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The problem asks for the compression in the joints of different stacks of cubes. Let's break it down step by step:

### Key Information:
- The weight of each cube is given as \( P = 10 \) (in arbitrary units).
- There are three scenarios to analyze:
  1. The compression at the joints of the **exempt stack** (the one on the left with six cubes).
  2. The compression at the joints of the stack supporting the **beam** (the structure on the right, with the beam placed on top of two stacks of cubes).
  3. The compression at the **top and bottom stacks** that are holding up the beam.

We will calculate the compression forces (which essentially means the sum of the weight acting on the joints) for each of these cases.

### Step 1: Compression in the joints of the **exempt stack** (left pile)
This is a vertical stack of six cubes, where each cube weighs 10 units. The compression at each joint is the total weight of the cubes above that joint.

For the stack:
- Compression at the bottom joint (near point \(B\)) will be the weight of all six cubes above it.
- Compression at the joint between cubes 1 and 2 (counting from the top) will be the weight of the five cubes above it, and so on.

#### Calculation for each joint:
- Joint 1 (top cube to second cube): compression = \( P \times 5 = 10 \times 5 = 50 \)
- Joint 2: compression = \( P \times 4 = 10 \times 4 = 40 \)
- Joint 3: compression = \( P \times 3 = 10 \times 3 = 30 \)
- Joint 4: compression = \( P \times 2 = 10 \times 2 = 20 \)
- Joint 5: compression = \( P \times 1 = 10 \times 1 = 10 \)
- Joint 6 (bottom joint at \(B\)): compression = \( P \times 0 = 0 \)

### Step 2: Compression in the joints of the **stack under the beam** (right pile)
There are two stacks of cubes holding up a horizontal beam, with one additional cube placed on top of the beam.

Let’s calculate the force distribution for the joints in the supporting piles:
- The beam and the cube above it weigh \( P \times 1 = 10 \) units.
- The beam itself is assumed to be uniformly distributed across the two stacks, but the problem indicates no weight for the beam, so we will not consider it for now.

#### Compression at each joint:
For each stack:
- Joint 1 (top to second cube): This joint supports the weight of the single cube above the beam. So, compression = \( P = 10 \).
- Joints further down: Since no other cubes are added, the compression at joints further down should account for the weight of the top cube and the cubes below.

### Step 3: Compression at the **supporting joints** (under the stacks)
We can calculate the compression at the bottom of these two stacks, similar to the exempt stack from step 1. However, without specific details about the height or number of cubes, we'll assume compression similar to the previous structure.

Would you like detailed calculations for the force distribution on the beam or further clarification on specific parts of the problem?

Here are some related questions to further explore the concept:
1. How does the height of the stack affect the compression at each joint?
2. How would adding a uniform weight for the beam affect the calculations?
3. What would the force distribution look like if the cubes were of different weights?
4. Can we consider friction between the cubes as part of the compression forces?
5. How would the forces change if the cubes were stacked unevenly?

**Tip**: Compression forces increase as you move downwards in a vertical structure because the joints must support the cumulative weight of all objects above them.

Si el peso, P de un cubito es de 10 (en unidades arbitrarias), determine la compresión que hay en las juntas de la pila exenta (hasta la de la base). Lo mismo en las juntas de la pila que hay sobre la viga (sin peso) y en las que la sostienen.

Determine the compression forces at each joint in a stack of cubes, including the exempt stack and those holding a beam. Each cube weighs 10 units, and the forces depend on the total weight above each joint.

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