Axial stress, Axial deformation

Axial stress is a topic that is very important in design of structures. In simple words, if I apply a force exactly normal to cross section and exactly at the center line, this kind of loading is called pure axial loading. That means there is no bending moment and no shear force.

In such cases, axial force transfers through the member and the deformation is symmetrical with respect to the centerline.
But if the load is applied in a inclined way, the angles has changed. Actually, this is because it also applies a shear component which is not pure axial loading anymore.
Now the question is what happens inside the material when the member is under axial force. well In simple words, the axial force transfers through the material to reach the end. And there it is counteracted by the reactional forces applied by the supports.

Axial stress

According to free body diagram of any part of the member, throughout the member, the amount of axial load remains the same. But what about the amount of axial stress? As you know, axial stress is equal to normal force divided by cross section area. So if the cross section is variable, the amount of axial stress is different from one section to the other.

Axial deformation

The general strategy we use to study a member with variable cross section, is to divide it into smaller parts. The main advantage of this method is that for each small part the amount of change in cross sections is negligible so that we can assume each they are equal. So according to this formula we can simply calculate the axial deformation of each part and then if we sum them, the resultant will be the overall deformation of the member under axial load.

Fortunately, in civil engineering most of structural members we use, have constant cross sections. So if I find a way simplify this equation it would be very useful. The second equation in here is the simplified version provided that the cross section remains constant alongside the member.

The video below will help you to learn this topic more easily. Here is a useful quiz to challenge yourself. You can send the answers back to us to be corrected.