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Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
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 ...
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 ]
Influence lines can be used with either concentrated or distributed loadings. For a concentrated (or point) load, a unit point load is moved along the structure. For a distributed load of a given width, a unit-distributed load of the same width is moved along the structure, noting that as the load nears the ends and moves off the structure only ...
Shear and moment diagram for a simply supported beam with a concentrated load at mid-span.. In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Applied loads may be represented either through boundary conditions or through the function (,) which represents an external distributed load. Using distributed loading is often favorable for simplicity. Boundary conditions are, however, often used to model loads depending on context; this practice being especially common in vibration analysis ...
Dead loads have small load factors, such as 1.2, because weight is mostly known and accounted for, such as structural members, architectural elements and finishes, large pieces of mechanical, electrical and plumbing (MEP) equipment, and for buildings, it's common to include a Super Imposed Dead Load (SIDL) of around 5 pounds per square foot ...
As in the previous step, this unbalanced moment is distributed to each member and then carried over to joint D and back to joint B. Joint D is a fixed support and carried-over moments to this joint will not be distributed nor be carried over to joint C.* Step 4: Joint B still has balanced moment which was carried over from joint C in step 3.