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Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly replaced by the more convenient and faster abacus.
Counting rods (чнн) are small bars, typically 3–14 cm (1" to 6") long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals.
For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. [8]
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.
This expression assumes that the rod is an infinitely thin (but rigid) wire. This is a special case of the thin rectangular plate with axis of rotation at the center of the plate, with w = L and h = 0. Thin rod of length L and mass m, perpendicular to the axis of rotation, rotating about one end.
For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as = where, F {\displaystyle F} is the force on the body δ {\displaystyle \delta } is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched ...
Then, using the triangle sine law, it is found that the crank to connecting rod angle is 88.21738° and the connecting rod angle is 18.60647° from vertical (see Piston motion equations#Example). When the crank is driven by the connecting rod, a problem arises when the crank is at top dead centre (0°) or bottom dead centre (180°). At these ...
Deflection (f) in engineering. In structural engineering, deflection is the degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load.