Bending stress is actually one of the main factors for which structural members are designed. Have you ever thought why the height of most of structural members is way larger than their width? Well, to answer this question you need to know about bending stress distribution. read through this article to gain insight into this topic.
Positive convention for bending moment
As you know, to identify the direction of a force, we need to define the convention of positive direction. In figure below, you can see the positive direction of internal loads. remember, a positive moment is also called sagging moment while a negative one is referred as hogging moment. All civil engineering students need to learn this convention by heart because it is necessary to solve any problem.
Bending stress distribution
So now the question is that how is the bending moment distributed on each cross section area of the beam. When a hogging moment is applied on the beam, the upper part of the cross section is under compressive stresses as if the bending moment is pushing them, and in the lower areas we have tension. In other words pressure gradually turns to tension.
This gradual change from tension to compression means in some area of cross section stress is zero. In the figure below, the blue line indicates the location of zero stress area alongside the beam. This line that is neither under tension nor under compression is called neutral zone.
Why neutral zone is so important for us
The first step of solving any problem is to find out where the neutral zone is. Neutral zone is very important because the magnitude of bending stress at any given point is a function of its distance from the neutral zone. so without knowing the location of neutral zone, we cannot calculate stress distributions.
How to find the location of neutral zone
Figure below shows the free body diagram of any cross section which is under bending stress. according to equilibrium equations the resultant of horizontal forces must be zero. So if you solve this equation, you finally reach to another equation that demonstrates the location of neutral axis. In simple words neutral axis lies on the centroid of the cross section.
Bending stress formula
The amount of bending stress at each point of cross section is equal to My/I
in this equation M is the amount of bending moment
y is the distance from the neural axis
and I is moment of inertia.