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Simply supported beam with a single eccentric concentrated load. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure. The first step is to find . The reactions at the supports A and C are determined from the balance of forces and moments as
As a consequence the three traction components that vary from point to point in a cross-section can be replaced with a set of resultant forces and resultant moments. These are the stress resultants (also called membrane forces, shear forces, and bending moment) that may be used to determine the detailed stress state in the structural element. A ...
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. [ 1 ]
A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "free" to move in response to forces and torques it may experience.
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 function. For example, consider a static uniform cantilever beam of length with an upward point load applied at the free end. Using boundary ...
To find the effect of a distributed load, the designer can integrate an influence line, found using a point load, over the affected distance of the structure. [5] For example, if a three-foot-long track acts between 5 feet and 8 feet along a beam, the influence line of that beam must be integrated between 5 and 8 feet.
The sum of the net force and torque is called the resultant force, which causes the object to rotate in the same way as all the forces acting upon it would if they were applied individually. [2] It is possible for all the forces acting upon an object to produce no torque at all. This happens when the net force is applied along the line of action.
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 is acting on a beam, then an infinitely small part distance apart from the left end of this beam can be seen as being under a concentrated load of magnitude .