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1d truss - 5 elements and 5 nodes

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Solution of a linear truss structure made of 5 bars and 5 nodes Applied Load (F) 1.00E+04 N Bar 01 Bar 02 Bar 03 Bar 04 D1 10 mm D2 12 mm D3 15 mm D4 L1 2 m L2 2 m L3 3 m L4 E1 2.50E+09 Pa E2 2.50E+09 Pa E3 2.50E+09 Pa E4 2.50E+ A1 7.854E-05m2 A2 1.131E-04m2 A3 1.767E-04m2 A4 1.767E- K1 9.82E+04 K2 1.41E+05 K3 1.47E+05 K4 1.47E+ Element Stifness Matrix Element Stifness Matrix Element Stifness Matrix Element Stifness Matrix 9.82E+04 -9.82E+04 1.41E+05 -1.41E+05 1.47E+05 -1.47E+05 1.47E+05 -1.47E+ -9.82E+04 9.82E+04 -1.41E+05 1.41E+05 -1.47E+05 1.47E+05 -1.47E+05 1.47E+ Connectivities bar01 Connectivities bar03 Connectivities bar03 Connectivities bar04 Node 1 1 Node 1 2 Node 1 3 Node 1 Node 2 3 Node 2 3 Node 2 4 Node 2 Bar 01 in global stifness matrix Bar02 in global stifness matrix Bar 03 in global stifness matrix Bar 04 in global stifnes 98174.7704247 0 -98174.7704247 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 141371.669 -141371.67 0 0 0 0 0 0 0 0 -98174.7704247 0 98174.7704247 0 0 0 -141371.669 141371.669 0 0 0 0 147262.2 -147262.16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -147262 147262.156 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Final problem R1 98174.7704247 0 -98174.77 0 0 0 R2 0 141371.669 -141371.67 0 0 0 0 = -98174.7704247 -141371.67 534070.751 -294524.31 0 * u3 0 0 0 -294524.31 441786.467 -147262.16 u4 1.00E+04 0 0 0 -147262.16 147262.156 u5 Linear system to be solved a!ter a""lying bo#ndar conditons$ 0 534070.751 -294524.31 0 u3 0 = -294524.31 441786.467 -147262.16 * u4 10000 0 -147262.16 147262.156 u5 Sol#tion o! t%e linear system 4.1745559E-006 4.175E-006 4.1745559E-006 0 0.04174556 4.1745559E-006 7.570E-006 7.5698613E-006 * 0 = 7.57E-02 4.1745559E-006 7.570E-006 1.4360472E-005 10000 1.44E-01 Calc#latoin o! &nal de!ormation u3 0.042 m u4 0.076 m u5 0.144 m Validation of the results -4.10E+03 98174.7704247 0 -98174.77 0 0 0.000 -5.90E+03 0 141371.669 -141371.67 0 0 0.000 0.00E+00 = -98174.7704247 -141371.67 534070.751 -294524.31 0 * 0.042 0.00E+00 0 0 -294524.31 441786.467 -147262.16 0.076 1.00E+04 0 0 0 -147262.16 147262.156 0.144 Strains and stresses e1 2.087E-02 s1 52.18 Pa e2 2.087E-02 s2 52.18 Pa e3 1.132E-02 s3 28.29 Pa e4 1.132E-02 s4 28.29 Pa e5 2.264E-02 s4 56.59 Pa

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5elems&5nodesSolution of a linear truss structuremade of 5 bars and 5 nodesApplied Load (F)1.00E+04NBar 01Bar 02Bar 03Bar 04Bar 05D110mmD212mmD315mmD415mmD515mmL12mL22mL33mL43mL53mE12.50E+09PaE22.50E+09PaE32.50E+09PaE42.50E+09PaE52.50E+09PaA17.854E-05m2A21.131E-04m2A31.767E-04m2A41.767E-04m2A51.767E-04m2K19.82E+04K21.41E+05K31.47E+05K41.47E+05K51.47E+05Element Stiffness MatrixElement Stiffness MatrixElement Stiffness MatrixElement Stiffness MatrixElement Stiffness Matrix9.82E+04-9.82E+041.41E+05-1.41E+051.47E+05-1.47E+051.47E+05-1.47E+051.47E+05-1.47E+05-9.82E+049.82E+04-1.41E+051.41E+05-1.47E+051.47E+05-1.47E+051.47E+05-1.47E+051.47E+05Connectivities bar 01Connectivities bar 03Connectivities bar 03Connectivities bar 04Connectivities bar 05Node 11Node 12Node 13Node 13Node 14Node 23Node 23Node 24Node 24Node 25Bar 01 in global stiffness matrixBar 02 in global stiffness matrixBar 03 in global stiffness matrixBar 04 in global stiffness matrixBar 05 in global stiffness matrix98174.7704246810-98174.7704246810000000000000000000000000000141371.669411541-141371.66941154100000000000000000-98174.770424681098174.770424681000-141371.669411541141371.6694115410000147262.155637022-147262.155637022000147262.155637022-147262.155637022000000000000000000-147262.155637022147262.155637022000-147262.155637022147262.1556370220000147262.155637022-147262.15563702200000000000000000000000-147262.155637022147262.155637022Final problemR198174.7704246810-98174.770424681000R20141371.669411541-141371.6694115410000=-98174.770424681-141371.669411541534070.751110265-294524.3112740430*u3000-294524.311274043441786.466911065-147262.155637022u41.00E+04000-147262.155637022147262.155637022u5Linear system to be solved (after applying boundar conditons)0534070.751110265-294524.3112740430u30=-294524.311274043441786.466911065-147262.155637022*u4100000-147262.155637022147262.155637022u5Solution of the linear system0.00000417460.00000417460.000004174600.04174555880.00000417460.00000756990.0000075699*0=7.57E-020.00000417460.00000756990.0000143605100001.44E-01Calculatoin of final deformationu30.042mu40.076mu50.144mValidation of the results-4.10E+0398174.7704246810-98174.770424681000.000-5.90E+030141371.669411541-141371.669411541000.0003.64E-12=-98174.770424681-141371.669411541534070.751110265-294524.3112740430*0.0420.00E+0000-294524.311274043441786.466911065-147262.1556370220.0761.00E+04000-147262.155637022147262.1556370220.144Strains and stressese12.087E-02s152.18MPae22.087E-02s252.18MPae31.132E-02s328.29MPae41.132E-02s428.29MPae52.264E-02s456.59MPa

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