Why do we calculate STRESS, when we have FORCES?

In the structural analysis classroom of our engineering degree, we are taught how to determine the internal forces (Axial force, Bending Moment & Shear forces) for a structure based on the applied load by several analysis methods. 

If we take a quick shift to the design classroom, a new parameter would be ruling the class called "STRESS".

I used to wonder, why we are concerned about "STRESS" when there are "INTERNAL FORCES"? 

Whether the internal forces are not enough to design a member?

Let me explain this by asking a series of several other questions that pave the way to better understanding.

For our clarity, let me concentrate on "Shear Stress" alone.

Let’s begin with the first question:

what is a shear force?

Consider a beam with any pattern of loading and support condition, because of the applied load, it deforms. As a result, internal forces (shear force & bending moment) gets generated in the beam to maintain equilibrium.

Shear force is one of the internal forces. It acts parallel to the cross-section of the beam. If we take any section of the beam along its length, the vertical force that acts on the section to satisfy the equilibrium condition is called the Shear force.

To put it in a very simple way, “they are the tearing forces which act parallel to the cross-section of a member.” (see the attached image).

So far, you might have got certain level of understanding or visualization regarding the shear force. 

Then arises the next question:

Whether it remains same throughout the length of the member?

Definitely not. It varies along the length of the member. That is the reason why we plot the shear force diagram. The following image shows the shear force diagram for a simply supported beam with a uniformly distributed load along its length.

Now, the time for the next question:

What are the factors that affect the shear force?

    1. The load which acts on the beam.

    2. The support condition.

    3. The length of the beam.

You might have been aware of this earlier. 

The reason for asking this question is not to know what are the factors that affect the shear force.

It is to think about the factors which are not considered, such as “Depth of the beam”, “Cross-sectional shape of the beam” and most importantly “Material” of the beam.

What do we infer from this?

For the same loading, support condition and length of the beam:

The shear force will be the same for -

    1. A beam with a rectangular cross-section and I section.

    2. A beam that is 500 mm deep and 700 mm deep.

    3. A beam that is made up of steel and wood.

So, there comes “STRESS”, which includes the factors that are neglected in the calculation of shear force.

Even though the shear force of a steel beam and wooden beam is the same, the shear stress of them varies. Steel beams have higher allowable stress than the wooden beam.

Stress is the value, that an engineer compares with different material properties and cross-sectional properties.

To answer the question, Why do we calculate stress?

“If we are about to design a beam or a member. We need stress value to compare with different cross-sectional shapes and different material properties to arrive at a feasible section.”

This is the reason why we calculate stress (in our case, the shear stress).