tercer laboratorio de resistencia de materiales

7/23/2019 Tercer Laboratorio de Resistencia de materiales

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5.4. CALCULOS

DESCRIPCION GENERAL DE LA MUESTRA

las muestras para este ensayo será un tubo de fierro de 1/2" X 1 1/2 " de espesor 2mm

tenemos así la siguiente sección en cm

L(cm)= 43 cm

A(cm2) 1.872 cm2

I(cm4) 0.463237 cm4

RG(cm) 0.49744916

l= 86.4409951

con estos resultados se puede constatar que la esbeltez es mayor de 80 como lo

sugirió el docente

COLUMNA 1

ITEM T(S) d(DIAL) d(cm) P(DIAL) P(Kg)

1 0 0 0 0 0

2 3 7.8 0.019812 8.5 62.9

3 6 12.5 0.03175 15 111

4 9 18 0.04572 21.5 159.1

5 12 24 0.06096 31 229.4

6 15 31.1 0.078994 38 281.2

7 18 41.3 0.104902 47.9 354.46

8 21 51 0.12954 56 414.4

9 24 60 0.1524 68 503.2

10 27 69.2 0.175768 78 577.2

11 30 78.2 0.198628 89 658.6

12 33 87.4 0.221996 101 747.4

13 36 96.1 0.244094 112.5 832.5

14 39 104.9 0.266446 127 939.8

15 42 114 0.28956 137 1013.8

16 45 123.3 0.313182 144 1065.617 48 132.1 0.335534 153 1132.2

18 51 140.6 0.357124 159 1176.6

19 54 147.5 0.37465 163 1206.2

20 57 153.1 0.388874 164.8 1219.52

21 60 154.9 0.393446 165.4 1223.96



0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5

P ( K g )

(cm)

GRÁFIC C RG VS

DEFORM CIÓN

y = 3426.7x - 2.9035

R² = 0.9977

-200

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4

P ( K g )

(cm)

GRÁFIC P VS R NGO

ELÁSTICO



Aplicando la fórmula de columna con excentricidad

A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.46324 cm4

L(cm)= 43 cm

E*(1/cm)= 3426.7 1/cm

E(Kg/cm2)= 341940 kg/cm2

Pcr= 845.504 Kg

s1= 865.568 kg/cm2

s2= 37.7488 kg/cm2

Mmax 283.695 kg*cm

COLUMNA 2


1 0 0 0 0 0

2 3 7 0.01778 6.9 51.06

3 6 12 0.03048 11.8 87.32

4 9 17.2 0.043688 17 125.8

5 12 25 0.0635 25 1856 15 32.4 0.082296 33 244.2

7 18 40 0.1016 41.3 305.62

8 21 51 0.12954 50.5 373.7

9 24 62 0.15748 61 451.4

10 27 65 0.1651 68.9 509.86

11 30 76.9 0.195326 77.5 573.5

12 33 87.2 0.221488 86 636.4

13 36 97.4 0.247396 96.5 714.1

14 39 106 0.26924 105.7 782.18

15 42 113.3 0.287782 113.3 838.42

16 45 124.8 0.316992 124.8 923.52

17 48 134 0.34036 133.7 989.38

18 51 141.6 0.359664 141.6 1047.84

19 54 150 0.381 147 1087.8

20 57 167 0.42418 153.9 1138.86

21 60 183 0.46482 160 1184



0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5

P ( K g )

(cm)

GRÁFIC C RG VS

DEFORM CIÓN

y = 2905.3x + 2.058

R² = 0.9994

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4

P ( K g )

(cm)

GRÁFIC P VS R NGO

ELÁSTICO



Aplicando la formula de columna con excentricidad

A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.463237 cm4

L(cm)= 43 cm

E*(1/cm)= 2905.3 1/cm

E(Kg/cm2)= 289910.98 kg/cm2

Pcr= 716.85404 Kg

s1= 757.32654 kg/cm2

s2= 48.478276 kg/cm2

Mmax 243.98844 kg*cm

COLUMNA 3


1 0 0 0 0 0

2 3 6.9 0.017526 7 51.8

3 6 11.8 0.029972 13.9 102.86

4 9 18.2 0.046228 19.4 143.56

5 12 26.1 0.066294 31 229.4

6 15 32.8 0.083312 38 281.2

7 18 41.3 0.104902 47.2 349.28

8 21 51 0.12954 56 414.4

9 24 61 0.15494 68 503.2

10 27 68.9 0.175006 77.5 573.5

11 30 77.5 0.19685 93 688.2

12 33 86 0.21844 97.4 720.76

13 36 96.5 0.24511 112.8 834.72

14 39 104 0.26416 129 954.6

15 42 113.3 0.287782 137.6 1018.24

16 45 123.4 0.313436 144.9 1072.26

17 48 134 0.34036 153 1132.2

18 51 142 0.36068 161.8 1197.32

19 54 147.2 0.373888 164.3 1215.82

20 57 154.2 0.391668 165 1221

21 60 167 0.42418 166.7 1233.58



0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6

P ( K g )

(cm)

GRÁFIC C RG VS

DEFORM CIÓN

y = 3454x - 9.7242

R² = 0.9966

-200

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4

P ( K g )

(cm)

GRÁFIC P VS R NGO

ELÁSTICO




A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.46324 cm4

L(cm)= 43 cm

E*(1/cm)= 3454 1/cm

E(Kg/cm2)= 344664 kg/cm2

Pcr= 852.24 Kg

s1= 852.879 kg/cm2

s2= 57.634 kg/cm2

Mmax 290.069 kg*cm

COLUMNA 4


1 0 0 0 0 0

2 3 6.9 0.017526 8.6 63.64

3 6 11.8 0.029972 14.2 105.08

4 9 17 0.04318 18.7 138.38

5 12 25 0.0635 31.5 233.1

6 15 33 0.08382 38.2 282.68

7 18 41.3 0.104902 46.9 347.06

8 21 50.5 0.12827 57 421.8

9 24 61 0.15494 66.8 494.32

10 27 68.9 0.175006 76.9 569.06

11 30 77.5 0.19685 94 695.6

12 33 86 0.21844 97 717.8

13 36 96.5 0.24511 113.6 840.64

14 39 105.7 0.268478 130 962

15 42 113.3 0.287782 138.5 1024.9

16 45 124.8 0.316992 143.9 1064.86

17 48 133.7 0.339598 154.6 1144.04

18 51 141.6 0.359664 162.3 1201.02

19 54 147 0.37338 165 1221

20 57 153.9 0.390906 166.9 1235.06

21 60 160 0.4064 168 1243.2



0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5

P ( K g )

(cm)

GRÁFIC C RG VS

DEFORM CIÓN

y = 3410.6x - 2.335

R² = 0.9966

-200

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4

P ( K g )

(cm)

GRÁFIC P VS R NGO

ELÁSTICO




A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.463237 cm4

L(cm)= 43 cm

E*(1/cm)= 3410.6 1/cm

E(Kg/cm2)= 340333.3 kg/cm2

Pcr= 841.5318 Kg

s1= 841.2837 kg/cm2

s2= 57.7888 kg/cm2

Mmax 285.7825 kg*cm

COLUMNA 5


1 0 0 0 0 0

2 3 6.5 0.01651 5.9 43.66

3 6 13.2 0.033528 15.1 111.74

4 9 20.5 0.05207 25.8 190.92

5 12 27.9 0.070866 33 244.2

6 15 33.8 0.085852 39 288.6

7 18 45.2 0.114808 51.4 380.36

8 21 49.1 0.124714 60.5 447.7

9 24 58.2 0.147828 72.1 533.54

10 27 66 0.16764 79 584.6

11 30 75.3 0.191262 92.8 686.72

12 33 91.2 0.231648 102.8 760.72

13 36 97 0.24638 115 851

14 39 107.2 0.272288 127.8 945.72

15 42 113 0.28702 137 1013.8

16 45 121.5 0.30861 149 1102.6

17 48 128.4 0.326136 156.9 1161.06

18 51 135.2 0.343408 163.4 1209.16

19 54 140.2 0.356108 164.9 1220.26

20 57 148 0.37592 167.4 1238.76

21 60 153 0.38862 168.2 1244.68



0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6

P ( K g )

(cm)

GRÁFIC C RG VS

DEFORM CIÓN

y = 3534.2x - 6.7472

R² = 0.9978

-200

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4

P ( K g )

(cm)

GRÁFIC P VS

R NGO ELÁSTICO




A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.463237 cm4

L(cm)= 43 cm

E*(1/cm)= 3402.3 1/cm

E(Kg/cm2)= 339505.0859 kg/cm2

Pcr= 839.4838763 Kg

s1= 843.6206906 kg/cm2

s2= 53.26379266 kg/cm2

Mmax 288.285479 kg*cm

COLUMNA 6


1 0 0 0 0 0

2 3 7 0.01778 6 44.4

3 6 11.9 0.03023 15.5 114.7

4 9 17.9 0.04547 27.8 205.72

5 12 25 0.0635 35.2 260.48

6 15 31.5 0.08001 37.4 276.76

7 18 41.3 0.1049 49 362.6

8 21 52.1 0.13233 60.5 447.7

9 24 60 0.1524 65.2 482.48

10 27 68.5 0.17399 76 562.4

11 30 77.1 0.19583 95.2 704.48

12 33 92 0.23368 104.2 771.08

13 36 98.2 0.24943 118.2 874.68

14 39 105 0.2667 128.5 950.9

15 42 113.7 0.2888 134 991.6

16 45 123.5 0.31369 142.9 1057.46

17 48 133.4 0.33884 157.9 1168.46

18 51 141 0.35814 163.5 1209.9

19 54 147.7 0.37516 167 1235.8

20 57 154.7 0.39294 170.2 1259.48

21 60 160.6 0.40792 172 1272.8



0

200

400

600

800

1000

1200

1400

0 0.2 0.4 0.6

P ( K g )

(cm)

GR FIC C RG VS

DEFORM CION

y = 3397.9x + 8.458

R² = 0.995

0

200

400

600

800

1000

1200

1400

0 0.2 0.4

P ( K g )

(cm)

GR FIC P VS

R NGO EL STICO




A(cm2) 1.872 cm2

e(cm)= 0.2 cm

I(cm4)= 0.46324 cm4

L(cm)= 43 cm

E*(1/cm)= 3253.3 1/cm

E(Kg/cm2)= 324637 kg/cm2

Pcr= 802.72 Kg

s1= 801.644 kg/cm2

s2= 55.962 kg/cm2

Mmax 271.99 kg*cm

VI. RESULTADOS

1. MODULO DE ELASTICIDAD DE LA COLUMNA

1.1.primer proceso de descarte

E1= 341939.887 Kg/cm2

E2= 289910.98 Kg/cm2

E3= 344664.07 Kg/cm2

E4= 340333.318 Kg/cm2

E5= 339485.129 Kg/cm2

E6= 324626.854 Kg/cm2

Epromedio 330160.04 Kg/cm2

E-10%E E+10%E

297144.0356 363176.0435

E1= 341939.887 Kg/cm2 OK

E2= 289910.98 Kg/cm2 NO

E3= 344664.07 Kg/cm2 OKE4= 340333.318 Kg/cm2 OK

E5= 339485.129 Kg/cm2 OK

E6= 324626.854 Kg/cm2 OK

1.2.segundo proceso de descarte

E1= 341939.887 Kg/cm2



E3= 344664.07 Kg/cm2

E4= 340333.318 Kg/cm2

E5= 339485.129 Kg/cm2

E6= 324626.854 Kg/cm2

Epromedio 338209.852 Kg/cm2E-10%E E+10%E

304388.8664 372030.8367

E1= 341939.887 Kg/cm2 OK

E3= 344664.07 Kg/cm2 OK

E4= 340333.318 Kg/cm2 OK

E5= 339485.129 Kg/cm2 OK

E6= 324626.854 Kg/cm2 OK

por tantoE= 338209.852 Kg/cm2

2.CARGA CRITICA


Pcr1= 845.504335 Kg

Pcr2= 716.854042 Kg

Pcr3= 852.24034 Kg

Pcr4= 841.531819 Kg

Pcr5= 839.483876 Kg

Pcr6= 802.7196 Kg

P cr promedio 816.389002 kg

P-10%P P+10%P

734.7501018 898.0279023

Pcr1= 845.504335 Kg OK

Pcr2= 716.854042 Kg MAL

Pcr3= 852.24034 Kg OK

Pcr4= 841.531819 Kg OK

Pcr5= 839.483876 Kg OK

Pcr6= 802.7196 Kg OK


Pcr1= 845.504335 Kg

Pcr3= 852.24034 Kg



Pcr4= 841.531819 Kg

Pcr5= 839.483876 Kg

Pcr6= 802.7196 Kg

P cr promedio 836.295994 kg

P-10%P P+10%P752.6663947 919.9255935

Pcr1= 845.504335 Kg OK

Pcr3= 852.24034 Kg OK

Pcr4= 841.531819 Kg OK

Pcr5= 839.483876 Kg OK

Pcr6= 802.7196 Kg OK

por tanto:

Pcr= 836.295994 Kg

3.ESFUERZO MAXIMO EN LA FIBRA INTERIOR

smax= 865.57 Kg/cm2

smax= 757.33 Kg/cm2

smax= 852.24 Kg/cm2

smax= 841.28 Kg/cm2

smax= 843.62 Kg/cm2

smax= 801.64 Kg/cm2

sprom= 826.95 Kg/cm2

s-10%s s+10%s

744.25 909.64

smax= 865.57 Kg/cm2 OK!








por tanto:

smax= 826.95 Kg/cm2

4.ESFUERZO MAXIMO EN LA FIBRA EXTERIOR


smax= 37.749 Kg/cm2

smax= 48.478 Kg/cm2

smax= 57.634 Kg/cm2

smax= 57.789 Kg/cm2

smax= 53.264 Kg/cm2

smax= 55.962 Kg/cm2


s-10%s s+10%s

46.63 56.99

smax= 37.749 Kg/cm2 MAL








4.2. segundo proceso de descarte

smax= 48.478 Kg/cm2

smax= 53.264 Kg/cm2

smax= 55.962 Kg/cm2


s-10%s s+10%s

47.31 57.82

smax= 48.478 Kg/cm2 OK



5.MOMENTO MAXIMO


Mmax= 283.695452 Kg.cm

Mmax= 243.988442 Kg.cm

Mmax= 290.068522 Kg.cm

Mmax= 285.782523 Kg.cm

Mmax= 288.285479 Kg.cm

Mmax= 271.990298 Kg.cm

M cr promedio 277.301786 kg.cm

P-10%P P+10%P

249.5716073 305.0319645

Mmax= 283.695452 Kg.cm OK

Mmax= 243.988442 Kg.cm MAL








Mmax= 283.695452 Kg.cm

Mmax= 290.068522 Kg.cm

Mmax= 285.782523 Kg.cm

Mmax= 288.285479 Kg.cm

Mmax= 271.990298 Kg.cm

M cr promedio 283.964455 kg.cm

P-10%P P+10%P

255.5680093 312.3609002






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