Understanding Beams, Poisson's Ratio, and Hooke's Law

 simply supported beam is a structural element supported at both ends, typically resting on supports that allow notation but prevent vertical olisplacement. It is is free to bend under applied loads and is commonly used in bridges and buildings///continuas beam is a structural element that extends over multiple supports, with more than two supports along its length. It distributes loads. Mare evenly, reducing bending moments and deflection compared.//////Overhanging beam An overhanging beam is a beam that extends beyond one or both of its supports, creating a cantilevered section. This type of beam combines characteristics of both simply supported and cantilever beams, experiencing bending moments and shear forced in the overhanging portion./////A cantilever beam is a beam fixed at one end while the other end is free, allowing it to project outwards without support, It carries loads aler it's length, length, creating bending shear stresses, Sade alerg commonly used in balconies and bridges.//////Fixed ended Beam:A Fixed-ended beam is a beam with both ends rigidly fixed, preventing both rotation and displacement. This constraint creates high bending moments at the supports and reduces cleflection, making it more stable and efficient for worlying lands in application-

Poisson's ratio is “the ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force.// Hooke's law is a fundamental principle in solid mechanics and rock mechanics that describes how stress and strain are proportionally related within an object's elastic limit/ the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior// UDL stands for uniformly distributed load, which is a load that is spread evenly across the entire length of a beam or slab. The magnitude of the load remains constant throughout the beam /Section modulus represented by the symbol \(Z\), is a geometric property that measures a structural member's ability to resist bending stress.