Hey guys, so I'm trying to understand how stress analysis is done through hand calculation. The picture below shows my analysis of an example problem that I'd worked at. From that picture, I got the value of the stresses on the object which are σ1, σ2, and σ3. However, if I do the analysis differently as shown in the picture below, then... I got a different value for the stresses which are σA, σB, and σC. This got me confused, because I don't know which analysis should I use, and which distribution is the right one. Please help me solve this problem. Thank you.

Your part is not fully constrained. Your reaction force is a point load directly under the middle F. If any of the 3 forces are not perfectly balanced around the middle the part rotates. Fix that and you might be able to get an answer. Your second analysis is missing a lot of internal forces. When you break a solid block you must add the internal shear and bending moment force from A to B etc.

Okay, maybe I didn't define the problem well. Consider the object is supported by a frictionless ground, thus R is generated from the ground. There is no force on the x-direction. Maybe the picture below could illustrate the initial problem better. Also, the force F acts as a distributed load towards each step. So, it's considered three individual forces, despite the same magnitude.

Update: I've tried to simulate my problem using autodesk inventor, and below is the result. This aligns to the results obtained through the second solution. However, it still bugs my mind because I don't understand why the first solution is wrong.