e-armadura 2do examen

EJEMPLO 01RELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarra123456E (kg/cm)2.00E+062.00E+062.00E+062.00E+062.00E+062.00E+06A (cm)222222RELACION S - R - CL (cm)200400316.23316.23424.26424.26SRCAngulo (grados)0071.57108.43135.0045.00180PI200Grados (Rad)0.000000000.000000001.249045771.892546882.356194490.78539816Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de una armadura

Paso 03Podemos encontrar esta matriz para todas las barras de la armadura de la sgte manera:Coordenadas Globales ( Barra de Armadura )BARRA 1E2.00E+06Kg/cm12341234A2cm110-10120000.0000.000-20000.0000.000L200.00cmk1 =2000020000=20.0000.0000.0000.000Angulo03-10103-20000.0000.00020000.0000.000Radianes04000040.0000.0000.0000.000COS1SEN0

BARRA 2E2.00E+06Kg/cm56785678A2cm510-10510000.0000.000-10000.0000.000L400.00cmk1 =1000060000=60.0000.0000.0000.000Angulo07-10107-10000.0000.00010000.0000.000Radianes08000080.0000.0000.0000.000COS1SEN0

BARRA 3E2.00E+06Kg/cm56125612A2cm50.10.3-0.1-0.351264.9113794.733-1264.911-3794.733L316.23cmk1 =12649.1106460.30.9-0.3-0.9=63794.73311384.200-3794.733-11384.200Angulo71.571-0.1-0.30.10.31-1264.911-3794.7331264.9113794.733Radianes1.2490457722-0.3-0.90.30.92-3794.733-11384.2003794.73311384.200COS0.316227766SEN0.948683298

BARRA 4E2.00E+06Kg/cm78347834A2cm70.1-0.3-0.10.371264.911-3794.733-1264.9113794.733L316.23cmk1 =12649.110648-0.30.90.3-0.9=8-3794.73311384.2003794.733-11384.200Angulo108.433-0.10.30.1-0.33-1264.9113794.7331264.911-3794.733Radianes1.89254688140.3-0.9-0.30.943794.733-11384.200-3794.73311384.200COS-0.31622777SEN0.948683298

BARRA 5E2.00E+06Kg/cm78127812A2cm70.5-0.5-0.50.574714.045-4714.045-4714.0454714.045L424.26cmk1 =9428.090428-0.50.50.5-0.5=8-4714.0454714.0454714.045-4714.045Angulo135.001-0.50.50.5-0.51-4714.0454714.0454714.045-4714.045Radianes2.35619449020.5-0.5-0.50.524714.045-4714.045-4714.0454714.045COS-0.70710678SEN0.707106781

BARRA 6E2.00E+06Kg/cm56345634A2cm50.50.5-0.5-0.554714.0454714.045-4714.045-4714.045L424.26cmk1 =9428.0904260.50.5-0.5-0.5=64714.0454714.045-4714.045-4714.045Angulo45.003-0.5-0.50.50.53-4714.045-4714.0454714.0454714.045Radianes0.7853981634-0.5-0.50.50.54-4714.045-4714.0454714.0454714.045COS0.70710678SEN0.707106781

12345678125978.956-919.312-20000.0000.000-1264.911-3794.733-4714.0454714.0452-919.31216098.2450.0000.000-3794.733-11384.2004714.045-4714.0453-20000.0000.00025978.956919.312-4714.045-4714.045-1264.9113794.73340.0000.000919.31216098.245-4714.045-4714.0453794.733-11384.2005-1264.911-3794.733-4714.045-4714.04515978.9568508.778-10000.0000.0006-3794.733-11384.200-4714.045-4714.0458508.77816098.2450.0000.0007-4714.0454714.045-1264.9113794.733-10000.0000.00015978.956-8508.77884714.045-4714.0453794.733-11384.2000.0000.000-8508.77816098.245

Paso 04A partir de las matrices de todas las barras se obtiene esta matriz de toda la estructura sumando las componentes de cada matriz en funcin de sus grados de libertad con lo cual tenemos una matriz de 8x8 que luego particionamos como se indica

1234567812345678

17414.214Kg2-1414.214Kg30.000Kg4-4000.000Kg

1234125978.956-919.312-20000.0000.0002-919.31216098.2450.0000.0003-20000.0000.00025978.956919.31240.0000.000919.31216098.245

Paso 05Para invertir la matriz (kff) seleccionamos las celdas (E170:H173) la funcion es =MINVERSA(E161:H164) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter

123410.00009525440.00000543960.0000734805-0.000004196220.00000543960.00006242920.0000041962-0.000000239630.00007348050.00000419620.0000952544-0.00000543964-0.0000041962-0.0000002396-0.00000543960.0000624292

Paso 06Para Multiplicar una matriz con el vector de cargas nodales seleccionamos las celdas (E187:E190) la funcion es =MMULT(E170:H173,E149:E152) y sin soltar presionamos "CTROL" + "SHIFT", sin soltar damos enter

10.7153284645cm2-0.0469991306cm30.5606240101cm4-0.280489485cm

5-2047.04Kg6-3500.00Kg7-5367.17Kg88914.21Kg

EJEMPLO 02RELACION S - R - CSRC180PI200Paso 01Numeramos las barras Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructuraBarraUnd.123456E KN/M2.00E+062.00E+062.00E+062.00E+062.00E+062.00E+06A M0.050.050.050.050.050.05LM101010.0010.0014.1414.14Angulo GRADOS0090.0090.0045.00135.00Grados RADIANES0.000000000.000000001.570796331.570796330.785398162.35619449Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de una armadura

12345678Paso 03Podemos encontrar esta matriz para todas las barras de la armadura de la sgte manera:Coordenadas Globales ( Barra de Armadura )BARRA 1E2.00E+06KN/M12651265A0.05M110-101100000-100000L10.00Mk1 =10000.0020000=20000Angulo06-10106-100000100000Radianes05000050000COS1SEN0

BARRA 2E2.00E+06KN/M34783478A0.05M310-103100000-100000L10.00Mk1 =10000.0040000=40000Angulo07-10107-100000100000Radianes08000080000COS1SEN0

BARRA 3E2.00E+06KN/M12341234A0.05M100-0-010.000.00-0.00-0.00L10.00Mk1 =10000.00201-0-1=20.0010000.00-0.00-10000.00Angulo90.003-0-0003-0.00-0.000.000.00Radianes1.5707963274-0-1014-0.00-10000.000.0010000.00COS0.000000000SEN1.000000000

BARRA 4E2.00E+06KN/M65786578A0.05M600-0-060.000.00-0.00-0.00L10.00Mk1 =10000.00501-0-1=50.0010000.00-0.00-10000.00Angulo90.007-0-0007-0.00-0.000.000.00Radianes1.5707963278-0-1018-0.00-10000.000.0010000.00COS0.00000000SEN1.000000000

BARRA 5E2.00E+06KN/M12781278A0.05M10.50.5-0.5-0.513535.533535.53-3535.53-3535.53L14.14Mk1 =7071.0720.50.5-0.5-0.5=23535.533535.53-3535.53-3535.53Angulo45.007-0.5-0.50.50.57-3535.53-3535.533535.533535.53Radianes0.7853981638-0.5-0.50.50.58-3535.53-3535.533535.533535.53COS0.70710678SEN0.707106781

BARRA 66E2.00E+06KN/M65346534A0.05M60.5-0.5-0.50.563535.53-3535.53-3535.533535.53L14.14Mk1 =7071.075-0.50.50.5-0.5=5-3535.533535.533535.53-3535.53Angulo135.003-0.50.50.5-0.53-3535.533535.533535.53-3535.53Radianes2.35619449040.5-0.5-0.50.543535.53-3535.53-3535.533535.53COS-0.70710678SEN0.707106781

12345678113535.533535.53-0.00-0.000.00-10000.00-3535.53-3535.5323535.5313535.53-0.00-10000.000.000.00-3535.53-3535.533-0.00-0.0013535.53-3535.533535.53-3535.53-10000.000.004-0.00-10000.00-3535.5313535.53-3535.533535.530.000.0050.00-10000.003535.53-3535.5313535.53-3535.53-0.00-10000.0060.000.00-3535.533535.53-3535.5313535.53-0.00-0.007-3535.53-3535.53-10000.000.00-0.00-10000.0013535.533535.538-3535.53-3535.530.000.00-0.00-0.003535.5313535.53


1234567812345678

10.00KN20.00KN32.00KN4-4.00KN50.00KN


1234510.000100-0.000100-0.000017-0.000083-0.0000172-0.0001000.0003830.0000660.0003170.0000663-0.0000000.0000000.0000830.000017-0.0000174-0.0001000.0003830.0000830.0004000.0000835-0.0001000.0003830.0000490.0003340.000149

60.00M


10.0002970563M2-0.0011372583M30.0000970563M4-0.0014343146M5-0.001240202M

6-1.03KN72.00KN82.97KN

A-1 (b)

RELACION S - R - CMRPTAR2AREA EXT.SRC9.810 cm23.14159265362.00 pulg81.07 cm2180PI200 ext4.00 pulgR2AREA INT.espesor :0.125 pulg3.14159265361.875 pulg71.26 cm2

DRPTAR2AREA EXT.Paso 01Numeramos las barras 3.720 cm23.14159265361.50 pulg45.60 cm2Numeramos los Grados de Libertad ( DOF ) libres y restringidos de la estructura ext3.00 pulgR2AREA INT.espesor :0.063 pulg3.14159265361.438 pulg41.88 cm2

BSRPTAR2AREA EXT.7.280 cm23.14159265361.50 pulg45.60 cm2 ext3.00 pulgR2AREA INT.espesor :0.125 pulg3.14159265361.375 pulg38.32 cm2

BIRPTAR2AREA EXT.4.980 cm23.14159265362.00 pulg81.07 cm2 ext4.00 pulgR2AREA INT.espesor :0.063 pulg3.14159265361.938 pulg76.09 cm2Paso 02Esta es la matriz de RIGIDEZ en coordenadas globales para la barra de una armadura

Paso 03Podemos encontrar esta matriz para todas las barras de la armadura de la sgte manera:

Coordenadas Globales ( Barra de Armadura )

1CO,CA1.00E-45300.00

E2.10E+06Kg/cmA7.280cmL300.00cm12341234Angulo0.00110-1-0150960.0000.000-50960.000-0.000Radianes0K 1 =50960200-0-0=20.0000.000-0.000-0.000COS13-1-0103-50960.000-0.00050960.0000.000SEN04-0-0004-0.000-0.0000.0000.000

2CO,CA200.00250.00

E2.10E+06Kg/cmA3.720cmL320.16cm56345634Angulo141.3450.61-0.49-0.610.49514878.408-11902.726-14878.40811902.726Radianes2K 2 =24400.58855747586-0.490.390.49-0.39=6-11902.7269522.18111902.726-9522.181COS-13-0.610.490.61-0.493-14878.40811902.72614878.408-11902.726SEN140.49-0.39-0.490.39411902.726-9522.181-11902.7269522.181

3CO,CA1.00E-45250.00

E2.10E+06Kg/cmA4.980cmL250.00cm78567856Angulo0.00710-1-0741832.0000.000-41832.000-0.000Radianes0K 3 =41831.9999999999800-0-0=80.0000.000-0.000-0.000COS15-1-0105-41832.000-0.00041832.0000.000SEN06-0-0006-0.000-0.0000.0000.000

4CO,CA1.00E-45500.00

E2.10E+06Kg/cmA4.980cmL500.00cm9107891078Angulo0.00910-1-0920916.0000.000-20916.000-0.000Radianes0K 4 =209161000-0-0=100.0000.000-0.000-0.000COS17-1-0107-20916.000-0.00020916.0000.000SEN08-0-0008-0.000-0.0000.0000.000

5CO,CA200.00200.00

E2.10E+06Kg/cmA3.720cmL282.84cm9101291012Angulo45.0090.50.5-0.5-0.5913809.79513809.795-13809.795-13809.795Radianes1K 5 =27619.5908731465100.50.5-0.5-0.5=1013809.79513809.795-13809.795-13809.795COS11-0.5-0.50.50.51-13809.795-13809.79513809.79513809.795SEN12-0.5-0.50.50.52-13809.795-13809.79513809.79513809.795

6CO,CA200.00500.00

E2.10E+06Kg/cmA3.720cmL538.52cm9103491034Angulo21.8090.860.34-0.86-0.34912505.6215002.248-12505.621-5002.248Radianes0K 6 =14506.5198183913100.340.14-0.34-0.14=105002.2482000.899-5002.248-2000.899COS13-0.86-0.340.860.343-12505.621-5002.24812505.6215002.248SEN04-0.34-0.140.340.144-5002.248-2000.8995002.2482000.899

7CO,CA200.00300.00

E2.10E+06Kg/cmA3.720cmL-360.56cm78127812Angulo146.3170.69-0.46-0.690.467-14999.9479999.96414999.947-9999.964Radianes3K 7 =-21666.58966455748-0.460.310.46-0.31=89999.964-6666.643-9999.9646666.643COS-11-0.690.460.69-0.46114999.947-9999.964-14999.9479999.964SEN120.46-0.31-0.460.312-9999.9646666.6439999.964-6666.643

8CO,CA1.00E-45200.00

E2.10E+06Kg/cmA9.810cmL200.00cm78347834Angulo0.0071.000.00-1.00-0.007103005.0000.000-103005.000-0.000Radianes0K 8 =10300580.000.00-0.00-0.00=80.0000.000-0.000-0.000COS13-1.00-0.001.000.003-103005.000-0.000103005.0000.000SEN04-0.00-0.000.000.004-0.000-0.0000.0000.000

12345678910149769.8490.038-1.000-0.0000.0000.000-0.6920.462-0.500-0.50020.0380.808-0.000-0.0000.0000.0000.462-0.308-0.500-0.5003-1.000-0.0003.472-0.143-0.6100.488-1.000-0.000-0.862-0.3454-0.000-0.000-0.1430.5280.488-0.390-0.000-0.000-0.345-0.13850.0000.000-0.6100.4881.610-0.488-1.000-0.0000.0000.00060.0000.0000.488-0.390-0.4880.390-0.000-0.0000.0000.0007-0.6920.462-1.000-0.000-1.000-0.0003.692-0.462-1.000-0.00080.462-0.308-0.000-0.000-0.000-0.000-0.462-0.462-0.000-0.0009-0.500-0.500-0.862-0.3450.0000.000-1.000-0.0002.3620.84510-0.500-0.500-0.345-0.1380.0000.000-0.000-0.0000.8450.638


10Kg2-2000Kg33000Kg40Kg50Kg60Kg


12345610.0000200927-0.00000095680.0000100463-0.0000251159-0-0.00003767382-0.00000095681.2380952837-0.00000047840.00000119600.00000179430.0000100463-0.00000047840.5000050232-1.2500125579-0-1.87501883694-0.00002511590.000001196-1.250012557910.3750313948011.93754709225-00-0011.256-0.00003767380.000001794-1.875018836911.93754709221.2518.4063206384


10.0320526226cm2-2476.1920025058cm31500.0160263113cm4-3750.0400657783cm5-0cm6-5625.0600986674cm

7-2642.90Kg8761.92Kg91238.08Kgreacciones101238.08Kg

2m3m2.5m2m15268734

e-armadura 2do examen

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