moment
The term "point of contraflexure" is often used in structural engineering, specifically in the context of analyzing and designing beams subjected to bending loads. In simple terms, the point of contraflexure is the location along the length of a beam where the bending moment is zero. When a beam is subjected to bending loads, it experiences tensile (positive) bending moments and compressive (negative) bending moments along its length. The bending moment varies along the beam, reaching a maximum at the points where the bending is the most significant. These points are usually located near the supports of the beam. However, in some cases, particularly in continuous beams or beams with complex loading conditions, there may be a section along the beam where the bending moment changes direction from positive to negative or vice versa. This section is known as the point of contraflexure. At the point of contraflexure, the bending moment is zero, and the beam's curvature changes direction. This point is essential in the analysis and design of structures as it affects the internal forces and stresses within the beam. Identifying the point of contraflexure is crucial for engineers to ensure the beam's stability and design it appropriately to handle the bending loads effectively. The bending moment diagram is used to visualize the variation of bending moments along the length of the beam and to locate the point of contraflexure if it exists.
Take a beam as an example. Moment is responsible for a beam to rotate about some axis. Whereas bending moment are a pair of moments which will not rotate the beam but it will deflect it.
To calculate the bending moment of any point:WL/2 x X - WX x X/2W = WeightL = Length of beamX = distance
When a cantilever beam is loaded with a Uniformly Distributed Load (UDL), the maximum bending moment occurs at the fixed support or the point of fixation. In other words, the point where the cantilever is attached to the wall or the ground experiences the highest bending moment. A cantilever beam is a structural element that is fixed at one end and free at the other end. When a UDL is applied to the free end of the cantilever, the load is distributed uniformly along the length of the beam. As a result, the bending moment gradually increases from zero at the free end to its maximum value at the fixed support. The bending moment at any section along the cantilever can be calculated using the following formula for a UDL: Bending Moment (M) = (UDL × distance from support) × (length of the cantilever - distance from support) At the fixed support, the distance from the support is zero, which means that the bending moment at that point is: Maximum Bending Moment (Mmax) = UDL × length of the cantilever Therefore, the maximum bending moment in a cantilever beam loaded with a UDL occurs at the fixed support. This information is essential for designing and analyzing cantilever structures to ensure they can withstand the applied loads without failure.
Bending moment is the same throughout the beam.
Contrafluctre, or contraflecture, is the point in a bending beam in which no bending occurs. This is more readily and easily observed in an over hanging beam.
Bending moment With "bending" you really mean the bending moment. The bending moment in an inner stress within a member (usually beam) that allows it to carry a load. The bending moment doesn't say anything about how much a beam would actually bend (deflect). Deflection Deflection measures the actual change in a material you could call "bending." It measures the physical displacement of a member under a load.
Curtailment is a theoretical point where some of the reinforcement is cut-off along the span of the beam where the bending moment reduces, given that the remaining reinforcement will be able to support the reduced bending moment. (A.P Nangolo)
The answer is not formulatic. There will be a parabolic shape from the dead load and a discontinuity at the point load.
Sagging bending moment causes the beam to bend in a way to make concavity downward (cup-shaped) and it results in developing tensile stress in lower half of the beam x-section.
Parabolic, max moment at midspan of value wL^2/8 where w is the distributed load and L the length of the beam.
The internal moment that tends to want a beam to bend around the center axis