Lab / Structural Workbench
Build a pin-jointed truss, solve member forces, and read the method-of-joints walkthrough.
Indeterminate (redundancy 2): m + r = 58 > 2j = 56. Method-of-joints alone cannot solve this — compatibility equations are required. Remove 2 redundant members or reactions for a hand-calc walkthrough. The matrix result above is still valid.
| Member | From | To | Section | A (mm^2) | L | EA/L | c vector |
|---|---|---|---|---|---|---|---|
| B1B2 | B1 | B2 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T1T2 | T1 | T2 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B2B3 | B2 | B3 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T2T3 | T2 | T3 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B3B4 | B3 | B4 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T3T4 | T3 | T4 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B4B5 | B4 | B5 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T4T5 | T4 | T5 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B5B6 | B5 | B6 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T5T6 | T5 | T6 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B6B7 | B6 | B7 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T6T7 | T6 | T7 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B7B8 | B7 | B8 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T7T8 | T7 | T8 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B8B9 | B8 | B9 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T8T9 | T8 | T9 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B9B10 | B9 | B10 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| T9T10 | T9 | T10 | IPE 160 | 2,010 | 4.031 | 104,710.12 | (0.992, 0.124) |
| B10B11 | B10 | B11 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| T10T11 | T10 | T11 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| B11B12 | B11 | B12 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| T11T12 | T11 | T12 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| B12B13 | B12 | B13 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| T12T13 | T12 | T13 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| B13B14 | B13 | B14 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| T13T14 | T13 | T14 | IPE 160 | 2,010 | 4 | 105,525 | (1, 0) |
| B1T1 | B1 | T1 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B2T2 | B2 | T2 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B3T3 | B3 | T3 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B4T4 | B4 | T4 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B5T5 | B5 | T5 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B6T6 | B6 | T6 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B7T7 | B7 | T7 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B8T8 | B8 | T8 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B9T9 | B9 | T9 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B10T10 | B10 | T10 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B11T11 | B11 | T11 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B12T12 | B12 | T12 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B13T13 | B13 | T13 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B14T14 | B14 | T14 | IPE 160 | 2,010 | 5 | 84,420 | (0, 1) |
| B1T2 | B1 | T2 | IPE 160 | 2,010 | 6.801 | 62,066.82 | (0.588, 0.809) |
| T2B3 | T2 | B3 | IPE 160 | 2,010 | 6.021 | 70,106.99 | (0.664, -0.747) |
| B3T4 | B3 | T4 | IPE 160 | 2,010 | 6.801 | 62,066.82 | (0.588, 0.809) |
| T4B5 | T4 | B5 | IPE 160 | 2,010 | 6.021 | 70,106.99 | (0.664, -0.747) |
| B5T6 | B5 | T6 | IPE 160 | 2,010 | 6.801 | 62,066.82 | (0.588, 0.809) |
| T6B7 | T6 | B7 | IPE 160 | 2,010 | 6.021 | 70,106.99 | (0.664, -0.747) |
| B7T8 | B7 | T8 | IPE 160 | 2,010 | 6.801 | 62,066.82 | (0.588, 0.809) |
| T8B9 | T8 | B9 | IPE 160 | 2,010 | 6.021 | 70,106.99 | (0.664, -0.747) |
| B9T10 | B9 | T10 | IPE 160 | 2,010 | 6.801 | 62,066.82 | (0.588, 0.809) |
| T10B11 | T10 | B11 | IPE 160 | 2,010 | 6.403 | 65,920.94 | (0.625, -0.781) |
| B11T12 | B11 | T12 | IPE 160 | 2,010 | 6.403 | 65,920.94 | (0.625, 0.781) |
| T12B13 | T12 | B13 | IPE 160 | 2,010 | 6.403 | 65,920.94 | (0.625, -0.781) |
| B13T14 | B13 | T14 | IPE 160 | 2,010 | 6.403 | 65,920.94 | (0.625, 0.781) |
Assemble every member into the global matrix, remove fixed DOFs, and solve the reduced system. The matrix preview is truncated so the page stays readable.
| Kff | B2.x | B2.y | B3.x | B3.y | B4.x | B4.y | B5.x | B5.y | B6.x | B6.y |
|---|---|---|---|---|---|---|---|---|---|---|
| B2.x | 206,198.4 | 25,774.8 | -103,099.2 | -12,887.4 | 0 | 0 | 0 | 0 | 0 | 0 |
| B2.y | 25,774.8 | 87,641.85 | -12,887.4 | -1,610.92 | 0 | 0 | 0 | 0 | 0 | 0 |
| B3.x | -103,099.2 | -12,887.4 | 258,613.94 | 20,486.73 | -103,099.2 | -12,887.4 | 0 | 0 | 0 | 0 |
| B3.y | -12,887.4 | -1,610.92 | 20,486.73 | 167,400.12 | -12,887.4 | -1,610.92 | 0 | 0 | 0 | 0 |
| B4.x | 0 | 0 | -103,099.2 | -12,887.4 | 206,198.4 | 25,774.8 | -103,099.2 | -12,887.4 | 0 | 0 |
| B4.y | 0 | 0 | -12,887.4 | -1,610.92 | 25,774.8 | 87,641.85 | -12,887.4 | -1,610.92 | 0 | 0 |
| B5.x | 0 | 0 | 0 | 0 | -103,099.2 | -12,887.4 | 258,613.94 | 20,486.73 | -103,099.2 | -12,887.4 |
| B5.y | 0 | 0 | 0 | 0 | -12,887.4 | -1,610.92 | 20,486.73 | 167,400.12 | -12,887.4 | -1,610.92 |
| B6.x | 0 | 0 | 0 | 0 | 0 | 0 | -103,099.2 | -12,887.4 | 206,198.4 | 25,774.8 |
| B6.y | 0 | 0 | 0 | 0 | 0 | 0 | -12,887.4 | -1,610.92 | 25,774.8 | 87,641.85 |
Kff size: 51 x 51.
| DOF | Load | Displacement |
|---|---|---|
| B2.x | 0 | 0 |
| B2.y | 0 | 0 |
| B3.x | 0 | 0 |
| B3.y | 0 | 0 |
| B4.x | 0 | 0 |
| B4.y | 0 | 0 |
| B5.x | 0 | 0 |
| B5.y | 0 | 0 |
| B6.x | 0 | 0 |
| B6.y | 0 | 0 |
| B7.x | 0 | 0 |
| B7.y | 0 | 0 |
| B8.x | 0 | 0 |
| B8.y | 0 | 0 |
| B9.x | 0 | 0 |
| B9.y | 0 | 0 |
| B10.x | 0 | 0 |
| B11.x | 0 | 0 |
| B11.y | 0 | 0 |
| B12.x | 0 | 0 |
| B12.y | 0 | 0 |
| B13.x | 0 | 0 |
| B13.y | 0 | 0 |
| T1.x | 0 | 0 |
| T1.y | 0 | 0 |
| T2.x | 0 | 0 |
| T2.y | 0 | 0 |
| T3.x | 0 | 0 |
| T3.y | 0 | 0 |
| T4.x | 0 | 0 |
| T4.y | 0 | 0 |
| T5.x | 0 | 0 |
| T5.y | 0 | 0 |
| T6.x | 0 | 0 |
| T6.y | 0 | 0 |
| T7.x | 0 | 0 |
| T7.y | 0 | 0 |
| T8.x | 0 | 0 |
| T8.y | 0 | 0 |
| T9.x | 0 | 0 |
| T9.y | 0 | 0 |
| T10.x | 0 | 0 |
| T10.y | 0 | 0 |
| T11.x | 0 | 0 |
| T11.y | 0 | 0 |
| T12.x | 0 | 0 |
| T12.y | 0 | 0 |
| T13.x | 0 | 0 |
| T13.y | 0 | 0 |
| T14.x | 0 | 0 |
| T14.y | 0 | 0 |
| DOF | Applied load | Reaction |
|---|---|---|
| B1.x | 0 | 0 |
| B1.y | 0 | 0 |
| B10.y | 0 | 0 |
| B14.x | 0 | 0 |
| B14.y | 0 | 0 |
| Member | Calculation | Force | Sense |
|---|---|---|---|
| B1B2 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T1T2 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B2B3 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T2T3 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B3B4 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T3T4 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B4B5 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T4T5 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B5B6 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T5T6 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B6B7 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T6T7 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B7B8 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T7T8 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B8B9 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T8T9 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B9B10 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| T9T10 | N = 104,710.12 · c · (uB - uA) | 0 kN | zero |
| B10B11 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| T10T11 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| B11B12 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| T11T12 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| B12B13 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| T12T13 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| B13B14 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| T13T14 | N = 105,525 · c · (uB - uA) | 0 kN | zero |
| B1T1 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B2T2 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B3T3 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B4T4 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B5T5 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B6T6 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B7T7 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B8T8 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B9T9 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B10T10 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B11T11 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B12T12 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B13T13 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B14T14 | N = 84,420 · c · (uB - uA) | 0 kN | zero |
| B1T2 | N = 62,066.82 · c · (uB - uA) | 0 kN | zero |
| T2B3 | N = 70,106.99 · c · (uB - uA) | 0 kN | zero |
| B3T4 | N = 62,066.82 · c · (uB - uA) | 0 kN | zero |
| T4B5 | N = 70,106.99 · c · (uB - uA) | 0 kN | zero |
| B5T6 | N = 62,066.82 · c · (uB - uA) | 0 kN | zero |
| T6B7 | N = 70,106.99 · c · (uB - uA) | 0 kN | zero |
| B7T8 | N = 62,066.82 · c · (uB - uA) | 0 kN | zero |
| T8B9 | N = 70,106.99 · c · (uB - uA) | 0 kN | zero |
| B9T10 | N = 62,066.82 · c · (uB - uA) | 0 kN | zero |
| T10B11 | N = 65,920.94 · c · (uB - uA) | 0 kN | zero |
| B11T12 | N = 65,920.94 · c · (uB - uA) | 0 kN | zero |
| T12B13 | N = 65,920.94 · c · (uB - uA) | 0 kN | zero |
| B13T14 | N = 65,920.94 · c · (uB - uA) | 0 kN | zero |