Why do cracks occur at 45 degrees in a beam?

The cracks happen due to the diagonal shear.

It is a very good question and trobled me a lot in my college days. Maximum professors will tell you due to shear. But why exactly due to shear?

Let me explain you this answer by concepts of shear stress.

Remember there are three types of crack that can appear on a beam due to applied load

1. Flexure crack ( vertical cracks)

2. Shear crack (diagonal cracks at 45 degree angle)

3. Flexure shear crack ( 45 degree at ends but gradually becomes vertical at mid span of the r.c.c beam)

SHEAR CRACK

It is the crack formed due to shear stress only.

Let's see how does shear stress form in a section.

As you can see the shear stresses are acting on the surface and resulting a diagonal tension. So due to this tension crack will be formed at 45 degree angle. ( do one simple test, take a square paper and apply tension as shown in figure. You will be surprised to see that crack propagation is similar to the figure)

So the main cause of 45 degree crack is diagonal tension as a result of shear stresses. Practically, this crack is more likely to be seen near the supports ( I.e. Columns) because the maximum shear force due to all loads practically is likely to occur at supports.

Flexure crack which is vertical if you see the elevation of the beam is more likely to happen in the mid span because the bending moment and deflection of the beam is maximum at mid span.

[ This analysis is based on simply supported beam as that is generalised case]

Hope your concept is clear. All points are here not explained so as not to make the answer unnecessarily long. If you have any conceptual problems at all understanding any terms or any small detail. Feel free to ask. Fundamental details solves many doubts later if we clear them at early stages.