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Typically partial uniformly distributed loads (u.d.l.) and uniformly varying loads (u.v.l.) over the span and a number of concentrated loads are conveniently handled using this technique. The first English language description of the method was by Macaulay . [ 1 ]
The curve () describes the deflection of the beam in the direction at some position (recall that the beam is modeled as a one-dimensional object). is a distributed load, in other words a force per unit length (analogous to pressure being a force per area); it may be a function of , , or other variables.
The two cases with distributed loads can be derived from the case with concentrated load by integration. For example, when a uniformly distributed load of intensity q {\displaystyle q} is acting on a beam, then an infinitely small part d x {\displaystyle dx} distance x {\displaystyle x} apart from the left end of this beam can be seen as being ...
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.
Moments are calculated by multiplying the external vector forces (loads or reactions) by the vector distance at which they are applied. When analysing an entire element, it is sensible to calculate moments at both ends of the element, at the beginning, centre and end of any uniformly distributed loads, and directly underneath any point loads.
When an arch carries a uniformly distributed vertical load, the correct shape is a parabola. When an arch carries only its own weight, the best shape is a catenary. [3] A catenary, in blue, graphed against a parabola, in red
A statically determinate beam, bending (sagging) under a uniformly distributed load. A beam is a structural element that primarily resists loads applied laterally across the beam's axis (an element designed to carry a load pushing parallel to its axis would be a strut or column).
The method adapts the strip method and is based on an elastic analysis of torsionally restrained two-way rectangular slabs with a uniformly distributed load. Marcus introduced a correction factor to the existing Rankine Grashoff theory in order to account for torsional restraints at the corners.