Fase positiva

Output results are not created unless the user specifically demands them. Firstly, it is defined for what the results are required (e.g. load case number), then comes the choice of the quantities (e.g. section forces), a possible component (e.g. mx) and finally the

presentation form (e.g. isolines), which can still be influenced by certain parameters. From a list one first chooses for what the results are wanted. The list contains S All input load cases

S Any defined load case combinations

S All automatically or manually produced limit state specifications S Required reinforcement

Load case combinations are fixed combinations of load cases provided with arbitrary factors, of which the user can define as many as desired. In the output of results they are treated in exactly the same way as individual load cases.

The quantities for load cases and load case combinations

Deformations:

With the deformations it is a question of settlement as well as the rotations about the x and yaxes, respectively, in each node of the FE mesh. The rotations of nodes not acting as supports are output in the global coordinate system. For point and line sup ports the xdirection of the input object is adopted and the ydirection normal to it. The xaxis of line supports shows the support direction.

Section forces:

The slab section forces consist of the moments mx, my, mxy and the shear forces vx, vy.

The following figure shows the forces acting on an infinitesimal slab element: The output of the slab section force is carried out in zonewise definable output direc tions. The transformation formulas are as follows (Mohr’s circle for the moments and vector transformation for the shear forces):

Depending on the form of output the principal moments or the maximum shear forces are output.

A 2 Basic Theory Part A Base Module

x y mxy mxy mxy mxy mx mx my my vx vx vy x y z mxy mxy vx vy mx my vy mxy mxy mx my vx vy x y f

mx+ mxcos2f ) mysin2f ) 2mxysinf cos f

my+ mxsin2f ) mycos2f * 2mxysinf cos f

mxy+ * (mx* my) sinf cos f ) mxy(cos2f * sin2f)

vx+ vxcosf ) vysinf

vy+ * vxsinf ) vycosf

vmax+ v

Ǹ

Reactions:

The reactions, arranged node− and elementwise, are output according to the individual supports. In the graphical output of the line supports the possibility exists, of combining the nodal reactions in sections, provided the section length is given.

For nodes with prescribed support movement, for the corresponding load cases no reac tions can be output.

Storage of reactions:

The reactions can also be stored and introduced as loading on an underlying floor.

Quantities for limit state specifications (envelope values)

Deformations:

One can obtain the envelope values of bending deflection with the associated rotations.

Reactions:

All kind of reactions results are available as envelope values, except the combined nu mericalgraphical output, .

Reinforcement moments:

The slab section forces are combined to reinforcement moments according to the com bination rules specified in the limit state specifications.

The reinforcement moments at a point are the four moments required to determine the slab reinforcement in two orthogonal directions. Their calculation is based on the well known linearised plasticity conditions (cf. e.g. SIA 162 (1989) Art. 3 25 23):

mbx+ = Max ( mx+mxy , mx−mxy)

mbx− : negative reinforcement moment in xdirection (top reinforcement )

mby+ : positive reinforcement moment in ydirection (bottom reinforcement )

mby− : negative reinforcement moment in ydirection (top reinforcement )

The output directions are defined for each zone.

Maximum shear forces:

The maximum shear forces for a load case are calculated from vmax+ v

Ǹ

cannot be directly combined to envelope values, since a particular direction, which can be different for each load case, is associated with this maximum value. Nevertheless, in order to obtain reasonable results for such limit states, CEDRUS5 uses the following method:

vmax is not determined for each load case, but the shear force in all eight directions

shown left.

In each of these eight directions the maximum value (all positive values) and the mini mum value (all negative values) are evaluated in building the limit state values and at the end from the sixteen values carried through the evaluation the maximum absolute value is output as the envelope value.

In this way the combination of envelope values is possible and one obtains a value which is normally sufficiently accurate. The associated directions are also part of the numerical output, in addition to the envelope values.

Required reinforcement

The required top and bottom reinforcement of the slab in two orthogonal directions (axt

and ayt for the top, axb and ayb for the bottom) is determined on the basis of design limit

values of the reinforcement moments described above.

For the dimensioning of the reinforcement in slab zones the following points are relevant:

S Dimensioning is based on the chosen limit state specification, i.e. envelop values in the from of reinforcement moments (see above).

S Each limit state specification has an associated analysis parameter set, which is specified in the limit state specification dialog. The analysis parameter set (denoted APxx) is a series of criteria for the design of a reinforced cross section. Generally two different concepts for the dimensioning of the longitudinal reinforcement are sup ported:

Strain limits for concrete in compression and reinforcement in tension: This cri terion is activated in the analysis parameter set ’AP2: ULS verification’. The AP2 is assigned by default to the limit state specification ’!Ultimate limit state’.

Tensile stress limit for the reinforcement: This criterion, providing a minimum reinforcement ratio for crack control, is activated in the analysis parameter set ’AP1: SLS verification’. The AP1 is assigned by default to the limit state specification ’!Ser viceability’. The tensile stress limit is a parameter of AP1 and must be set by the user. Besides the two criteria the user can specify a number of other parameters in the sets APx, e.g. the partial safety factors for the materials and the strain−stress relation for concrete and reinforcement steel.

S The dimensioning according to the specified code and the selected analysis para meter set is based on pure bending action of a rectangular cross section. The result is the required reinforcement area per unit width, if necessary acting in tension and compression (Therefore it could result in a bottom reinforcement at a column sup port, without a positive reinforcement moment!).

S The dimensioning for punching shear is realized independent of the bending design in the punching verification (see A 2.6).

A 2 Basic Theory Part A Base Module

1 top concrete cover bottom concrete cover reinforcement moment

S The vertical position of the reinforcement is defined via the reinforcement cover, specified in the dialogs of the material zones and downstanding beams.

. Note: the reinforcement cover is the vertical distance from the edge of the concrete body to the center of gravity of the reinforcement layer.

S In the same dialogs the material properties for concrete and reinforcement and the reinforcement direction are specified.

For the dimensioning of beam sections all the points mentioned above also apply. The following addition points, however must be noted:

S The dimensioning is based on a beam section cut off from the slab. The extension of this beam is defined by the userdefined width of the section:

width of the section top concrete cover bottom concrete cover reinforcement moment integrated over the cross section

In a beam section, like in any rectangular cross section, there is just one reinforce ment layer to be dimensioned at the top and one at the bottom. If, due to different material zones, the upper or lower edges are not constant (like in the figure above), the zone with the most eccentric edge is used for dimensioning. Note that the dimen sioning is based on pure bending only, i.e. not taking shear into account.

S Downstanding beams are treated just like ordinary beam sections, with the effective slab width determining the width of the section.

S In all beam sections the reinforcement direction is automatically taken from the direction of the section.

S The reinforcement moments to dimension for are calculated by integrating the calcu lated slab moments over the width of the section.

Forms of Presentation

The following table provides information about the possible forms of presentation for the different derived quantities:

*) Sections: These are simple sections through the corresponding contour plot. In the case of design limit values and reinforcement these section results can only be deter mined in zones, whose output direction coincides with that of the section direction or

Load cases and load case combina tions:

Reinforcement: Limit state values:

displacements

reinforcement moments displacements

stored reactions reactions columns/walls

maximum shear forces

Principal value graph. Numericalgraphical Table Axonometrical Sections *)

reactions area support zones

section forces

Beamsections **)

reactions columns

Load case file

reinforcement sections / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

Results and their form of presentation:

punching shear verifications /

Contour plot

tions. The value of the result in a point of the beam is given by the integral of the quan tities. On the other hand, in the case of reinforcement not the required reinforcement contents are integrated but the cross section of the cut out beam (e.g. a T−section in the case of an underbeam) dimensioned for the integrated action.

ÏÏÏ ÏÏÏ DS1 3) Punching shear 2) Load area 1) 2) 3) 1) Punching shear obje

(Attributebox)

(column section or polygon)

polygon

A 2 Basic Theory Part A Base Module