We were discussing basic concept of shear force and bending moment in our previous session. We have also discussed strain energy and expression for strain energy due to various types of loading such strain energy stored due to gradual applied load.
Now we are going ahead to start new topic in strength of material and that is bending stress. First we will understand here the meaning and importance of bending stress.
We have already seen various types of stress in strength of materials such as tensile stress, compressive stress and shear stress. Today we will see another type of stress in loaded member i.e. bending stress.
Let us go ahead step by step for easy understanding, however if there is any issue we can discuss it in comment box which is provided below this post.
Let us consider one structural member such as beam with rectangular cross section, we can select any type of cross section for beam but we have considered here that following beam has rectangular cross section.
Let us assume that following beam AB is horizontal and supported at its two extreme ends i.e. at end A and at end B, therefore we can say that we have considered here the condition of simply supported beam.
Let us think that a load W is applied over the beam AB as displayed in above figure, now someone want to ask one question that what you will see when load W will be applied over the beam AB?
Once load W will be applied over the simply supported horizontal beam AB as displayed above, beam AB will be bending in the form of a curve and we have tried to show the condition of bending of beam AB due to load W in above figure.
As we have seen above that horizontal beam AB will be bending due to the load W which is applied over the beam AB and therefore we can say that load W will be the responsible for the bending action of the horizontal beam AB.
Now, material of the horizontal beam AB will resist the bending action of load W and hence material of the horizontal beam will provide the internal resistance against load W and this internal resistance per unit area will be termed as bending stress.
Therefore we can define bending stress as the internal resistance per unit area developed by material of the beam against the external load.
Formula and unit of bending stress
Unit of bending stress will be similar as the unit of stress i.e. N/m2.
We have shown above one small section of the beam AB after loading condition i.e. after bending of the beam. We have used few letters above in diagram of small section of the beam; let us see the nomenclature of those terms/letters.
R: Radius of curvature
N.A: Neutral axis of the beam AB
We must note it here that due to bending action, top portion of the beam will be in compression whereas bottom portion of the beam AB will be in tension and we have displayed it in above figure.
We will discuss assumptions made in the theory of simple bending in the category of strength of material in our next post.
Strength of material, By R. K. Bansal
Image Courtesy: Google
Shear force and bending moment diagrams for a simply supported beam with a point load acting at midpoint of the loaded beam