Bending Moment at a section of beam - Definition, equation, calculation and diagram
Bending moment at a section of a structural element is defined as the reaction developed in a structural element when an external force or moment is applied to the element that causes the element to be bent.
Bending moment at a section of beam is calculated as the algebraic sum of the moment of all the forces acting on one side of the section. For example consider the following figure which shows the free body diagram of a simply supported beam having F1, F2, F3 and F4 as the applied loads on the beam and RA, RB as the support reactions.
It is very important to define the sign convention for bending moment before calculating the values. The possible bending of a beam is shown in the following figure.
When the beam bends in such a way that it forms concavity downwards (cup-shaped) it is called as sagging. Whereas the bending which results in convexity upwards (like a hump); is known as hogging.
Sagging bending moment is taken as +ve, it results in developing tension in the bottom fibers and compression in the top fibers of the beam.
Hogging bending moment is taken as -ve, and it develops compression in the bottom fibers and tension in the top fibers.
Based on these sign conventions we can write the equation of bending moment at section x-x of the beam given above;
Considering forces on the left of the section x-x
Mx = RALA - F1x1 - F2x2
We can also get the values of Mx by considering the forces on the right of section x-x.
Mx = RBLB - F3x3 - F4x4
The above expression is called as bending moment equation which can be written depending upon the loading on the beam. A graphical representation of the bending moment equation along the span of the beam is known as bending moment diagram (BMD).
Bending moment is required for design of beam and also for the calculation of slope and deflection of beam
Get more information about bending moment diagram shape and curvature due to different loading cases.
You can also visit our Bending moment calculator for calculation of shear force and bending moment different load cases.
You can also use following calculators for Bending moment and shear forceBending moment calculator for Cantilever
Stress Transformation Calculator
Calculate Principal Stress, Maximum shear stress and the their planes
Calculator for Moving Load Analysis
To determine Absolute Max. B.M. due to moving loads.
Moment of Inertia Calculator
Calculate moment of inertia of plane sections e.g. channel, angle, tee etc.
Reinforced Concrete Calculator
Calculate the strength of Reinforced concrete beam
Moment Distribution Calculator
Solving indeterminate beams
Deflection & Slope Calculator
Calculate deflection and slope of simply supported beam for many load cases
Fixed Beam Calculator
Calculation tool for bending moment and shear force for Fixed Beam for many load cases
BM & SF Calculator for Cantilever
Calculate SF & BM for Cantilever
Deflection & Slope Calculator for Cantilever
For many load cases of Cantilever
Overhanging beam calculator
For SF & BM of many load cases of overhanging beam
Civil Engineering Quiz
Test your knowledge on different topics of Civil Engineering
Research Papers, Thesis and Dissertation
List of skyscrapers of the world
Containing Tall building worldwide
Containing the List of civil engineering conferences, seminar and workshops
Profile of Civil Engineers
Get to know about distinguished Civil Engineers
Worldwide Civil Engineers Professional Societies
Keep visiting for getting updated or Join our mailing list
Please Tell your Friends about us