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Masonry Buildings according to Eurocode 6

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Design   Methodology

  • masonry design according to Eurocode6, EN 1996-1-1:2005
  • concrete design according to Eurocode 2
  • foundation design according to Eurocode 7
  • seismic design according to Eurocode 8
  • roof design according to Eurocode 5

The Design of the masonry buildings is based on the assumption that the maximum part of the vertical and horizontal loads are taken from the masonry.
The design of concrete floors in vertical loading is performed considering the beams as space grillage. The live loads are placed on the spans to obtain the worse loading conditions. The concrete slabs are solved using the Marcus method.

The horizontal seismic forces on each floor are considered as equivalent static loads. The floors are assumed to act as horizontal stiff diaphragms. For the distribution of the seismic forces on the walls,  the stiffness of each wall is computed using  finite element analysis. 

The wall stresses are computed by finite element analysis of each wall on its plane. These stresses are used for the strength checks according to Eurocode 6.

If some checks for the masonry are not verified they will appear with red font in the reports. In that case you must change masonry dimensions or materials, or masonry mortar 

  Slabs

The topology of slabs, the surrounding beams and walls, the shape and elements needed for the slab analysis are automatically recognised by the program expert system. The user has complete overview of the topology and all the analytical computations in the reports. The design of concrete slabs is based on the Marcus method.

In masonry building, in most cases, the plate arrangement is simple and almost orthogonal. In that case the solution using the Marcus method produces satisfactory results. This method is based on the solution of unit plate strips located at mid spans, with equal deflections at the plate center. From this assumption  the plate load distribution in the two main  directions is obtained. The advantage of the plate torsional resistance is not taken into account. Each plate strip is solved as a continuous beam. The solution is obtained through specific coefficients, which are obtained from the solution of continuous beams of equal spans. These coefficients are considered having such values as to obtain the maximum internal forces. The minimum (maximum in absolute value) support bending moments are obtained using the most unfavourable position of live loads in an equivalent continuous beam. The maximum (minimum in absolute value) support moments are obtained using the most favourable position of the live loads. From these support moments  the maximum span moments are obtained using span loading 1.35g+1.50 q.

The loads transferred on the beams and the walls are obtained by loading with live loads both slabs on the left and right side of the beam or wall. In the case of slabs with span ratio over 2, or load factor <0.10, the load is transferred only in one direction. In this case the beams which doe not take load from the slab are loaded with a minimum uniform load equal to wL/4, where w=1.35g+1.50q. (g,q dead and live load of the plate, L the beam span).

The design for ultimate strength is done according to Eurocode 2 �4.3.1. The design for serviceability conditions is base on control of the slenderness ratio (EC2 �4.4.2.3). In addition the minimum steel reinforcement requirements are verified. The minimum cover for steel reinforcement is set to 20 mm which satisfies the code requirements (EC2 �4.1.3.2) for dry or humid environment.

  Beams

The concrete floor beam system is designed as a system of beam grid. The structural analysis is done with finite elements. The finite elements are beams with 3 degrees of freedom per node, rotations around x-x and y-y axis and vertical displacement along the z-z axis. The grid is supported on the walls and the columns. When the wall is not parallel to the beam axis the rotations are zero. For the computation of the beam stiffness the effective flange width is taken 0.70L/10 for each beam flange (left or right).

The solution is done for unit uniform loads on each span of the grid. The most unfavourable load combinations are obtained with combination of the results of the unit loads (1.35g and 1.50 q). The solution is performed using Gauss method for symmetric banded matrices.

The dimensioning of beams is according to Eurocode 2. For the design the support bending moments are taken at a distance 10 cm from the support (wall or column) axis. The design shearing force values are taken at a distance d (beam height) from the support face (EC2 �4.3.2.3). The effective flange width is taken 0.70L/10 for each beam flange left or right. The minimum reinforcing steel coverage is set to 50 mm that satisfies the code requirements (EC2 �4.1.3.2) for dry or humid environment. Only straight reinforcing steel bars are used for main reinforcement, and the shear force is taken only with vertical stirrups. The minimum requirements for steel reinforcement are verified. The verification of crack width requirements and maximum deformations are done according to (EC2 �4.4.2).

    Masonry Walls

The masonry walls are carrying most of the vertical and all the horizontal loads.

The computation of the horizontal seismic forces for each floor level is based on equivalent static loads.  The floors are assumed to act as horizontal stiff diaphragms. The vertical distribution of the seismic loads is "reverse triangular". The horizontal seismic force acts at the mass center of each floor. The center of rigidity of each floor is computed using the stiffnesses of the walls at each floor. The wall stiffness depends on the wall dimensions and the dimensions and positions of the openings. The wall stiffness is computed with a finite element analysis of each wall, for unit relative displacement between the top and bottom wall ends. The eccentricity between the rigidity center and the center of mass of each floor is taken into account, in the distribution of the horizontal seismic forces on the walls. After the computation of the horizontal loads the evaluation of the internal stresses of the walls is also done with a finite element analysis, for the various load combinations.

The design for the masonry is performed for the ultimate limit state based on Eurocode 6, chapter 4. All the checks for loading cases 1.35g+1.50q, and  1.00g+0.30q+earthquake, are performed for compression, and shear. In addition verification of slenderness ratio requirements and checks for strength at stress concentrations are performed according to Eurocode 6.

The stresses of each element normal stresses �xx, �yy, and shearing stress �xy are printed on the report. Color view or printouts of the stress distribution for each loading case, can be obtained.

 

 

The design checks according to Eurocode 6 are

 Nsd<Nrd, Nrd =design vertical load resistance (Eurocode 6 �4.4.1).

Nsd  Vertical design load (vertical load per unit length). It is obtained from the results of finite element solution (the regions of stress concentrations at beam supports are excluded).

 

  •  �i,m is the capacity reduction factor, which takes into account the effects of slenderness and eccentricity of the loading. The eccentricities for the computation of capacity reduction factors are computed from the loads on the slabs and beams based on Eurocode6 �4.4.3 and appendix C.

  • t : is the wall thickness,

  • fk : is the characteristic compressive strength of the masonry which is obtained based on Eurocode 6 chapter 3, for each masonry type depending on the masonry units, and the masonry mortar.

  • �M : is the partial safety factor for the material according to Eurocode 6 table 2.3.                                                                                 

The slenderness ratio check is performed based on Eurocode 6 �4.4.4.3. The effective height of the wall is taken hef=�h h. The coefficient is computed for partial or complete restrain on the top and bottom of the wall and we consider �3=�4=1 for vertical wall edges, as most unfavourable.

The shear verification is done according to Eurocode 6 �4.5.3.

Vsd<Vrd.

Vsd is the applied shear load (horizontal force per unit length). It is obtained from the results of finite element analysis (excluding stress concentrations at beam supports).

 

 The maximum compressive stresses obtained from finite element analysis at the places of beam supports are verified according to �4.4.8 to be less than fk/fM.

 
  • Foundation

The building foundation is assumed in the same ground level. All the footings are connected in both directions with foundation beams. The minimum width of foundation is computed according to Eurocode 7.

  • Seismic Design

The seismic design is based on equivalent static loads at the level of each floor according to Eurocode 8. The total seismic force is defined proportional to the total vertical load, by a factor defined as the ratio of the horizontal seismic ground acceleration to the acceleration of gravity g. The distribution of the seismic force is a reverse triangular distribution. At each floor the eccentricity of the horizontal loading is computed. The horizontal load of each floor is applied to the mass center of the floor, and the building is assumed to rotate around an elastic axis. The elastic axis is defined as the axis passing through the elastic center of the floor, which is more near to the level 0.8H, where H is the building height. A factor (with default value=0), can be adjusted in the program, and it multiplies (increasing) the computed load eccentricity.

  The Finite Element method

With the finite element method a continuum with infinite number of degrees of freedom is approximated with a discrete system of elements connected only at a finite number of nodal points. The solution of the problem is reduced to a discrete number of equations, from which the unknown values at the nodal points are obtained.

The method of finite elements has founded in the end of 1950 by Argyris, Turner and Clough. After that an increasable number of theoretical work and computer programs together with the rapid developments in computer power made the finite element method a powerful tool of analysis in all the branches of applied science.

In the program we use plane stress quadrilateral elements with four nodes. The finite mesh is obtained automatically keeping an element ratio (width to height) less than 2. The solution algorithm and the accuracy of the results have been checked with other well established programs, SAPIV, STRUDL.

Basic directions

Which Buildings can be designed with the program

With the program you can design buildings, for which the major part of the loads is taken from the masonry. All the horizontal seismic forces are taken from the masonry. There may exist some columns from reinforced concrete but they do not take any seismic loads. The stiffness of the columns is negligible compared with the masonry wall stiffness.

The shape of the building must be simple and the shape of the slabs about orthogonal.You enter only the bearing walls, not the non-bearing separation walls.

Codes that are applied

The dimensioning of the concrete elements (slabs, beams, columns, footings) is based on Eurocode 2. The masonry dimensioning is based on Eurocode 6. The timber roof design is based on Eurocode 5. The load evaluation and action combinations are based on Eurocode 1. The foundation design is according to Eurocode 7. The seismic forces are computed according general acceptable methods in most seismic design codes and Eurocode 8.

Slabs

Slabs are designed with the method of Marcus. Non-orthogonal slab shapes must be avoided.

Beams

Beams are designed as space grid.

Masonry

On the top and along each masonry wall, and on top of the openings, we assume the existence of small concrete beams that are taking the small tension stresses.

Columns

The columns must have orthogonal cross section, with about equal dx and dy dimensions. Long columns must be replaced with masonry elements. The columns are designed in biaxial bending and the reinforcing steel is considered symmetric on each column side.

Column Footings

Colunm Footings are considered as centric footings. Some small moments are taken from connecting foundation beams.

 

What you cannot do

1) You cannot have columns on top of slabs, beams, or walls. A column must continue with a column underneath.
2) You cannot have a wall under two walls or a wall on top of two walls. A wall must have a wall underneath.
3) You cannot have flat slabs.

 


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