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What is the kinematic indeterminacy of truss and frame structure in 3D?

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In the context of structural analysis, kinematic indeterminacy refers to the number of redundant or excess degrees of freedom that a structure possesses beyond those required for equilibrium. 1. **Truss Structures in 3D:** - A truss structure is typically 3D if it spans in three dimensions. The...
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In the context of structural analysis, kinematic indeterminacy refers to the number of redundant or excess degrees of freedom that a structure possesses beyond those required for equilibrium. 1. **Truss Structures in 3D:** - A truss structure is typically 3D if it spans in three dimensions. The kinematic indeterminacy of a 3D truss is given by: \[ I = 3n - 6 \] where \( n \) is the number of joints. This formula accounts for the fact that in 3D space, each joint has 3 degrees of freedom (translations in x, y, and z directions), and the overall structure has 6 degrees of freedom (3 translational and 3 rotational). 2. **Frame Structures in 3D:** - For frame structures in 3D, the kinematic indeterminacy depends on whether it is a rigid frame or a flexible frame. However, a general formula for 3D frame structures is: \[ I = 3m - 6 \] where \( m \) is the number of joints. This is analogous to trusses but takes into account the additional degrees of freedom due to the possibility of rotational movements and the structural rigidity (or flexibility) of the members. In both cases, the formula \( 3n - 6 \) for trusses and \( 3m - 6 \) for frames indicates the excess number of degrees of freedom beyond what is necessary for a structure to maintain equilibrium under applied loads. read less
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