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statically

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STATICALLY - In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient for determining the inter...

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Statically description
In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure. * Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are* * * * ∑ * * * * F * → * * * * = * 0 * * * {\displaystyle \sum {\vec {F}}=0} * : the vectorial sum of the forces acting on the body equals zero. This translates toΣ H = 0: the sum of the horizontal components of the forces equals zero; * Σ V = 0: the sum of the vertical components of forces equals zero; * * * * ∑ * * * * M * → * * * * = * 0 * * * {\displaystyle \sum {\vec {M}}=0} * : the sum of the moments (about an arbitrary point) of all forces equals zero. * In the beam construction on the right, the four unknown reactions are VA, VB, VC and HA. The equilibrium equations are: * Σ V = 0: * * VA − Fv + VB + VC = 0Σ H = 0: * * HA = 0Σ MA = 0: * * Fv · a − VB · (a + b) - VC · (a + b + c) = 0.Since there are four unknown forces (or variables) (VA, VB, VC and HA) but only three equilibrium equations, this system of simultaneous equations does not have a unique solution. The structure is therefore classified as statically indeterminate. Considerations in the material properties and compatibility in deformations are taken to solve statically indeterminate systems or structures. * *

Statically description

In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure.
* Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are*
*
*
* ∑
*
*
*
* F
* →
*
*
*
* =
* 0
*
*
* {\displaystyle \sum {\vec {F}}=0}
* : the vectorial sum of the forces acting on the body equals zero. This translates toΣ H = 0: the sum of the horizontal components of the forces equals zero;
* Σ V = 0: the sum of the vertical components of forces equals zero;
*
*
*
* ∑
*
*
*
* M
* →
*
*
*
* =
* 0
*
*
* {\displaystyle \sum {\vec {M}}=0}
* : the sum of the moments (about an arbitrary point) of all forces equals zero.
* In the beam construction on the right, the four unknown reactions are VA, VB, VC and HA. The equilibrium equations are:
* Σ V = 0:
*
* VA − Fv + VB + VC = 0Σ H = 0:
*
* HA = 0Σ MA = 0:
*
* Fv · a − VB · (a + b) - VC · (a + b + c) = 0.Since there are four unknown forces (or variables) (VA, VB, VC and HA) but only three equilibrium equations, this system of simultaneous equations does not have a unique solution. The structure is therefore classified as statically indeterminate. Considerations in the material properties and compatibility in deformations are taken to solve statically indeterminate systems or structures.
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*

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