stress and strain

stress and strain are two basic concepts in civil engineering.  Stress is simply the amount of force divided by the cross section on which the force is applied.

Normal Stress , Shear Stress

If the load is normal to the cross section we call this ratio normal stress. And if the force is applied alongside the surface we call it shear stress.
As you see in the formula, stress is a function of cross section area alone. so as long as the area of cross sections and the forces are the same, identical objects are experiencing equal amounts of stress, no matter they are constructed from different materials.
as I said earlier, normal force causes normal stress, and shear loads creates shear stress. so if the load is either normal to surface or alongside it we can simply calculate the amount of stress. But in some problems the force is neither normal to the surface nor alongside it.

Norma stress

shear stess

shear and normal components

You may confront with an inclined load that intersects with the angle of α. in such a problem first you need to decompose the force to its perpendicular components, and then you can calculate the amount of normal stress and shear stress by diving the related component by the cross section area.

 Normal Strain

Normal strain is the ratio of how much the material deforms divided by its original length . in this picture for example, the member is under compression, and obviously it deforms a bit. So we can simply calculate the normal strain by dividing the amount of Longitudinal deformation by the original length. This ration is sometimes called strain, but normal strain is a more accurate name

normal strain

Shear Strain

If the direction of the force is alongside the surface, it does not change the length of the member, instead it changes the angles. shear strain is an indicator of how much a 90 degree angle is deformed because of a shear force.

shear strain


We have a cubic member with given dimensions An inclined load deforms is shape like this. And we need to calculate the amount of normal and shear stress, the amount of normal strain, and shear strain.

question 1

Here is a free video lesson in which I expail this topic in more details.