Appunti di teoria

Mechanical behaviour of masonry

Mixing mode of composite material

Mortar + Bricks/Stones = Masonry

• Ductile
• Brittle
• A mean behavior between mortar and bricks/stones

The behavior depends on the regularity of the pattern or layout.

Anisotropic behavior

Anisotropic behavior refers to how the behavior depends on the direction considered. There are different ratios of moments significance, referred to as autotension, which positively affect the global strength of masonry in certain conditions.

1. Uniaxial stresses: Both mortar and brick have a low tensile strength σ_t; whereas they have relatively high compressive strength σ_c. No ci sono nei diagrammi (σ-ɛ).
2. We can set a masonry failure criterion under multi-axial stresses: Mohr-Coulomb.

• |-σ_c| >> σ_t
• ϕ = angle of di distacco interno
• c = coesione. If ϕ = 0, → non devi accept for coesione → MC becomes Tresca Criterion per Materiali Dutili

In terms of principal stresses

The field of admissible stresses is: [ -σ_c ≤ σ₁, σ₂ ≤ σ_t ]

3. MC matches the experimental data obtained on brittle materials, such as concrete, mortar, and brick. It shows that the quarry transform is an algebra. MC and σ_c understand the strength of the material in two terms.

Mechanical behaviour of masonry slide 02

Mixing mode of composite material

MORTAR + BRICKS/STONES = MASONRY

• Ductile
• Brittle
• A mean behavior between mortar and bricks/stones

The behavior depends on the regularity of the pattern or layout.

Anisotropic behavior

Different ratio of moments significance (AUTOTENSION) which positively affect the global strength of masonry in certain conditions.

1. Uniaxial stress: both MORTAR + BRICK have a low tensile strength σ_t; whereas they have a relatively high compressive strength σ_c (see σ - ε DIAGRAM).
2. We can set a masonry failure criterion under multi-axial stresses: Mohr-Coulomb.

• If φ = 0 ⇒ max shear except for cohesion ⇒ MC becomes Treca Criterion for Materials (Max stress σ allowable) Ductile.
• c in terms of principal stresses. The field of admissible stress is: MC matches the experimental data obtained on brittle materials.
• M-C + G-C underestimates the strength of the materials in some tension.
• Failure in uniaxial compression: σ is a representative solid portion of a brick masonry...

Theory for the estimation of flexure bed joints out of the brick courses. Reinforced normal component to height and width: pure stress state (Φ value) such as in the linear.

We can set the equations needed to solve the problem for uniaxial compression force S. Assumptions:

• Homogeneous, isotropic, linearly elastic material
• Combining equilibrium equations: Eq. value of km, σm is anisotropic.

We can now limit the load-bearing capacity of the masonry.

Hilsdorf’s proposal

(Less terms, simple):

1. Mild to obey to H-S
2. This example is required to safeguard failure parallel to the wall mid-plane

Fractures get into the principle tensile stresses weaker than any bar joint in characteristics of...

Note: The failure is mixed because of the appearance of vertical cracks in the micro mortar.

Fig. 6: Rigid moving block resting on a flat base

• Vertical constant load P
• Horizontal thrust T (with 1 non-dimensional multiplier)
• Friction is used to resist sliding + any overturning activated (Ad)
• Att = PB / 2FH3 = a_s ≤ a_k ≤ a_s = A totally unusable load multiplier inside known intrinsically.

1. Sliding only for small μ.
2. When overturning starts φ₀ not able to balance:

ATTENTION: Φatio [a ] N ≥ [1, Ad]

Σq = Σq₃, q_p2 = Flat* H2Φ = E→ ST R = FB

1. Shear can't be taken into account, bearing assumed starting to beam bending with all perfect behavior
2. Re-consider beam-section run-conex