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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.
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
This is theoretically the maximum bending moment that the section can resist – when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation. [1] In practice most materials are work-hardened resulting in increased stiffness and moment resistance until the material ...
Therefore, beams should also be checked for local buckling, local crippling, and global lateral–torsional buckling modes of failure. Note that the deflections necessary to develop the stresses indicated in a plastic analysis are generally excessive, frequently to the point of incompatibility with the function of the structure.
By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. It is known as the collapse mechanism. For each degree of static indeterminacy of the beam, an additional plastic hinge must be added to form a collapse mechanism.
Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple nor fixed). In reality ...
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Further increment in load does not increase the moment at the points where the plastic hinges are formed. The increased load increases the moment in the less stressed sections of the beam; hence due to this, further plastic hinges are formed. This process of shift of application of moment in the beam is termed as moment redistribution in a beam ...
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