Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining equilibrium, leading to a surplus of unknown reactions over the available equilibrium equations.

The statical indeterminacy is resolved by considering the reaction at point C as redundant and releasing it from its support. This redundant reaction is treated as an additional load. The superposition method is then deployed to determine the deformation in each section of the rod structure. By combining these individual deformations, the total deformation expression for the entire structure is derived. Considering the expressions, the total deformation of the rod structure equals zero, and the summation of all the loads equals zero, the unknown reaction forces are determined. Finally, the deflection at point B is calculated by summing the deformations in the rod structure sections preceding point B.

タグ
Statically IndeterminateProblem SolvingInternal ForcesReactionsCylindrical RodsSteelBrassSupportsEquilibriumStatical IndeterminacyRedundant ReactionSuperposition MethodDeformationTotal DeformationDeflection

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18.10 : Statically Indeterminate Problem Solving

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18.1 : 軸荷重下での垂直ひずみ

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18.2 : 応力-ひずみ図

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18.3 : 応力-ひずみ線図 - 延性材料

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18.4 : 応力-ひずみ図 - 脆性材料

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18.5 : 真応力と真ひずみ

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18.6 : フックの法則

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18.7 : プラスチックの挙動

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18.8 : 疲労

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18.9 : 多重荷重下での部材の変形

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18.11 : 熱ひずみ

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18.12 : 温度依存変形

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18.13 : ポアソン比

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18.14 : 一般化フックの法則

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18.15 : 体積弾性率

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