VERTICAL BOND BEAM STIFFNESSES

The earthquake code states that vertical bond beams may suitably be used at building corners, at wall intermediate sections, and at the edges of door and window openings, but no guidance is given on how they should be accounted for in calculations. Therefore, there is no obligation to consider the stiffnesses of vertical bond beams under the earthquake code or the hazardous building regulation.

Assuming that the user may not wish to account for vertical bond beam stiffness, the program does not automatically split walls into segments when a vertical bond beam is drawn. If the stiffness of vertical bond beams is to be considered, it may be appropriate to draw the walls in two parts so that the vertical bond beam does not pass through the interior of each part.

If the option to include vertical bond beam stiffnesses in the calculation is checked, the stiffnesses of the vertical bond beams are taken into account. The program treats the vertical bond beam as a wall with a special stiffness coefficient acting in both the X and Y directions.

The program calculates vertical bond beam stiffness using the following formula:

Vertical Bond Beam Relative Stiffness := abs(Edh_Eds * vertical bond beam short side length (cm) * vertical bond beam long side length (cm) / 100 / 100 / Free height adjacent to vertical bond beam (m);

In the formulation:

   Edh\_Eds: Ratio of the modulus of elasticity of the vertical bond beam to the modulus of elasticity of the wall. (Relative stiffness multiplier of the vertical bond beam with respect to the walls)

   Free height adjacent to vertical bond beam: When a door or window opening exists adjacent to the vertical bond beam in the relevant direction, the free height of the vertical bond beam is the smaller of the door and window heights in the direction being calculated. When no door or window exists adjacent to the vertical bond beam in the relevant earthquake direction, the free height of the vertical bond beam is taken equal to the storey height.

   2007 Earthquake Code Table 2.1 B1 — The weak storey formula for reinforced concrete buildings is given as follows:

ΣAe = Effective shear area at any storey in the earthquake direction being considered

ΣAg = Sum of cross-sectional areas of structural system members acting as shear walls in the direction parallel to the earthquake direction being considered at any storey

ΣAk = Sum of masonry infill wall areas (excluding door and window openings) parallel to the earthquake direction being considered at any storey

Aw = Effective web area of column cross-section (excluding the area of column projections perpendicular to the earthquake direction)

ΣAw = Sum of effective web areas Aw of column cross-sections at any storey

As understood from the formula, the relative stiffness of reinforced concrete members compared to walls is 1/0.15 = 6.66 times greater. In our opinion, the value of Edh_Eds may be taken as 6.66.

In the book "Introduction to Earthquake Engineering" by Prof. Dr. Zekai CELEP, the ratio of the modulus of elasticity of the retrofit jacket to the modulus of elasticity of the wall (relative stiffness multiplier of the retrofit jacket with respect to the walls) is taken as 5. Since vertical bond beams are also reinforced concrete members, it may be considered appropriate by a similar approach to take the ratio as 5.

If vertical bond beams are considered as wall-like members acting in both directions, their stiffnesses may be taken as 1.

The earthquake code requires masonry buildings to be checked only for shear force. Furthermore, the stiffness formulation is incompatible with reinforced concrete (since relative stiffness values are used and it is a simplified/approximate formula). Therefore (also considering our discussions with academic circles), we do not regard the use of purely elastic modulus ratios as a safe method for assigning relative stiffness values to vertical bond beams.

In a consultation with Prof. Dr. Zekai Celep, he did not consider it appropriate to specially account for vertical bond beam stiffnesses in masonry structural systems that do not form a proper frame.

During visual inspections of numerous buildings carried out by our team after the Van earthquake, the following observations were made in single-storey timber-floor buildings: cracks caused by out-of-plane movement of up to 2–4 cm were observed at building corners and at wall intermediate sections; in reinforced concrete floor buildings without vertical bond beams (2–3 storeys), X-shaped diagonal shear cracks were observed in solid wall panels between door and window openings with thicknesses of 0.5–1.5 cm; in buildings with 20/20 vertical bond beams at wall intermediate sections, X-shaped shear cracks on the order of 0–0.5 mm were observed. The wall material in nearly all of the approximately 300 masonry buildings inspected was hollow block.

The initiative regarding vertical bond beam stiffnesses belongs to the user and/or the supervising engineers.