Order of work
1. Determine the bar buckling form according to the given fix scheme and draw elastic curve axis. determine the number of half-wave n and length coefficient μ.
2. calculate the cross-section dimension using the allowable stress [σ] for simple compression.
the analysis should be carried out by the successive approach method preliminarily choosing the factor φ = 0.5 ... 0.6 (Table 13).
Table 13
Slenderness |
Factor for |
||||||
Steels |
Alloys |
||||||
Steel 20 Steel 25 |
Steel 35 Steel 45 |
14Г2 15ХСНД |
АДЗ1-Т АМгМ |
АМгП АМгбМ |
АВ-ТІ |
Д16Т |
|
0 |
1,00 |
1,00 |
1,00 |
1,000 |
1,000 |
1,000 |
1,000 |
10 |
0,99 |
0,98 |
0,98 |
0,973 |
0,998 |
0,998 |
0,990 |
20 |
0,97 |
0,96 |
0,95 |
0,945 |
0,997 |
0,996 |
0,980 |
30 |
0,95 |
0,93 |
0,92 |
0,917 |
0,943 |
0,900 |
0,835 |
40 |
0,92 |
0,89 |
0,89 |
0,870 |
0,830 |
0,780 |
0,700 |
50 |
0,89 |
0,85 |
0,84 |
0,770 |
0,725 |
0,660 |
0,568 |
60 |
0,86 |
0,80 |
0,78 |
0,685 |
0,628 |
0,553 |
0,455 |
70 |
0,81 |
0,74 |
0,71 |
0,603 |
0,538 |
0,463 |
0,352 |
80 |
0,75 |
0,67 |
0,63 |
0,530 |
0,460 |
0,387 |
0,290 |
90 |
0,69 |
0,59 |
0,54 |
0,465 |
0,388 |
0,332 |
0,227 |
100 |
0,60 |
0,50 |
0,46 |
0,415 |
0,332 |
0,285 |
0,185 |
110 |
0,52 |
0,43 |
0,39 |
0,365 |
0,283 |
0,236 |
0,153 |
120 |
0,45 |
0,37 |
0,33 |
0,327 |
0,243 |
0,200 |
0,127 |
130 |
0,40 |
0,32 |
0,29 |
0,296 |
0,210 |
0,171 |
0,110 |
140 |
0,36 |
0,28 |
0,25 |
0,265 |
0,184 |
0,147 |
0,095 |
150 |
0,32 |
0,25 |
0,23 |
0,235 |
0,160 |
0,128 |
0,083 |
160 |
0,29 |
0,23 |
0,21 |
- |
- |
- |
- |
170 |
0,26 |
0,21 |
0,19 |
- |
- |
- |
- |
180 |
0,23 |
0,19 |
0,17 |
- |
- |
- |
- |
190 |
0,21 |
0,17 |
0,15 |
- |
- |
- |
- |
200 |
0,19 |
0,15 |
0,13 |
- |
- |
- |
- |
3. determine critical force Fcr and critical stress cr for found cross section dimensions.
use Euler’s formula if λ > λlim or Yasinsky’s formula cr = a – b if λ0 λ λlim and strength condition for compression by the yield point cr = y – for plastic material and by the conventional yield point cr = 0,2 – for brittle material.
4. Draw a conclusion about the strength of determined safety factor by the stability.