Dados:α1 0.84307 β1α2 -0.59307 β2

Pcr1 0.62772 0.31386 kNPcr2 6.37228 3.18614 kN

C 0.5 kNmL 1 m

αo 1 0.017453 2 0.034907 3 0.05236 -1 -0.017453 -21 0.017453 2 0.034907 3 0.05236 -1 -0.017453 -2

β [rad] P [kN] β [rad] P [kN] β [rad] P [kN] β [rad] P [kN] β [rad]

-3.0 0.317309 -3.0 0.32076 -3.0 0.32421 -3.0 0.310409 -3.0-2.8 0.317556 -2.8 0.321252 -2.8 0.324949 -2.8 0.310162 -2.8-2.6 0.31784 -2.6 0.321821 -2.6 0.325802 -2.6 0.309878 -2.6-2.4 0.318172 -2.4 0.322485 -2.4 0.326798 -2.4 0.309546 -2.4-2.2 0.318564 -2.2 0.323269 -2.2 0.327974 -2.2 0.309154 -2.2-2.0 0.319034 -2.0 0.32421 -2.0 0.329385 -2.0 0.308683 -2.0-1.8 0.319609 -1.8 0.32536 -1.8 0.331111 -1.8 0.308108 -1.8-1.6 0.320328 -1.6 0.326798 -1.6 0.333267 -1.6 0.307389 -1.6-1.4 0.321252 -1.4 0.328646 -1.4 0.33604 -1.4 0.306465 -1.4-1.2 0.322485 -1.2 0.331111 -1.2 0.339736 -1.2 0.305233 -1.2-1.0 0.32421 -1.0 0.334561 -1.0 0.344912 -1.0 0.303508 -1.0-0.8 0.326798 -0.8 0.339736 -0.8 0.352675 -0.8 0.30092 -0.8-0.6 0.331111 -0.6 0.348362 -0.6 0.365614 -0.6 0.296607 -0.6-0.4 0.339736 -0.4 0.365614 -0.4 0.391492 -0.4 0.287981 -0.4-0.2 0.365614 -0.2 0.417369 -0.2 0.469124 -0.2 0.262104 -0.2-0.1 0.382866 -0.1 0.451873 -0.1 0.52088 -0.1 0.244852 -0.1-0.1 0.417369 -0.1 0.52088 -0.1 0.62439 -0.1 0.210349 -0.10.0 0.52088 0.0 0.7279 0.0 0.934921 0.0 0.106838 0.0

0.1 0.106838 0.1 -0.100182 0.1 -0.307203 0.1 0.52088 0.10.1 0.210349 0.1 0.106838 0.1 0.003328 0.1 0.417369 0.10.2 0.244852 0.2 0.175845 0.2 0.106838 0.2 0.382866 0.20.2 0.262104 0.2 0.210349 0.2 0.158593 0.2 0.365614 0.20.4 0.287981 0.4 0.262104 0.4 0.236226 0.4 0.339736 0.40.6 0.296607 0.6 0.279355 0.6 0.262104 0.6 0.331111 0.60.8 0.30092 0.8 0.287981 0.8 0.275042 0.8 0.326798 0.81.0 0.303508 1.0 0.293157 1.0 0.282806 1.0 0.32421 1.01.2 0.305233 1.2 0.296607 1.2 0.287981 1.2 0.322485 1.21.4 0.306465 1.4 0.299072 1.4 0.291678 1.4 0.321252 1.41.6 0.307389 1.6 0.30092 1.6 0.294451 1.6 0.320328 1.61.8 0.308108 1.8 0.302358 1.8 0.296607 1.8 0.319609 1.82.0 0.308683 2.0 0.303508 2.0 0.298332 2.0 0.319034 2.02.2 0.309154 2.2 0.304449 2.2 0.299744 2.2 0.318564 2.22.4 0.309546 2.4 0.305233 2.4 0.30092 2.4 0.318172 2.4

βo

Tabela N°01: Caminho não linear de equilibrio quando a imperfeição tem a forma do primeiro modo de flambagem.

2.6 0.309878 2.6 0.305897 2.6 0.301915 2.6 0.31784 2.62.8 0.310162 2.8 0.306465 2.8 0.302768 2.8 0.317556 2.83.0 0.310409 3.0 0.306958 3.0 0.303508 3.0 0.317309 3.0

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

-0.034907 -3 -0.05236 αo 1 0.017453 2 0.034907 3 0.05236-0.034907 -3 -0.05236 1 0.017453 2 0.034907 3 0.05236

P [kN] β [rad] P [kN] β [rad] P [kN] β [rad] P [kN] β [rad] P [kN]

0.306958 -3.0 0.303508 -3.0 3.181237 -3.0 3.176332 -3.0 3.1714270.306465 -2.8 0.302768 -2.8 3.180886 -2.8 3.175631 -2.8 3.1703760.305897 -2.6 0.301915 -2.6 3.180482 -2.6 3.174823 -2.6 3.1691630.305233 -2.4 0.30092 -2.4 3.180011 -2.4 3.17388 -2.4 3.1677490.304449 -2.2 0.299744 -2.2 3.179453 -2.2 3.172765 -2.2 3.1660770.303508 -2.0 0.298332 -2.0 3.178784 -2.0 3.171427 -2.0 3.164070.302358 -1.8 0.296607 -1.8 3.177967 -1.8 3.169792 -1.8 3.1616180.30092 -1.6 0.294451 -1.6 3.176945 -1.6 3.167749 -1.6 3.158552

0.299072 -1.4 0.291678 -1.4 3.175631 -1.4 3.165121 -1.4 3.1546110.296607 -1.2 0.287981 -1.2 3.17388 -1.2 3.161618 -1.2 3.1493560.293157 -1.0 0.282806 -1.0 3.171427 -1.0 3.156713 -1.0 3.1419990.287981 -0.8 0.275042 -0.8 3.167749 -0.8 3.149356 -0.8 3.1309630.279355 -0.6 0.262104 -0.6 3.161618 -0.6 3.137094 -0.6 3.112570.262104 -0.4 0.236226 -0.4 3.149356 -0.4 3.11257 -0.4 3.0757840.210349 -0.2 0.158593 -0.2 3.11257 -0.2 3.038998 -0.2 2.9654260.175845 -0.1 0.106838 -0.1 3.088046 -0.1 2.98995 -0.1 2.8918540.106838 -0.1 0.003328 -0.1 3.038998 -0.1 2.891854 -0.1 2.744711-0.100182 0.0 -0.307203 0.0 2.891854 0.0 2.597567 0.0 2.30328

0.7279 0.1 0.934921 0.1 3.480429 0.1 3.774716 0.1 4.0690030.52088 0.1 0.62439 0.1 3.333285 0.1 3.480429 0.1 3.627572

0.451873 0.2 0.52088 0.2 3.284237 0.2 3.382333 0.2 3.4804290.417369 0.2 0.469124 0.2 3.259713 0.2 3.333285 0.2 3.4068570.365614 0.4 0.391492 0.4 3.222928 0.4 3.259713 0.4 3.2964990.348362 0.6 0.365614 0.6 3.210666 0.6 3.235189 0.6 3.2597130.339736 0.8 0.352675 0.8 3.204535 0.8 3.222928 0.8 3.241320.334561 1.0 0.344912 1.0 3.200856 1.0 3.21557 1.0 3.2302850.331111 1.2 0.339736 1.2 3.198404 1.2 3.210666 1.2 3.2229280.328646 1.4 0.33604 1.4 3.196652 1.4 3.207162 1.4 3.2176720.326798 1.6 0.333267 1.6 3.195338 1.6 3.204535 1.6 3.2137310.32536 1.8 0.331111 1.8 3.194316 1.8 3.202491 1.8 3.2106660.32421 2.0 0.329385 2.0 3.193499 2.0 3.200856 2.0 3.208213

0.323269 2.2 0.327974 2.2 3.19283 2.2 3.199518 2.2 3.2062070.322485 2.4 0.326798 2.4 3.192273 2.4 3.198404 2.4 3.204535

βo

Caminho não linear de equilibrio quando a imperfeição tem a forma do primeiro modo de flambagem. Tabela N°02: Caminho não linear de equilibrio quando a imperfeição tem a forma do segndo modo de flambagem.

0.321821 2.6 0.325802 2.6 3.191801 2.6 3.19746 2.6 3.203120.321252 2.8 0.324949 2.8 3.191397 2.8 3.196652 2.8 3.2019070.32076 3.0 0.32421 3.0 3.191046 3.0 3.195951 3.0 3.200856

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

-4 -3 -2 -1 0 1 2 3 4CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

αo=βo=-1°αo=βo=-2°αo=βo=-3°

αo=βo=1°

-1 -0.017453 -2 -0.034907 -3 -0.05236 αo=βo=2°-1 -0.017453 -2 -0.034907 -3 -0.05236 αo=βo=3°

β [rad] P [kN] β [rad] P [kN] β [rad] P [kN]

-3.0 3.191046 -3.0 3.195951 -3.0 3.200856-2.8 3.191397 -2.8 3.196652 -2.8 3.201907-2.6 3.191801 -2.6 3.19746 -2.6 3.20312-2.4 3.192273 -2.4 3.198404 -2.4 3.204535-2.2 3.19283 -2.2 3.199518 -2.2 3.206207-2.0 3.193499 -2.0 3.200856 -2.0 3.208213-1.8 3.194316 -1.8 3.202491 -1.8 3.210666-1.6 3.195338 -1.6 3.204535 -1.6 3.213731-1.4 3.196652 -1.4 3.207162 -1.4 3.217672-1.2 3.198404 -1.2 3.210666 -1.2 3.222928-1.0 3.200856 -1.0 3.21557 -1.0 3.230285-0.8 3.204535 -0.8 3.222928 -0.8 3.24132-0.6 3.210666 -0.6 3.235189 -0.6 3.259713-0.4 3.222928 -0.4 3.259713 -0.4 3.296499-0.2 3.259713 -0.2 3.333285 -0.2 3.406857-0.1 3.284237 -0.1 3.382333 -0.1 3.480429-0.1 3.333285 -0.1 3.480429 -0.1 3.6275720.0 3.480429 0.0 3.774716 0.0 4.069003

0.1 2.891854 0.1 2.597567 0.1 2.303280.1 3.038998 0.1 2.891854 0.1 2.7447110.2 3.088046 0.2 2.98995 0.2 2.8918540.2 3.11257 0.2 3.038998 0.2 2.9654260.4 3.149356 0.4 3.11257 0.4 3.0757840.6 3.161618 0.6 3.137094 0.6 3.112570.8 3.167749 0.8 3.149356 0.8 3.1309631.0 3.171427 1.0 3.156713 1.0 3.1419991.2 3.17388 1.2 3.161618 1.2 3.1493561.4 3.175631 1.4 3.165121 1.4 3.1546111.6 3.176945 1.6 3.167749 1.6 3.1585521.8 3.177967 1.8 3.169792 1.8 3.1616182.0 3.178784 2.0 3.171427 2.0 3.164072.2 3.179453 2.2 3.172765 2.2 3.1660772.4 3.180011 2.4 3.17388 2.4 3.167749

Caminho não linear de equilibrio quando a imperfeição tem a forma do segndo modo de flambagem.

2.6 3.180482 2.6 3.174823 2.6 3.1691632.8 3.180886 2.8 3.175631 2.8 3.1703763.0 3.181237 3.0 3.176332 3.0 3.171427

-4 -3 -2 -1 0 1 2 3 4CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

Dados:α1 0.84307 β1α2 -0.59307 β2

Pcr1 0.62772 0.31386 kNPcr2 6.37228 3.18614 kN

C 0.5 kNmL 1 m

αo 1 0.017453 2 0.034907 3 0.05236 -1 -0.017453 -21 0.017453 2 0.034907 3 0.05236 -1 -0.017453 -2

β P β P β P β P β

-3 0.317309 -3 0.32076 -3 0.32421 -3 0.310409 -3-2.8 0.317556 -2.8 0.321252 -2.8 0.324949 -2.8 0.310162 -2.8-2.6 0.31784 -2.6 0.321821 -2.6 0.325802 -2.6 0.309878 -2.6-2.4 0.318172 -2.4 0.322485 -2.4 0.326798 -2.4 0.309546 -2.4-2.2 0.318564 -2.2 0.323269 -2.2 0.327974 -2.2 0.309154 -2.2-2 0.319034 -2 0.32421 -2 0.329385 -2 0.308683 -2

-1.8 0.319609 -1.8 0.32536 -1.8 0.331111 -1.8 0.308108 -1.8-1.6 0.320328 -1.6 0.326798 -1.6 0.333267 -1.6 0.307389 -1.6-1.4 0.321252 -1.4 0.328646 -1.4 0.33604 -1.4 0.306465 -1.4-1.2 0.322485 -1.2 0.331111 -1.2 0.339736 -1.2 0.305233 -1.2-1 0.32421 -1 0.334561 -1 0.344912 -1 0.303508 -1

-0.8 0.326798 -0.8 0.339736 -0.8 0.352675 -0.8 0.30092 -0.8-0.6 0.331111 -0.6 0.348362 -0.6 0.365614 -0.6 0.296607 -0.6-0.4 0.339736 -0.4 0.365614 -0.4 0.391492 -0.4 0.287981 -0.4-0.2 0.365614 -0.2 0.417369 -0.2 0.469124 -0.2 0.262104 -0.2

-0.15 0.382866 -0.15 0.451873 -0.15 0.52088 -0.15 0.244852 -0.15-0.1 0.417369 -0.1 0.52088 -0.1 0.62439 -0.1 0.210349 -0.1

-0.05 0.52088 -0.05 0.7279 -0.05 0.934921 -0.05 0.106838 -0.05

0.05 0.106838 0.05 -0.100182 0.05 -0.307203 0.05 0.52088 0.050.1 0.210349 0.1 0.106838 0.1 0.003328 0.1 0.417369 0.1

0.15 0.244852 0.15 0.175845 0.15 0.106838 0.15 0.382866 0.150.2 0.262104 0.2 0.210349 0.2 0.158593 0.2 0.365614 0.20.4 0.287981 0.4 0.262104 0.4 0.236226 0.4 0.339736 0.40.6 0.296607 0.6 0.279355 0.6 0.262104 0.6 0.331111 0.60.8 0.30092 0.8 0.287981 0.8 0.275042 0.8 0.326798 0.81 0.303508 1 0.293157 1 0.282806 1 0.32421 1

1.2 0.305233 1.2 0.296607 1.2 0.287981 1.2 0.322485 1.21.4 0.306465 1.4 0.299072 1.4 0.291678 1.4 0.321252 1.41.6 0.307389 1.6 0.30092 1.6 0.294451 1.6 0.320328 1.61.8 0.308108 1.8 0.302358 1.8 0.296607 1.8 0.319609 1.82 0.308683 2 0.303508 2 0.298332 2 0.319034 2

2.2 0.309154 2.2 0.304449 2.2 0.299744 2.2 0.318564 2.22.4 0.309546 2.4 0.305233 2.4 0.30092 2.4 0.318172 2.4

βo

Tabela N°01: Caminho não linear de equilibrio quando a imperfeição tem a forma do primeiro modo de flambagem.

2.6 0.309878 2.6 0.305897 2.6 0.301915 2.6 0.31784 2.62.8 0.310162 2.8 0.306465 2.8 0.302768 2.8 0.317556 2.83 0.310409 3 0.306958 3 0.303508 3 0.317309 3

-3 3.181237 -3 3.176332 -3 3.171427 -3 3.191046 -3-2.8 3.180886 -2.8 3.175631 -2.8 3.170376 -2.8 3.191397 -2.8-2.6 3.180482 -2.6 3.174823 -2.6 3.169163 -2.6 3.191801 -2.6-2.4 3.180011 -2.4 3.17388 -2.4 3.167749 -2.4 3.192273 -2.4-2.2 3.179453 -2.2 3.172765 -2.2 3.166077 -2.2 3.19283 -2.2-2 3.178784 -2 3.171427 -2 3.16407 -2 3.193499 -2

-1.8 3.177967 -1.8 3.169792 -1.8 3.161618 -1.8 3.194316 -1.8-1.6 3.176945 -1.6 3.167749 -1.6 3.158552 -1.6 3.195338 -1.6-1.4 3.175631 -1.4 3.165121 -1.4 3.154611 -1.4 3.196652 -1.4-1.2 3.17388 -1.2 3.161618 -1.2 3.149356 -1.2 3.198404 -1.2-1 3.171427 -1 3.156713 -1 3.141999 -1 3.200856 -1

-0.8 3.167749 -0.8 3.149356 -0.8 3.130963 -0.8 3.204535 -0.8-0.6 3.161618 -0.6 3.137094 -0.6 3.11257 -0.6 3.210666 -0.6-0.4 3.149356 -0.4 3.11257 -0.4 3.075784 -0.4 3.222928 -0.4-0.2 3.11257 -0.2 3.038998 -0.2 2.965426 -0.2 3.259713 -0.2

-0.15 3.088046 -0.15 2.98995 -0.15 2.891854 -0.15 3.284237 -0.15-0.1 3.038998 -0.1 2.891854 -0.1 2.744711 -0.1 3.333285 -0.1

-0.05 2.891854 -0.05 2.597567 -0.05 2.30328 -0.05 3.480429 -0.05

0.05 3.480429 0.05 3.774716 0.05 4.069003 0.05 2.891854 0.050.1 3.333285 0.1 3.480429 0.1 3.627572 0.1 3.038998 0.1

0.15 3.284237 0.15 3.382333 0.15 3.480429 0.15 3.088046 0.150.2 3.259713 0.2 3.333285 0.2 3.406857 0.2 3.11257 0.20.4 3.222928 0.4 3.259713 0.4 3.296499 0.4 3.149356 0.40.6 3.210666 0.6 3.235189 0.6 3.259713 0.6 3.161618 0.60.8 3.204535 0.8 3.222928 0.8 3.24132 0.8 3.167749 0.81 3.200856 1 3.21557 1 3.230285 1 3.171427 1

1.2 3.198404 1.2 3.210666 1.2 3.222928 1.2 3.17388 1.21.4 3.196652 1.4 3.207162 1.4 3.217672 1.4 3.175631 1.41.6 3.195338 1.6 3.204535 1.6 3.213731 1.6 3.176945 1.61.8 3.194316 1.8 3.202491 1.8 3.210666 1.8 3.177967 1.82 3.193499 2 3.200856 2 3.208213 2 3.178784 2

2.2 3.19283 2.2 3.199518 2.2 3.206207 2.2 3.179453 2.22.4 3.192273 2.4 3.198404 2.4 3.204535 2.4 3.180011 2.42.6 3.191801 2.6 3.19746 2.6 3.20312 2.6 3.180482 2.62.8 3.191397 2.8 3.196652 2.8 3.201907 2.8 3.180886 2.83 3.191046 3 3.195951 3 3.200856 3 3.181237 3

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

-0.034907 -3 -0.05236 αo 1 0.017453 2 0.034907 3 0.05236-0.034907 -3 -0.05236 1 0.017453 2 0.034907 3 0.05236

P β P β P β P β P

0.306958 -3 0.3035080.306465 -2.8 0.3027680.305897 -2.6 0.3019150.305233 -2.4 0.300920.304449 -2.2 0.2997440.303508 -2 0.2983320.302358 -1.8 0.2966070.30092 -1.6 0.294451

0.299072 -1.4 0.2916780.296607 -1.2 0.2879810.293157 -1 0.2828060.287981 -0.8 0.2750420.279355 -0.6 0.2621040.262104 -0.4 0.2362260.210349 -0.2 0.1585930.175845 -0.15 0.1068380.106838 -0.1 0.003328-0.100182 -0.05 -0.307203

0.7279 0.05 0.9349210.52088 0.1 0.62439

0.451873 0.15 0.520880.417369 0.2 0.4691240.365614 0.4 0.3914920.348362 0.6 0.3656140.339736 0.8 0.3526750.334561 1 0.3449120.331111 1.2 0.3397360.328646 1.4 0.336040.326798 1.6 0.3332670.32536 1.8 0.3311110.32421 2 0.329385

0.323269 2.2 0.3279740.322485 2.4 0.326798

βo

Caminho não linear de equilibrio quando a imperfeição tem a forma do primeiro modo de flambagem. Tabela N°02: Caminho não linear de equilibrio quando a imperfeição tem a forma do segndo modo de flambagem.

0.321821 2.6 0.3258020.321252 2.8 0.3249490.32076 3 0.32421

3.195951 -3 3.2008563.196652 -2.8 3.2019073.19746 -2.6 3.20312

3.198404 -2.4 3.2045353.199518 -2.2 3.2062073.200856 -2 3.2082133.202491 -1.8 3.2106663.204535 -1.6 3.2137313.207162 -1.4 3.2176723.210666 -1.2 3.2229283.21557 -1 3.230285

3.222928 -0.8 3.241323.235189 -0.6 3.2597133.259713 -0.4 3.2964993.333285 -0.2 3.4068573.382333 -0.15 3.4804293.480429 -0.1 3.6275723.774716 -0.05 4.069003

2.597567 0.05 2.303282.891854 0.1 2.7447112.98995 0.15 2.891854

3.038998 0.2 2.9654263.11257 0.4 3.075784

3.137094 0.6 3.112573.149356 0.8 3.1309633.156713 1 3.1419993.161618 1.2 3.1493563.165121 1.4 3.1546113.167749 1.6 3.1585523.169792 1.8 3.1616183.171427 2 3.164073.172765 2.2 3.1660773.17388 2.4 3.167749

3.174823 2.6 3.1691633.175631 2.8 3.1703763.176332 3 3.171427

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

-4 -3 -2 -1 0 1 2 3 4

CE6605660al

CE6605660al

CE6605660al

αo=βo=1° αo=βo=2° αo=βo=3° αo=βo=-1° αo=βo=-2° αo=βo=-3°

COORDENADA GENERALIZADA β[rad]

CARG

A [k

N]

αo=βo=-1°αo=βo=-2°αo=βo=-3°

αo=βo=1°

-1 -0.017453 -2 -0.034907 -3 -0.05236 αo=βo=2°-1 -0.017453 -2 -0.034907 -3 -0.05236 αo=βo=3°

β P β P β P

Caminho não linear de equilibrio quando a imperfeição tem a forma do segndo modo de flambagem.