Let's break down the solution for each part of the question.

Part a)

You are tasked with finding the characteristic and design masonry strengths for a masonry unit used in a new construction, where:

• The unit strength $f_b$ is 12 MPa (provided).
• The masonry is made of concrete, with holes accounting for 35% of the total volume.

i) Characteristic Masonry Strength for 1:4 Cement Sand Mortar (10 mm thick)

The characteristic masonry strength depends on the unit strength and the type of mortar.

We use the formula:

$f_{m} = f_b \times (1 - k \times V_{holes})$

Where:

• $f_m$ is the characteristic masonry strength.
• $f_b$ is the unit strength of the block.
• $k$ is a constant that adjusts based on mortar type.
• $V_{holes}$ is the void fraction (35% or 0.35 in this case).

In this case, the mortar is 1:4 cement-sand, and a typical $k$ value for this type of mortar is approximately 0.15. We can plug the values into the formula for the final result.

ii) Characteristic Masonry Strength for 1:5 Cement Sand Mortar (2 mm thick)

For this case, we use the same general approach, but the difference in mortar composition can affect the $k$ value. For a 1:5 cement-sand mixture, $k$ will be slightly higher, around 0.12. Again, you would use the same equation, adjusting for the new mortar type.

iii) Design Masonry Strength with 1:4 Cement Sand Mortar (10 mm thick)

To calculate the design masonry strength, we use:

$f_{d} = \frac{f_m}{\gamma_{m}}$

Where:

• $f_d$ is the design masonry strength.
• $f_m$ is the characteristic masonry strength.
• $\gamma_m$ is the partial safety factor for masonry, which is typically 1.5.

This would be calculated using the value of $f_m$ obtained in the first part of the question.

Part b)

The owner is asking about the potential for a new opening in the restaurant wall.

Given:

• Wall thickness = 225 mm
• Brick strength = 4 N/mm² (provided)
• Mortar type = M4 (standard mortar)
• The lintel is 600 mm long and acts as a load-bearing structure.

You would calculate whether the wall can safely handle the load by determining the load distribution, the strength of the wall, and the requirements for lintel support. This would involve some structural engineering principles to check if the wall can bear the expected loads.

Part c)

The scenario involves constructing a 9” thick wall (which is approximately 225 mm) between two columns in a two-storey house.

i) Is the New Wall a Load-Bearing Wall?

You would determine if this wall is considered load-bearing by evaluating its structural position. If the wall is under a beam (as shown in the image) and supports the upper floor or roof, it is a load-bearing wall.

ii) Is it Possible to Reduce the Amount of Reinforcement in the Beam XX?

When adding a new load-bearing wall, the forces on the existing beam may change. The additional wall could transfer some of the loads from the beam to the new wall, potentially reducing the load on the beam and allowing for a reduction in the amount of reinforcement.

iii) Sketch the Load Path after the New Wall is Constructed

You would illustrate the flow of loads from the upper floor or roof to the columns and through the new wall. The load path would show how forces are transferred from the upper structures through the wall, the beam, and down to the foundation.

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If you'd like, I can assist with detailed calculations or structural analysis for these steps. Let me know if you'd like further explanations or to go through each calculation in detail.