The image you uploaded contains several structural analysis problems that seem to focus on beam analysis under different loading conditions. Below is an overview of the problems:

1. Problem 4.11: A beam $AC$ is supported at points $A$ (fixed) and $C$ (roller) with distributed and point loads applied. Distributed loads of 6 kN/m over 2 meters and 15 kN/m over 6 meters are applied between points $A$ and $B$, and another distributed load of 12 kN/m from point $B$ to $C$.

2. Problem 4.12: A continuous beam $AE$ supported at five points $A$ (fixed), $B$, $C$, $D$, and $E$ (rollers). It has both point loads and distributed loads applied, including a uniform load of 3 kN/m between $A$ and $B$, and point loads at other sections.

3. Problem 4.13: A beam $AE$ with four support points (at $A$, $B$, $C$, $D$) and a combination of point loads and distributed loads, including a 10 kN load at point $A$ and distributed loads of 8 kN/m and 6 kN/m over different sections.

4. Problem 4.14: A beam $AD$ subjected to distributed loads of 10 kN/m and 8 kN/m, as well as a smaller 5 kN/m distributed load. The beam is supported at points $A$, $B$, and $D$.

5. Problem 4.15: A cantilever beam with a moment $M_A$ and vertical reaction $V_A$ at the fixed end, and a 20 kN point load at the free end $B$.

6. Figure 4.44: Similar to Problem 4.15, but includes two regions of the beam, each with different flexural rigidity (denoted as $1.5EI$ and $EI$), indicating a varying cross-section or material along the length of the beam.

These problems generally involve solving for reactions, shear forces, and bending moments along the beams. You would likely need to:

• Apply equilibrium equations (sum of forces and moments).
• Use shear force and bending moment diagrams.
• Possibly use compatibility conditions or superposition for continuous beams.

Would you like help with solving a specific problem from these, or should I provide an example step-by-step solution?

Here are five related questions:

1. How do you calculate the reactions at supports for a simply supported beam with distributed loads?
2. What is the significance of shear force and bending moment diagrams in structural analysis?
3. How do you handle continuous beams with multiple supports when calculating internal forces?
4. How does varying flexural rigidity ($EI$) along a beam affect its deflection and internal moment distribution?
5. What are the key assumptions in solving structural beam problems, particularly for cantilevers and simply supported beams?

Tip: When analyzing beams with multiple sections, break them down into individual segments and solve for reactions and internal forces step-by-step to avoid confusion.