What is Point of Contra-flexure, Contra-shear, inflection point, position of maximum bending moment. Shear force and bending moment are examples of interanl forces that are induced in a structure when loads are applied to that structure. Loading tends to cause failure in two main ways: a) by shearing the beam across its cross-section. b) by bending the beam to an excessive amount.

For beams spanning between two simple pin-jointed supports (i.e. no cantilevers) moment will always be positive and, although the beam sags, moment is drawn above the axis. The maximum bending moment occurs at the point of zero shear force. To find the position of the maximum Bending moment, you have 2 ways:1. Equate shear force at distance x to zero ( in the beam portion where shear force is zero) ie, S.Fx=02. Find the bending moment at distance x and equate derivative of it w.r.t x to zero ie, d(Mx)/dx = 0 To find the point of contra flexure: B.Mx=0 Simply supported means that each end of the beam can rotate, therefore each end support has no bending moment. The ends can only react the shear load. Other beams can have both ends fixed, therefore each end support has both bending moment and shear reaction loads.In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely. If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "sagging", and a positive moment will cause "hogging". It is therefore clear that a point of zero bending moment within abeamis a point ofcontraflexurethat is the point of transition from hogging to sagging or vice versa. Failure in bending will occur when the bending moment is sufficient to induce tensile stresses greater than theyieldstress of the material throughout the entire cross-section. In structural analysis, this bending failure is called a plastic hinge, since the full load carrying ability of the structural element is not reached until the full cross-section is past the yield stress. It is possible that failure of a structural element inshearmay occur before failure in bending, however the mechanics of failure in shear and in bending are different. Critical values within the beam are most commonly annotated using abending moment diagram, where negative moments are plotted to scale above a horizontal line and positive below. Bending moment varies linearly over unloaded sections, and parabolically over uniformly loaded sections. To find the Bending Moment, you must cut the beam in two.Bending moment is INTERNAL, moment is EXTERNAL. Shear Force is in all beams, but usually only seen as a problem in SHORT beams. Long beams fail by bending. The SFD (Shear Force Diagram)tells you how much the beam wants to SLIDE apart. The BMD (Bending Moment Diagram)tells you how much the beam wants to BEND apart by rotation. Positive bending moment = SAGGING Negative bending moment = HOGGING ABuilt-inorencastre'support is frequently met . In practice, it is not usually possible to obtain perfect fixing and the fixing moment applied will be related to the angular movement of the support. When in doubt about the rigidity, it is safer to assume that the beam is freely supported. Zero shearing force corresponds to either maximum or minimum bending moment. At a point on the beam where the type of bending is changing from sagging to hogging, the bending moment must be zero, and this is called a point ofinflectionorcontraflexure.The following general conclusions can be drawn when only concentrated loads and reactions are involved. The shearing force suffers sudden changes when passing through a load point. The change is equal to the load. The bending Moment diagram is a series of straight lines between loads. The slope of the lines is equal to the shearing force between the loading points.Shearing Force F

Bending Moment MRate of loading w

In abendingbeam, a point is known as a point ofcontraflexureif it is a location at which no bending occurs. In abending momentdiagram, it is the point at which the bending moment curve intersects with the zero line. In other words where the bending moment changes its sign from negative to positive or vice versa. Flexural reinforcement may be reduced at this point. However, to omitreinforcementat the point of contraflexure entirely is inadvisable as the actual location is unlikely to realistically be defined with confidence. Additionally, an adequate quantity of reinforcement should extend beyond the point of contraflexure to develop bond strength and to facilitate shear force transfer. Indifferential calculus, aninflection point,point of inflection,flex, orinflection(inflexion) is a point on acurveat which the curve changes from beingconcave(concave downward) toconvex(concave upward), or vice versa. POISSONS RATIOWhen a bar is stretched in the axial direction it gets longer (AXIAL STRAIN) but correspondingly thinner (LATERAL STRAIN).Lateral strain is directly proportional to axial strain for HOMOGENEOUS materials, which have elastic properties identical in all directions normal to the axis (ORTHOTROPIC). The same is true for ISOTROPIC materials in which properties are uniform in ALL directions.For such materials : - (lateral strain)/(axial strain) = -e /e=n= POISSONS RATIOSo for ordinary materialsnis always positive. In theory for an isotropic materialnis around 1/3 and in practice for most materials 0.25