Hi, need to submit a 1250 words paper on the topic Understanding of the Bending Theory. Under load, a beam bends to form an arc. The centre of the beam is the neutral axis which does not deform. However, the layer above the neutral axis shortens while the layer below elongates. As a result, beam fibers above the neutral axis are under compression whereas those below are under tension.
Young’s modulus, or modulus of elasticity (E), is a stiffness measure for any material. This is the extent to which the material resists deformation under an applied load. For beams, the kind of deformation that takes place is majorly deflection (the degree to which a structural element is displaced under a load) (Bansal, 2010). Consider the beam below.
When loaded with a uniformly distributed load or a point load, the beam will be subjected to a bending moment. As a result, it will deflect as shown. Upon removal of the load, the whole strain caused by the load may disappear completely. When this occurs, the material is said to be perfectly elastic. Flexible materials have small values of E whereas stiff materials have large values of E. Graphically. E is equal to the slope of a load against deflection graph.
Much as the amount that a beam will bend when loaded will be determined by the modulus of elasticity of the material, the second moment of the area also determines the degree of deformation in part hence its relevance in the theory of bending. The size and shape of the object determine its second moment of area (Bansal, 2010).
The amount by which a structural element is displaced upon application of a load is called deflection. Depending on how the element is supported, how it will deflect and its degree of deflection will vary. A structural element can be: simply supported, fixed, pinned, supported on rollers or cantilevered. While deflection is least experienced at the supports of the element in question, it is greatest at midspan of the supporting element.