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The first English language description of the method was by Macaulay. [1] The actual approach appears to have been developed by Clebsch in 1862. [ 2 ] Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression, [ 3 ] to Timoshenko beams , [ 4 ] to elastic foundations , [ 5 ] and to problems in which the bending and ...
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. [1] Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that ...
Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body ...
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem.
In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.
Though there are many approximate solutions (such as Welch's t-test), the problem continues to attract attention [4] as one of the classic problems in statistics. Multiple comparisons: There are various ways to adjust p-values to compensate for the simultaneous or sequential testing of hypotheses. Of particular interest is how to simultaneously ...
The Euler equations can be generalized to any simple Lie algebra. [1] The original Euler equations come from fixing the Lie algebra to be s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} , with generators t 1 , t 2 , t 3 {\displaystyle {t_{1},t_{2},t_{3}}} satisfying the relation [ t a , t b ] = ϵ a b c t c {\displaystyle [t_{a},t_{b}]=\epsilon ...