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The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass. The deflected shape of a beam can be represented by the moment diagram, integrated (twice, rotated and translated to enforce support conditions).
The position of the centroidal axis (the center of gravity line for the frame) is determined by using the areas of the end columns and interior columns. 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 ...
In many flight dynamics applications, the Earth frame is assumed to be inertial with a flat x E,y E-plane, though the Earth frame can also be considered a spherical coordinate system with origin at the center of the Earth. The other two reference frames are body-fixed, with origins moving along with the aircraft, typically at the center of gravity.
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 slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney. [1] The slope deflection method was widely used for more than a decade until the moment distribution method was developed. In the book, "The Theory and Practice of Modern Framed Structures", written by J.B Johnson, C.W. Bryan ...
The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. [1] The method only accounts for flexural effects and ignores axial and shear effects.
Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams.Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.
where u is the deflection of the structure due to the applied load. Graphs of dynamic amplification factors vs non-dimensional rise time (t r /T) exist for standard loading functions (for an explanation of rise time, see time history analysis below). Hence the DAF for a given loading can be read from the graph, the static deflection can be ...