HEIGHT OPTIMIZATION OF A STEEL WELDED I-BEAM IN AREAS AT THE SUPPORTS

Abstract

 The  article  presents  the  results  of  optimization  of  the  consumption  of  steel  of  a 
single-span articulated beam loaded with a uniformly distributed linear load. It was assumed that its 
composite I-beam cross  section was  selected according to the  maximum  bending  moment  in the 
middle of the span from the condition of strength at normal stresses. It is taken into account that 
when  moving  away  from  the  middle  of  the  span  to  the  supports,  bending  moments  decrease. 
Accordingly, the necessary moment of resistance decreases. 
The  study  relied  on  the  fact  that  in  order  to  save  steel,  it  is  possible  to  reduce  the  cross-
sectional  dimensions  of  the  beam  in  areas  near  the  supports.  This  was  achieved  by  reducing  its 
height. 
The restrictions on the height of the beam on the support were taken into account, based on 
the condition of shear strength. 
The minimum slope of the lower belt was determined based on the fact that in any place along 
the length of the beam strength at normal stresses was ensured. This is due to the fact that with a 
fixed  height  of  the  beam  on  the  support  and  a  decrease  in  the  slope  of  the  lower  belt,  the 
consumption  of  steel  on  the  beam  decreases.  To  solve  this  problem,  an  analytical  formula  is 
obtained for the bearing capacity of the beam in the form of a maximum bending moment, which 
can perceive a cross section at a certain distance from the support. 
The slope of the lower belt was selected so that the bending moment from the load at each 
point of span did not exceed the load-bearing capacity of the beam. 
A technique is proposed for determining the height of the beam on the support, which satisfies 
the condition of shear strength and corresponds to the minimum consumption of steel on the beam. 
For this, the function of steel consumption for half the beam was compiled and its minimum was 
determined. Recommendations are given for solving this problem using a computer program. The 
graph  of  the  dependence  of  the  function  of  steel  consumption  from  the  beam  height  was 
constructed. This graph has a minimum. 
The effectiveness of reducing the height of the beam in areas near the supports was estimated 
by a coefficient that is the ratio of the minimum height of the beam  from the condition of shear 
strength to the height of the beam in the middle of the span. The smaller this coefficient, the closer 
to the plot of bending  moments from the calculated load will  be a graph of the bearing capacity 
function. In this case, the steel consumption will be less. 
It was found that with a decrease in the linear load on the beam and the flexibility of the wall, 
as well as with an increase in span, this coefficient becomes smaller. Therefore, it is recommended 
to  reduce  the  height  of  the  beam  in  areas  near  the  supports  at  relatively  small  loads  and  wall 
flexibility and relatively large spans.