Bending Moment Formula: Concept, Application, And Use

The field of bending theory contains the subfield of the bending equation. According to this hypothesis, a beam will bend when a force is applied to a point along the beam’s longitude axis. Hence, bending or flexural theory pertains to studying axial deformation generated by such forces.

Bending moment: Equation

A bending stress equation, often known as a bending equation, is a mathematical formula used to calculate the force exerted on a beam during a bending operation. Nevertheless, one must consider a set of assumptions imposed by the bending moment equation to get accurate data about flexural stresses. 

Bending moment: Key concepts

The greatest bending moment occurs at the point along the beam when the shear force reverses direction. The point of contra flexure is determined by locating the location at which the bending moment changes. It is said that a pure bending span is one in which the shear force value is 0 and the bending moment is constant.

Bending moment: Assumptions

• You can’t have a crooked beam. Moreover, its cross-section must be consistent and free of distortions.
• The beam must be constructed from a single, consistent material. It also has to be longitudinally symmetrical.
• As the bending moment equation is derived from the location of the applied load, it follows that the load must be centred along the member’s longitudinal axis.
• The assumption that buckling and not bending would lead to failure is fundamental to the bending equation.
• The elastic limit, denoted by “E,” is the same under tension as it is under compression.
• When the object bends, the plane cross-section maintains its flat shape.

Bending moment: Formula for bending force

Calculating the bending moment requires adding the applied load to the distance away from the origin using some algebraic formula. The total applied moments from the reference point will also induce bending moments.

The bending moment formula is used in structural analysis, material strength, reinforced cement concrete and steel analysis. The bending moment is proportional to the product of the following in the bending moment equation:

M/I = f/y = E/R

Where:

M = Bending moment, I = Moment of Inertia

f = Bending stress

y = Distance of outer fibre from C.G

E = Modulus of Elasticity

R = Radius of Curvature

Bending moment: Stress-strain graph

The bending moment is determined for a wide variety of support and load configurations, including but not limited to simply supported, cantilever supported, propped cantilever supported, overhanging supported, and continuously supported, and for a variety of load configurations, including point load, uniform load, gradually varied load, and direct moment. The bending moment of a structural part is calculated by multiplying the applied load or force by the span distance from a fixed point.

• In the area of the stress-strain graph where Hooke’s Law holds, the ratio of stress to strain remains proportional to the strain across the whole graph, and this region is known as the proportional limit. Young’s modulus is the name given to this fixed numerical number.

• The stress-strain curve’s “Breaking Point,” also known as the “Fracture or Breaking Point,” indicates where a material fails catastrophically, resulting in a break.

• When a load is removed from a material, the material will return to its original position up to a point on the stress-strain graph known as the elastic limit. Once a certain elastic limit is passed, plastic deformation begins to set in.

• The plastic deformation of a material begins at a point called the yield point on a Stress-strain diagram. When the yield point is exceeded, plastic deformation is irreversible.

• When a load is removed from a material, the material will return to its original position up to a point on the stress-strain graph known as the elastic limit. Once a certain elastic limit is passed, plastic deformation begins to set in.

• A single point on the stress-strain diagram, called the Ultimate Stress Point, represents the stress at which a material fails irreversibly.

Bending moment: Standard cases

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