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M- PANEL ELEMENTS
 

 
 
 
 
   
 
     
 
     
 
   

N-  ESTABLISHING GLOBAL-STIFFNESS MATRIX

                  [S] x [D] + [P ]= 0

After beam, column, and foundation elements are placed in general stiffness matrix in directions of their global stifnesses, general stiffness matrix is established.
General stifness matrix is arranged in a variable band and does not take into account regions with zeros. STA4 makes a special point optimization that provides economical usage of memory to solve equilibrium equations at high speed. This optimization technique of STA4 minimizes band matrix by use of minimum global matrix size. Variable band matrix, which can be seen in disc shape on diagonal during analysis, provides economical usage of memory. Use of Gauss elimination, blocking technique, and 16 digits (8 bytes) reduce error making percentage in multi-unknowns that occurs because of numeric operations.
 

 
 
 
 
 

O- MODAL  ANALYSIS

Modes and periods of system are found by modal superposition. While finding periods of structure, deflections without vibration and stiffnesses in rotation directions are also considered.
 

 
 
 
 
   
 
 
 
 

STA4 programme forms global rigidity matrix by taking into account effects of a nonorthogonal structure on rigidities of foundation and soil.  [K] KA matrix is obtained by eliminating part of [K] matrix that consists of non-vibrating deflections and rotations ( qx, qy, dz  components at joint point of structure and foundation). Therefore matrix that considers structure+foundation interaction participates in modal analysis. The matrix that is obtained is story matrix. 

Getting special values:
 

 
 
 
 
   
 
 
 
 

R- TRANSFORMING FROM FREQUENCY EQUATION TO SPECIAL VALUES
 

 
 
 
 
   
 
 
 
 

   Special values are obtained from above determinant by Jakobi method.

 

 
 
 
 
     
 
 
 
 

These equations are solved and special vectoral matrices of each mode are found.

a) Analysis option according to earthquake code

If T.D.Y. is applied, special period of structure is found by solving only 1. mode. By this special period;
 

 
 
 
 
     
 
 
 
 

b) Dynamic analysis option by modal superposition

In the same way, earthquake forces of floors in accordance with T.D.Y. are obtained. Calculating ratios for each i mode;
 

 
 
 
 
     
 
   
 
 

Sa and Sd (acceleration or displacement) spectrum values of each mode are taken from soil acceleration spectrum curves.
 

 
 
 
 
     
 
   
 
 

Matrices of force of inertia are found for each mode. Elastic earthquake forces are calculated for each mode.
 

 
 
 
 
     
 
     
 
   
 
 

If earthquake force found by dynamic analysis to earthquake force found by equivalent earthquake load method ratio is smaller than 1, in accordance with minimum equivalent earthquake method, increased by;
 

 
 
 
 
   

S- CALCULATING MAXIMUM VALUES OF BEAMS

Maksimum moment and shear forces at end points of beams are classified in following groups:

a) Dead load (1. Combination)
Mg      : Beam dead load end moment
Mdg    : Beam dead load reduction moment

b) Moving load (2-7 Combinations)
Mpu    : Maximum live load end moment
Mdpu  : Maximum live load reduction moment
Mpa    : Minimum live load end moment
Mdpa  : Minimum live load reduction moment

c) Soil Effect (8. Combination)
Mz      : Soil effect end moment
Mdz     : Soil effect reduction moment

d) Earthquake load (9-12 Combinations)
Me      : Earthquake loading end moment
Mde    : Earthquake loading reduction moment

e) Wind load (13-16 Combinations)
    Shear forces are found in the same way according to maximum values and  load combinations.
 

 
 
 
 
 

T- DEFINING BEAMS THAT ARE CONNECTED TO THIN SHEAR WALLS AS ELASTIC SUPPORTS

If elastic supporting that occurs due to local deformations in shear walls is to be considered in beams that are connected to thin shear walls perpendicularly by fixed supports, from options part of the programme first REINFORCED CONCRETE OPTION then BEAM REINFORCED CONCRETE OPTION is selected.
In 'elastic support at beam ends option' of menu, programme makes analysis according to the method offered by Muzaffer IPEK (Refer to bibl. 19) that takes into account fictitious column width as follows. However, due to rigidity assumption analysis is performed according to rigid connection assumption.

 

 
 
 
 
 
 
     
 
     
 
   
 
 

Due to tests made by STAAD-III programme;
 

 
 
 
 
     
 
   
 
 

Results that are obtained by considering local deformation effects of the beam that is connected tp wide shear walls by fixed supports in the above figure on the column that functions as a vertical slab due to elastic support hypothesis and results that are obtained by STA4CAD are compared below.

Elastic support analysis by STAAD-III
 

 
 
 
 
   
   
   
 
 

d) Analysis of wide shear wall column by considering slab element as finite elements;

Evaluation of results;
Beams that are put on strong columns perpendicularly are analysed by STAAD-III and STA4 programmes and analysis results are compared. In analyses that consider fictitious column widths and elastic supports, STA4 programme gets accurate results in accordance with values in (d) choice. Therefore, STA4 programme makes analysis by finite elements method in accordance with both elastic support and fictitious column width hypotheses.
 

 

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This site was last updated 08/05/10