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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 ]
Boundary conditions are, however, often used to model loads depending on context; this practice being especially common in vibration analysis. By nature, the distributed load is very often represented in a piecewise manner, since in practice a load isn't typically a continuous function. Point loads can be modeled with help of the Dirac delta ...
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 ...
For example, in designing a staircase, a dead load factor may be 1.2 times the weight of the structure, and a live load factor may be 1.6 times the maximum expected live load. These two "factored loads" are combined (added) to determine the "required strength" of the staircase.
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
A typical load case for design for serviceability (characteristic load cases; SLS) is: 1.0 x Dead Load + 1.0 x Live Load. Different load cases would be used for different loading conditions. For example, in the case of design for fire a load case of 1.0 x Dead Load + 0.8 x Live Load may be used, as it is reasonable to assume everyone has left ...
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).
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.