This linear relation between elongation and the axial force causing was first noticed by Sir Robert Hooke in 1678 and is called Hooke's Law that within the proportional limit, the stress is directly proportional to strain or See accompanying figure at (1 & 2). see, section modulus tells about the strength of a section under bending. from bending equation we have (sigma/y=M/I=E/R). This is nearly identical to the result obtained using the depletion approximation. σ YP ⇒ Yield Point - Stress at which there are large increases in … Elastic limit is the maximum stress to which a specimen may be subjected and still return to its original length upon release of the load. Thus, in beams covering long spans the compression flange may tend to … how??? It is obtained by observing the deviation from the straight-line portion of the stress-strain curve. Proportional limit is the highest stress at which stress is directly proportional to strain. PL ⇒ Proportional Limit - Stress above which stress is not longer proportional to strain. Proportional Limit and Hooke’s Law As seen in Fig. let us see. The bending moment diagram is obtained in the same way except that the moment is the sum of the product of each force and its distance(x) from the section. Proportional Limit (Hooke's Law) From the origin O to the point called proportional limit, the stress-strain curve is a straight line. Proportional limit is the point on a stress-strain curve at which it begins to deviate from the straight-line relationship between stress and strain. Stress Strain Curve . It is generally used in tests of bending strength to quantify the stress required to cause failure. These fundamental parameters include the elastic limit, which for "Hookean" materials is approximately equal to the proportional limit, and also known as yield point or yield strength, Young's Modulus (these, although mostly associated with tensile testing, may have compressive analogs) and compressive strength. This plot is a manifestation of Hooke’s law : Stress is proportional to strain; that is, σ= E Є (2.4) where E is material property known as the modulus of It is reported in units of psi. 2.3, the stress-strain diagram is a straight line from the origin O to a point called the proportional limit. Elastic limit is the greatest stress the material can withstand without any measurable permanent strain remaining on the complete release of load. If the maximum bending stress is less than the proportional limit when buckling occurs, the failure is elastic. Distributed loads are calculated buy summing the product of the total force (to the left of the section) and the distance(x) of the centroid of the distributed load. Fiber stress at proportional limit represents the maximum stress a board can be subjected to without exceeding the elastic range of the wood. The elastic limit is in principle different from the proportional limit, which marks the end of the kind of elastic behaviour that can be described by Hooke’s law, namely, that in which the stress is proportional to the strain (relative deformation) or equivalently that in which the load is proportional to the displacement. Otherwise, it is inelastic. Lateral Torsional Buckling The compressive flange of a beam behaves like an axially loaded column. σ EL ⇒ Elastic Limit - The maximum stress that can be applied without resulting in permanent deformation when unloaded. Let the shearing force at the section x be F and at .Similarly, the bending moment is M at x, and .If w is the mean rate of loading of the length , then the total load is , acting approximately (exactly if uniformly distributed) through the centre C.The element must be in equilibrium under the action of these forces and couples and the following equations can be obtained:-