Search results
Results from the WOW.Com Content Network
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
The starting point is the relation from Euler-Bernoulli beam theory = Where is the deflection and is the bending moment. This equation [7] is simpler than the fourth-order beam equation and can be integrated twice to find if the value of as a function of is known.
The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction.
The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium.
The cantilever method is considered one of the two primary approximate methods (the other being the portal method) for indeterminate structural analysis of frames for lateral loads. Its use is recommended for frames that are taller than they are wide, and therefore behave similar to a beam cantilevered up from the ground.
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 1873.
The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displacement. OR, This principle states that "ordinate of ILD for a reactive force is given by ordinate of elastic curve if a unit deflection is applied in the direction of reactive force."
The principle states that the influence line of a function will have a scaled shape that is the same as the deflected shape of the beam when the beam is acted upon by the function. To understand how the beam deflects under the function, it is necessary to remove the beam's capacity to resist the function.