0 0 0

-0.707 0.707 0 0 00 0 -1 0 10 0 0 1 00 0 0 0 -10 0 0 0 0.514

-0.13-0.070.27

[e] = 0.06 (mm)-0.10-0.13-0.71

5.-paso 5 [s] = [K] [e]

1060.66 0.00 0.00 0.00 0.000.00 1500.00 0.00 0.00 0.000.00 0.00 1060.66 0.00 0.00

[s] = 0.00 0.00 0.00 1600.00 0.000.00 0.00 0.00 0.00 960.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00

-141.31-100.19283.02

[s] = 99.90 (KN)-99.90

-200.10-583.66

6.-paso 6

0.707 0 -0.707 0 00.707 1 0.707 0 0-0.707 0 0 -1 0

[F]= -0.707 0 0 0 10 0 0 1 00 -1 0 0 00 0 0.707 0 0

-300.000.000.00

[F]= 0.00 (KN)0.00

-400.000.00

300 KN/mm2

A (mm2)15000150001500016000160001600016000

0 0 B1-1 0 B20 0.707 B30 0 B40 0 B50 1 B6

0.857 0 B7y3 x4

nudo3 nudo4

0 00 00 00 00 0

1600 00 823.2

0 0 1060.7 0 0 00 0 0 1500.0 0 00 0 0 0 1060.7 00 0 x 0 0 0 1600-1 0.514 0 0 0 00 0.857 0 0 0 01 0 0 0 0 0

0.00 0.00 0.707 0.707 -0.707 -0.7070.00 0.00 0 1 0 00.00 0.00 -0.707 0.707 0 00.00 0.00 x 0 0 -1 0

-1600.00 423.12 0 0 0 10.00 705.48 0 0 0 0

1600.00 0.00 0 0 0 0

0.00 -530.17-1500.00 530.17

0.00 0.000.00 0.00

362.61 -1600.002104.59 0.00

0.00 2130.17

-0.0034 0.0111 -3000.0015 -0.0028 0-0.0033 0.0107 00.0005 -0.0009 x 0-0.0036 0.0112 00.0022 -0.0040 -400-0.0040 0.0123 0

0 0 -2.04-1 0 0.070 0.707 -1.680 0 x -0.100 0 -1.610 1 0.14

0.857 0 -1.74

0.00 0.00 -0.130.00 0.00 -0.070.00 0.00 0.270.00 0.00 x 0.060.00 0.00 -0.10

1600.00 0.00 -0.130.00 823.19 -0.71

0 0 -141.310 0 -100.190 0 283.020 0 x 99.90-1 0.514 -99.900 0.857 -200.101 0 -583.66

0 0 0 0.707 0.707 -0.707 -0.7070 0 0 0 1 0 00 0 0 -0.707 0.707 0 00 0 0 x 0 0 -1 0

960 0 0 0 0 0 10 1600 0 0 0 0 00 0 823.2 0 0 0 0

0 0 00 -1 00 0 0.7071 0 00 0 0-1 0 1

0.514 0.857 0

0 0 00 -1 00 0 0.7071 0 00 0 0-1 0 1

0.514 0.857 0