E.9 Truss and Cable Elements
E.9.1 Plane Truss
For the planar truss shown in the figure, analyses were performed for the cases of a concentrated load, self-weight, and frequency analysis.
Figure E.9.1 Plane Truss Model
The solutions for the cases with a concentrated load and self-weight are shown in the figure, and the results of the frequency analysis are as follows.
Table E.9.1 Analysis Results
| MODE | Natural frequencies (Hz) | Remark | |
|---|---|---|---|
| CONSISTENT | LUMPED | ||
| 1 | 1.29239 | 1.25464 | |
| 2 | 1.91065 | 1.86042 | |
| 3 | 3.42578 | 2.99587 | |
| 4 | 4.60731 | 3.66674 | |
| 5 | 5.26115 | 4.15113 | |
| 6 | 6.97473 | 5.94759 | |
| 7 | 8.60843 | 6.60777 | |
| 8 | 10.1331 | 7.38025 | |
| 9 | 10.5681 | 8.01503 | |
| 10 | 10.847 | 8.25481 |
Input file
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ptruss.inp : Concentric load case, Self-weight case, Frequency analysis using consistent mass
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ptrussl.inp : Frequency analysis using lumped mass
E.9.2 User Defined Coordinate in Support, and Displacement, Concentric Load
For the same truss structure as in the previous section, the application of the UCS was verified for support constraints, displacement loads, and concentric loads. As shown in the figure, two models were prepared: Model 1 for verifying support constraints and concentric loads, and Model 2 for verifying displacement loads.
In Model 1, to verify the concentric load application, forces in the X and Y directions were separately defined at node 4 and then compared with the case where the same load vector was applied after rotation. The load vector is identical in both cases.
To simulate the effect of applying a displacement load or rotated support condition to a rotated location, case 1 in each model generated a separate node 100 and connected it to node 5, after which MPC constraints were applied. In each model, case 1 and case 2 must produce identical results.
Figure E.9.2 Analysis Models for the Verification of User Defined Coordiante
Input file
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ptrussOrient1.inp : Model 1 – Verificaton of Support, Concentric load
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ptrussOrient2.inp : Model 2 – Verifiction of Displacement load
E.9.3 Cable Element
As shown in Figure E.9.3, an analysis was performed on a simple structure composed of a cable and a beam to verify the elastic catenary element. The cable was modeled with a single elastic catenary element, and the beam was modeled with a single linear beam element. The vertical displacement at the free end A was calculated while varying the unstressed length \(\small L_{0}\) of the elastic catenary element, and the results were compared with those from the in-house program for cable-stayed bridge analysis developed by Prof. Hae-Sung Lee’s research team at Seoul National University (Lee et al., 2004), confirming exact agreement.
Figure E.9.3 Verificaiton of Cable Element
Input file
- cable.inp