Old theory

Question 1

The formula (6.4) of EC6 for the computation of the reduction coefficient for the strength of walls subjected to vertical loads is fi = 1 – 2 ei / t. Please explain (deducing - HÄRLED) why (1 - 2 e / t) appears in this expression.

Answer 1

From the formula: NRd=tfd
se härledning i dokumentet

Question 2

Please explain what intends to represent in the following w3L3/(4(n-1)) formula of EC6, Annex C (where ni = 4 or 3 depending on the boundary conditions).

Answer 2

This part represents the moment on the wall from the uniformly distributed load on number 3.

Question 3

Explain why the pavements deformability is a relevant issue for the seismic behaviour of buildings, particularly for masonry buildings. Which deformability are we talking about?

Answer 3

If floor/pavements have low deformability (like rigid floors, concrete) are more likely to distribute the force due seismic forces across the building’s frame, ensuring an even distribution of horizontal forces through the walls. This leads to that the forces are more evenly shared between the walls and support structure, potentially reducing localized stress points and preventing structural failure. Floor strucutres with high deformability are less likely to distribute the forces. While floors need to be rigid to distribute forces evenly and prevent collapse, walls need specific properties to work effectively with rigid floors. They need to be stiff enough to contribute to the stability of the building, but also ductile enough to deform without cracking or collapsing.

Flexural deformation - böjmotstånd - hänvisar till böjningen av ett element.

Question 4

Explain why the infill in the extrados of arches (and vaults) is important for the stability of the
arched structure.

Answer 4

Essential for distributing loads, providing structural support, increasing stability, and protecting the structure. Important due to:
- The compression increases the friction between the arch elements.
- The trust line has a profile closer to the circular.
- The trust line can “be outside” of the arch thickness.
- Horizontal (lateral) movement is restricted.

Question 5

Specify which commands are used to create blocks (only with respect to their geometry) in the construction of an UDEC arch model.

Answer 5

To create a block you use “block create polygon (x1,y1) (x2,y2) (x3,y3) (x4,y4)”
And to create a specific geometry for example an arch continues with “block cut crack (x1,y1) (x2,y2)” and then you need to do that for external and internal arches.

Question 6

Explain how it is possible in the UDEC software to assess the steady (or colapse) state of an arch without this being visible in the arch image that is displayed on the screen.

Answer 6

To check the unbalanced force diagram, to check if the point is stable or not.

Question 7

If, on the basis of simplistic hypotheses (e.g. those of the Mery method), the drawn pressure line (or thrust line) it is not within the thickness of the arc, what conclusion can be drawn about the stability of the arc?

Answer 7

If the arch is outside, it’s unstable.

Question 8

Assuming that the situations depicted in the following figure refer to a building with masonry structure with a reinforced concrete slab (indeformable diaphragm), explain if there is a difference between the two cases, with respect to the intensity of the seismic force which is transmitted to the wall A. Please justify your answer.

(ena är 2a och andra uppdelad i a och a)

Answer 8

The reinforced concrete slab acts as a rigid diaphragm, meaning it will distribute the seismic forces uniformly to the walls. In both scenarios, the short wall in the middle is connected to the reinforced concrete slab, and the slab will distribute the seismic forces to all connected walls. However, the total areas are still the same and therefore will the wall take up the same intensity in both cases.

Question 9

Describe the commands you should use in the UDEC software to create a 1m by 1m square block and then transform it into two 1m by 0.5m blocks.

Answer 9

Block create polygon (0,0) (0,1) (1,1) (1,0)
Block cut crack (0,0.5) (1,0.5)

Question 10

Explain how it is possible in the UDEC software to assess the collapse state of an arch without this being visible in the image of the blocks that is displayed on the screen.

Answer 10

Check the unbalanced force diagram to see if the forces reaches steady state or not.

Question 11

In current cases, in cavity walls only one of its leaves is vertically loaded. Explain how the unloaded leaf contributes to the strength of these walls and how the EC6 considers this effect in the safety assessment of cavity walls mainly subjected to vertical loads.

Answer 11

The effective thickness of a cavity wall in which both leaves are connected with wall ties should be determined by tef . Because we get a stronger element with the connections and can avoid buckling because both walls are working together and therefore we need to consider both of the thicknesses. Even though the unloaded leaf is not directly bearing vertical loads, it participates in the overall load distribution of the wall system. Non load bearing leaf is used to increase the stiffness of the leafs assembly

Question 12

A wall panel subjected to a shear load in his plane may collapse in three different ways. Identify these three shear failure modes and explain how EC6 considers these effects in the proposed methodology for the in-plane shear safety assessment.

Answer 12

Rocking&crushing
Sliding
Diagonal Cracking

EC6 provides guidelines for calculating the tensile and shear strength of masonry materials, accounting for factors such as material properties, mortar characteristics, and geometric configurations.

Question 13

Explain why differences in the deformability of the bed joint mortar and of the units is relevant
for the masonry compressive strength.

Answer 13

Differences in deformability between mortar and masonry units are relevant to the compressive strength of masonry due to how loads and deformations are distributed throughout the structure. This may involve selecting mortar with similar or compatible deformation characteristics to ensure that loads are evenly distributed and that the masonry maintains its structural integrity under compressive loads.

If the mortar is not stiff enough the wanted deformation of the mortar will produce tension in the unit.

Question 14

The simplified approach for calculating eccentricities at the top and bottom of walls proposed by British Standard 5628 (e = t / 6) gives reasonably good results in current situations and for interior walls. Explain why this methodology does not lead to good results for external walls (i.e. walls supporting slabs only in one of its sides).

Answer 14

The British standard can only be applied if the spans are almost equal on both sides. It should also be mentioned that the British standard can not be used due to uneven load distribution, increased eccentricity and risk for overestimation or underestimation. So, the British standard should not be used on external walls due to the unique loading conditions and support configurations.

Question 15

Explain why the use of wooden floors is not recommended in buildings with more than one
floor in areas of high seismic risk.

Answer 15

Wooden floors are more flexible than masonry ones. Wooden floors are not good to use in areas with high seismic risk due to its high deformability, that leads to that the wooden floors take up all horizontal (lateral) force and do not distribute the forces along the wall structure. Semic forces can have significant horizontal accelerations that create displacements in the building, and the floor must withstand these forces to maintain the structure.

Question 16

When designing structural masonry buildings the walls location and the floors nature are important issues to take into account. Please list the most important issues (from the structural point of view) to be taken into account while designing those buildings.

Answer 16

• The openings should be in the same location on all the planes, and avoid irregular distribution of the walls.
• Avoid discontinuous walls
• Avoid concentration of walls
• Openings should be limited
• Continuous load bearing walls from bottom to top of the building
• Shear walls in both directions
• Use rigid floors

Question 17

Explain why Eurocode 8 and other design rules indicate that the level of reinforcement in
reinforced masonry should not be too high.

Answer 17

• High levels of reinforcement can reduce the ductility of reinforced masonry structures. Ductility is the ability of a structure to undergo large deformations without failure, which is crucial in seismic design for absorbing and dissipating energy from earthquakes.
  Eurocode 8 specifically addresses the design of masonry structures in seismic regions and emphasizes the importance of balancing reinforcement levels to achieve desired seismic performance.

Question 18

Explain why the safety assessment rules and design methods for reinforced concrete structures
cannot be used in masonry arches.

Answer 18

Reinforced concrete structures and masonry arches have fundamentally different ways of carrying loads and reacting to stresses. In reinforced concrete, steel bars are added to carry tensile stresses, therefore concrete structures can be designed to handle both bending and shear, while arches are very weak in tension.

Reinforced concrete behaves as a relatively homogeneous material due to the integration of concrete and steel reinforcement. Masonry is a heterogeneous material with distinct units (bricks or stones) and mortar joints, leading to complex stress distributions and weaker points at the joints.

The collapse of arches occurs without high stresses or significant deformations, while reinforced concrete often yields or crushing of concrete..

Question 19

The discrete elements method is a dynamic method that simulates the movement of discrete
blocks. Explain the trick that allows this method to be used in static analysis..

Answer 19

The trick that allows the discrete element method to be used in static analysis is the application of dynamic relaxation.

Question 20

It is well known that the “box behaviour” in masonry buildings is an important issue for the seismic resistance of these buildings. List the aspects to be considered when designing and detailing masonry buildings to ensure this “box behaviour”.

Answer 20

“Box behaviour” in masonry buildings refers to the concept where the different components of the building (walls, floors, and roof) work together as a cohesive, three-dimensional unit to resist lateral forces such as those generated by earthquakes or wind loads. Achieving box behaviour is crucial for the structural integrity and seismic performance of masonry buildings. Buildings with effective box behaviour are better able to withstand seismic forces as the loads are distributed throughout the structure, reducing the risk of localized failures.

• Stiff Floors and Roofs (Rigid diaphragm floors): Design floors and roofs to act as rigid diaphragms that can transfer lateral loads to the walls.
• Shear walls: Strategically place shear walls to effectively resist lateral forces and distribute them throughout the structure. The shear walls are mobilized in their most favorable way (in their plane / INPLANE). Optimal distribution of horizontal loads by the shear walls.
• Shear walls in the 2 main directions of the building (continuously from the foundation to the roof).
• The location of these (shear) walls should be such that the centre of rigidity of the building and its centre of gravity are close together..
• Wall-to-Wall Connections: Use mechanical ties, steel reinforcements, or concrete beams at the intersections of walls to ensure rigid connections.

Question 21

Explain why the flexural strength of a masonry panel is substantially higher if the bending is of type b) shown in figure 1.

Answer 21

The characteristic flexural strength of masonry fxk2 is about 3 times the resistance in the other direction (fxk1). This is because in figure 1b) the structure is subjected to bending around the strong axis, while in figure 1a) we have bending around the weak axis. Bending around strong axis is generally more resilient due to the higher tensile strength of masonry units in this orientation.

Svårare att böja masonry inåt än vika ihop.

Question 22

Explain the importance of floor stiffness with regard to the seismic behaviour of masonry buildings. Which type of floor stiffness is relevant for this purpose – the horizontal or the vertical stiffness?

Answer 22

Horizontal stiffness is essential for seismic performance because it directly influences how well the floors can act as diaphragms. A floor with high horizontal stiffness can effectively transfer lateral loads to the vertical structural elements (walls and frames), ensuring a more uniform and stable response during an earthquake.

While vertical stiffness is important for the general load-bearing capacity of floors, vertical stiffness ensures that the floor can support vertical loads, such as the weight of occupants and furniture.

For the seismic behavior of masonry buildings, horizontal floor stiffness is of paramount importance. It ensures effective distribution of lateral forces, maintains structural integrity, minimizes deformations, and enhances the building’s ductility and energy dissipation capacity.

Question 23

Explain why Eurocodes 6 and 8 indicate that shear walls should be axially loaded.

Answer 23

Axial loading increases the compressive stress in shear walls, which enhances their ability to carry lateral loads. Proper axial loading contributes to the ductility of shear walls, which is essential during seismic events. Masonry is weak in tension. Axial loading helps ensure that the stresses within the wall remain compressive, thus preventing the formation of tensile cracks