SELECTING THE RATIONAL PITCH OF BEAMS FLOORING FOR THE BEAM CAGE OF A SIMPLIFIED TYPE

Abstract

The article presents the results of optimizing the pitch of beams in a beam cage of a 
simplified  type,  when  steel  beams  of  an  I-beam  profile  are  supported  on  vertical  supporting 
structures (walls, columns). Steel flooring is laid on them. 
The optimal pitch of the beams is selected so that the total consumption of steel on the beams 
and flooring is minimal. For this purpose, the objective function of the cost of steel for the flooring 
and beams per 1 m2 of flooring is compiled, the argument of which is the step of the beams. This 
function was investigated for extremum. The thickness of the flooring was adopted corresponding 
to the limiting ratio of the pitch of the  beams to this thickness  from the stiffness condition. It is 
accepted that two identical shelves and a wall of an I-beam have the form of rectangles. Moreover, 
the height of the beam is optimal and corresponds to the minimum cost of steel. 
When deriving the formula for the optimal beam pitch, it was assumed that the beam cross-
section is selected based on ensuring strength at normal stresses. In this case, the stiffness of the 
beam at the optimal pitch may not be provided. Therefore, a study was conducted for what values of 
the pitch, the rigidity of the beam is ensured when the left and right parts of the strength condition 
are equal to normal  stresses. It relied on the  solution of the  system of equations of strength and 
stiffness, which made it possible to obtain a formula for the minimum beam pitch from the stiffness 
condition. 
It was found out in which case, when the optimum pitch of the beams was found, its rigidity 
was ensured. For this, it is necessary that the flexibility of the beam wall should be at least a certain 
value. A formula is obtained for this minimum value. Her analysis showed that such flexibility is 
proportional to the design resistance of the steel to the sixth degree, that is, it grows very rapidly 
with  increasing  this  resistance.  Therefore,  in  order  to  ensure  the  rigidity  of  the  beams  at  their 
optimal  pitch,  the  strength  of  the  steel  should  be  sufficiently  small.  It  turned  out that there  is  a 
fundamental possibility to choose the step of the beams, which corresponds to the minimum cost of 
overlap. 
In  order  to  clarify  the  practical  applicability  of  the  results,  the  problem  was  solved  with 
control numerical data. The results confirmed the conclusion that low-strength steel should be used. 
In addition, it turned out that the problem makes sense with relatively large spans of beams.