(untitled) (Collection of scientific works «Modern structures of metal and wood», 2020)
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.