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If a load is applied sufficiently slowly, the inertia forces (Newton's first law of motion) can be ignored and the analysis can be simplified as static analysis. A static load is one which varies very slowly. A dynamic load is one which changes with time fairly quickly in comparison to the structure's natural frequency.
These dynamic loads may involve considerations such as impact, momentum, vibration, slosh dynamics of fluids and material fatigue. Live loads, sometimes also referred to as probabilistic loads, include all the forces that are variable within the object's normal operation cycle not including construction or environmental loads.
Physically, taking into account the added mechanisms of deformation effectively lowers the stiffness of the beam, while the result is a larger deflection under a static load and lower predicted eigenfrequencies for a given set of boundary conditions. The latter effect is more noticeable for higher frequencies as the wavelength becomes shorter ...
The dynamic response of a structure to dynamic loads (the natural frequency of a structure) is also dependent on its stiffness. In a structure made up of multiple structural elements where the surface distributing the forces to the elements is rigid, the elements will carry loads in proportion to their relative stiffness - the stiffer an ...
A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "free" to move in response to forces and torques it may experience.
The global displacement and force vectors each contain one entry for each degree of freedom in the structure. The element stiffness matrices are merged by augmenting or expanding each matrix in conformation to the global displacement and load vectors.
For example, sometimes the kilogram-force unit is used to measure loads. In such a case, the modulus of elasticity must be converted to k g f m 2 {\displaystyle \mathrm {\frac {kgf}{m^{2}}} } . Structural deflection
When the applied load reaches the Euler load, sometimes called the critical load, the column comes to be in a state of unstable equilibrium. At that load, the introduction of the slightest lateral force will cause the column to fail by suddenly "jumping" to a new configuration, and the column is said to have buckled.