Rigidez e Inercia - x

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

1.- EJE XMURO X1

0.15 m2L = n*t = 0.61 m2

0.15 m2

FIG. INICIAL FIG. TRANSFORMADAFIG. b h AREA B(m) H(m) AREA

1 1.50 0.10 0.15 1.50 0.10 0.15 0.05 0.0075 0.75 0.1125 0 0 0.000125 0.000125 0 0 0.000125 0.000125

AT 0.15 AT 0.15 TOTAL 0.0075 TOTAL 0.1125 0.000125 0.000125

Ycg =ΣAi.Yi =

0.05ΣAi

Xcg =ΣAi.Xi =

0.75ΣAi

kg/cm²

F = A2/A1

(Yicg-Ycg)² (Xicg-Xcg)²Yicg Ai*Yicg Xicg Ai*Xicg Yi² Ai*Yi² Iix= ΣIix= Xi² Ai*Xi² Iiy= ΣIiy=

Ix(m4)= IY(m4)=

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X2

0.24 m2L = n*t = 0.61 m2

0.43 m2

t = 0.136t = 0.78

0.25L = 0.350.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.1000 0.0122 0.00282 1.38 0.15 0.21 1.38 0.15 0.21 0.08 0.02 0.8900 0.1842 0.0802

kg/cm²

F = A2/A1

(Yicg-Ycg)²Yicg Ai*Yicg Xicg Ai*Xicg Yi²

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.00 0.00 0.00 0.13 0.78 0.10 1.00 0.10 0.0650 0.0066 0.4120

AT 0.24 AT 0.4304 TOTAL 0.154 TOTAL 0.203

Ycg =ΣAi.Yi =

0.358ΣAi

Xcg =ΣAi.Xi =

0.4717ΣAi

0.0003 0.0038 0.0041 0.14 0.0169 0.0004 0.01730.0166 0.0004 0.0170 0.17 0.0362 0.0329 0.0691

(Xicg-Xcg)²Ai*Yi² Iix= ΣIix= Xi² Ai*Xi² Iiy= ΣIiy=

0.0418 0.0051 0.0469 0.17 0.0168 0.0001 0.0169

0.0680 0.1032Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X3

0.27 m2L = n*t = 0.61 m2

0.7504 m2

t = 0.136t = 0.78

0.25L = 0.680.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.00092 2.70 0.15 0.41 2.70 0.15 0.41 0.08 0.03 1.35 0.5468 0.0402

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.00124 0.00 0.00 0.00 0.780 0.130 0.10 1.00 0.10 0.07 0.0066 0.5248

AT = 0.47 AT = 0.75 TOTAL 0.207 TOTAL 0.578

Ycg =ΣAi.Yi =

0.276ΣAi

Xcg =ΣAi.Xi =

0.770ΣAi

0.0001 0.0038 0.0039 0.45 0.0548 0.0004 0.05520.0163 0.0008 0.0171 0.34 0.1363 0.2460 0.3823

0.0001 0.0038 0.0039 0.45 0.0548 0.0001 0.05490.0532 0.0051 0.0584 0.50 0.0504 0.0004 0.0508

0.0832 0.5432Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X4

0.35 m2L = n*t = 0.61 m2

0.48 m2

1 2.30 0.15 0.35 2.00 0.15 0.30 0.08 0.02 0.08 0.0225 0.012 0.00 0.00 0.00 0.15 0.61 0.09 0.31 0.03 1.08 0.0984 0.02

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.00 0.00 0.00 0.15 0.61 0.09 0.31 0.03 2.23 0.2040 0.02

AT = 0.35 AT = 0.48 TOTAL 0.078 TOTAL 0.325

Ycg =ΣAi.Yi =

0.162ΣAi

Xcg =ΣAi.Xi =

0.673ΣAi

0.002 0.0006 0.0028 0.36 0.1072 0.1000 0.20720.002 0.0028 0.0047 0.16 0.0148 0.0028 0.0176

0.002 0.0028 0.0047 2.43 0.2219 0.0028 0.2247

0.0122 0.4496Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X5

0.18 m2L = n*t = 0.61 m2

0.5779 m2

t = 0.136t = 0.78

0.25L = 0.680.78

1 1.22 0.15 0.18 1.22 0.15 0.18 0.61 0.11 0.08 0.0137 0.06252 0.00 0.00 0.00 1.07 0.15 0.16 0.08 0.01 0.69 0.1099 0.0812

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

AT = 0.18 AT = 0.34 TOTAL 0.124 TOTAL 0.124

Ycg =ΣAi.Yi =

0.360ΣAi

Xcg =ΣAi.Xi =

0.360ΣAi

0.0114 0.0227 0.0341 0.08 0.0149 0.0003 0.01520.0130 0.0003 0.0133 0.11 0.0170 0.0153 0.0323

0.0475 0.0475Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X6

0.53 m2L = n*t = 0.61 m2

0.82 m2

t = 0.136t = 0.78

0.25L = 0.620.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.01752 2.48 0.15 0.37 0.78 0.13 0.10 1.00 0.10 0.10 0.0101 0.3165

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.15 0.65 0.10 0.65 0.15 0.10 0.94 0.09 1.08 0.1048 0.25264 0.15 0.20 0.03 2.48 0.15 0.37 0.08 0.03 1.44 0.5357 0.13135 0.00 0.00 0.00 0.15 0.61 0.09 0.31 0.03 2.76 0.2525 0.01756 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 2.76 0.2799 0.3165

AT = 0.53 AT = 0.89 TOTAL 0.387 TOTAL 1.195

Ycg =ΣAi.Yi =

0.437ΣAi

Xcg =ΣAi.Xi =

1.349ΣAi

0.0021 0.0038 0.0059 1.56 0.1904 0.0004 0.19080.0321 0.0001 0.0322 1.56 0.1583 0.0051 0.1634

0.0246 0.0002 0.0248 0.08 0.0073 0.0034 0.01080.0489 0.0007 0.0496 0.01 0.0031 0.1907 0.19370.0016 0.0002 0.0018 1.99 0.1821 0.0028 0.18490.0321 0.0002 0.0323 1.99 0.2018 0.0059 0.2077

0.1466 0.9514Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X7

0.31 m2L = n*t = 0.61 m2

0.82 m2

t = 0.136t = 0.78

0.25L = 0.470.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.10672 1.88 0.15 0.28 0.78 0.13 0.10 1.00 0.10 0.10 0.0101 0.1357

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.00 0.00 0.00 1.88 0.15 0.28 0.54 0.15 1.04 0.2933 0.00934 0.00 0.00 0.00 0.78 0.13 0.10 0.93 0.09 2.15 0.2175 0.0861

AT = 0.31 AT = 0.61 TOTAL 0.383 TOTAL 0.533

Ycg =ΣAi.Yi =

0.632ΣAi

Xcg =ΣAi.Xi =

0.879ΣAi

0.0130 0.0038 0.0168 0.61 0.0740 0.0004 0.07440.0138 0.0001 0.0139 0.61 0.0615 0.0051 0.0666

0.0026 0.0005 0.0032 0.03 0.0073 0.0831 0.09040.0087 0.0001 0.0089 1.60 0.1626 0.0051 0.1678

0.0427 0.3991Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X8

0.48 m2L = n*t = 0.61 m2

0.87 m2

t = 0.136t = 0.78

0.25L = 0.700.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.07542 2.81 0.15 0.42 2.81 0.15 0.42 0.54 0.23 1.61 0.6765 0.0020

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 3.11 0.3794 0.07274 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 0.10 0.0101 0.17675 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 3.11 0.3154 0.1767

AT = 0.48 AT = 0.87 TOTAL 0.503 TOTAL 1.394

Ycg =ΣAi.Yi =

0.580ΣAi

Xcg =ΣAi.Xi =

1.605ΣAi

0.0092 0.0038 0.0130 2.27 0.2763 0.0004 0.27670.0008 0.0008 0.0016 0.00 0.0000 0.2774 0.2774

0.0089 0.0038 0.0127 2.27 0.2763 0.0004 0.27670.0179 0.0001 0.0181 2.27 0.2297 0.0051 0.23480.0179 0.0001 0.0181 2.27 0.2297 0.0051 0.2348

0.0634 1.3005Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X9

0.38 m2L = n*t = 0.61 m2

0.77 m2

t = 0.136t = 0.78

0.25L = 0.540.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.04632 2.16 0.15 0.32 2.16 0.15 0.32 0.38 0.12 1.28 0.4147 0.0196

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 3.36 0.4099 0.04424 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 0.10 0.0101 0.23025 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 3.36 0.3407 0.2302

AT = 0.38 AT = 0.77 TOTAL 0.401 TOTAL 1.188

Ycg =ΣAi.Yi =

0.520ΣAi

Xcg =ΣAi.Xi =

1.541ΣAi

0.0056 0.0038 0.0094 2.08 0.2533 0.0004 0.25370.0064 0.0006 0.0070 0.07 0.0220 0.1260 0.1480

0.0054 0.0038 0.0092 3.31 0.4037 0.0004 0.40410.0233 0.0001 0.0235 2.08 0.2105 0.0051 0.21570.0233 0.0001 0.0235 3.31 0.3356 0.0051 0.3407

0.0726 1.3622Ix(m4)= IY(m4)=

RIGIDEZ E INERCIA

Em = 500*f'm = 42500

G = 0.4*Em = 17000

= 4.7Em

MURO X10

0.44 m2L = n*t = 0.61 m2

0.82 m2

t = 0.136t = 0.78

0.25L = 0.630.78

1 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 0.10 0.0122 0.07682 2.50 0.15 0.38 2.50 0.15 0.38 0.54 0.20 1.45 0.5438 0.0022

kg/cm²

F = A2/A1

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

��= ℎ ³)/12+ (� � �� (�1�� - Ycg)2

��= ℎ ³)/12+ (� � �� (�1�� - xcg)2

3 0.20 0.15 0.03 0.20 0.61 0.12 0.31 0.04 2.80 0.3416 0.07414 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 0.10 0.0101 0.17465 0.00 0.00 0.00 0.78 0.13 0.10 1.00 0.10 2.80 0.2839 0.1746

AT = 0.44 AT = 0.82 TOTAL 0.478 TOTAL 1.192

Ycg =ΣAi.Yi =

0.582ΣAi

Xcg =ΣAi.Xi =

1.450ΣAi

0.0094 0.0038 0.0132 1.82 0.2223 0.0004 0.22280.0008 0.0007 0.0015 0.00 0.0000 0.1953 0.1953

0.0090 0.0038 0.0128 1.82 0.2223 0.0004 0.22280.0177 0.0001 0.0178 1.82 0.1848 0.0051 0.18990.0177 0.0001 0.0178 1.82 0.1848 0.0051 0.1899

0.0632 1.0207Ix(m4)= IY(m4)=

Rigidez e Inercia - x

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