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== Proračuni ==
{{rut}}
Krutost, -{''k''}-, tela je mera otpornosti koju elastično telo ispoljava pri deformaciji. Za elastično telo sa jednim [[Степени слободе (механика)|stepenom slobode]] (DOF) (na primer, istezanje ili kompresija šipke), krutost je definisana kao
Krutost, -{''k''}-, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single [[Degrees of freedom (mechanics)|degree of freedom]] (DOF) (for example, stretching or compression of a rod), the stiffness is defined as
:<math>k=\frac {F} {\delta} </math>
: -{''F''}- je sila na telo
: <math> \delta </math> je [[displacementВектор (vector)помераја|displacementpomeraj]] producedproizveden bysilom theduž forceistog alongstepena the same degree of freedomslobode (forna instanceprimer, promena the change in length of a stretcheddužine springopruge)
In the [[International System of Units]], stiffness is typically measured in [[Newton (unit)|newton]]s per meter.
In Imperial units, stiffness is typically measured in [[Pound (force)|pound]]s(lbs) per inch.
Generally speaking, [[Deflection (engineering)|deflections]] (or motions) of an infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum of six DOF at a point). For example, a point on a horizontal [[Euler–Bernoulli beam equation|beam]] can undergo both a vertical [[Displacement (vector)|displacement]] and a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M [[Matrix (mathematics)|matrix]] must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. In industry, the term '''influence coefficient''' is sometimes used to refer to the coupling stiffness.
U [[Међународни систем јединица|Internacionalnom sistemu jedinica]], krutost se tipično meri u [[Newton (unit)|njutnima]] po metru. U imperijalnim jedinicama, krutost se tipično meri u [[Pound (force)|funtama]] (-{lbs}-) po inču.
It is noted that for a body with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom) but also those along with other directions.
Uopšteno govoreći, [[Deflection (engineering)|pomeraji]] (ili pokreti) infinitezimalnog elementa (koji se posmatra kao tačka) u elastičnom telu mogu se javiti duž više stepeni slobode (maksimalno šest stepena slobode u jednoj tački). Na primer, tačka na horizontalnoj [[Euler–Bernoulli beam theory|gredi]] može podleći vertikalnom [[Displacement (vector)|pomeranju]] i rotaciji u odnosu na njenu nedeformisanu osu. Kada postoji M stepeni slobode, M x M [[Матрица (математика)|matrica]] se mora koristiti za opis krutosti u tački. Dijagonalni izrazi u matrici su direktno vezani za krutost (ili jednostavno krutosti) duž istog stepena slobode, a vandijagonalni članovi su krutosti sprege između dva različita stepena slobode (ili na istoj ili različitim tačkama) ili isti stepen slobode na dve različite tačke. U industriji se pojam koeficijenta uticaja ponekad koristi za označavanje krutosti spojnice.
For a body with multiple DOF, in order to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF is left free while the remaining should be constrained. Under such a condition, the above equation can be used to obtain the direct-related stiffness for the degree of freedom which is unconstrained. The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.
Poznato je da za telo s višestrukim stepenima slobode, gore navedena jednačina generalno ne važi, jer primenjena sila ne stvara samo otklon uzduž vlastitog smera (ili stupana slobode), nego i duž drugih smerova. Za telo sa višestrukim stepenima slobode, da bi se izračunala krutost u datom pravcu (dijagonalni izrazi), korespondirajući stepen slobode se ostavlja slobodnim, dok se preostali ograničavaju. Pod takvim uslovima, gornja jednačina se može koristiti za dobijanje krutosti datog stepena slobode koji nije ograničen. Odnosi između reakcionih sila (ili momenata) i proizvedenog otklona su krutosti sprezanja. Opis koji uključuje sve moguće parametre istezanja i smicanja je dat [[Hukov zakon|tenzorom elastičnosti]].
A description including all possible stretch and shear parameters is given by the [[Hooke's law|elasticity tensor]].
== Fleksibilnost ==
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