WORKING STRESS
1 WORKING STRESS
1.1 Problem definition
Determinate the total elongation for a bar of a given cross section.
Figure 2: Model by Timoshenko
Figure 1: Rohr2 model
1.2 References (Timoshenko)
S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, Chapter 1.4, pg. 10.
A steel bar, which is classified in three parts, is stressed by four axial forces. At the upper and lower portion, the forcevectors leave the object. The both average force vectors point to the beam center. Timoshenko gives the following parameters:

Cross section

Length

Action force (Q, P) ,

Modulus of Elasticity
,
Where:
Variable 
Description 
Unit 
Used Value 
Elongation 
inch 
0,008333 

Length 
inch 
10,00 
Modulus of Elasticity 
lbs/ inchÂ² 
30000000 

Cross section 
inchÂ² 
1,00 

Force 
lbf 
10000 

Force 
lbf 
5000 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
The ROHR2 model consists of three equal vertical parts of a cylindrical carbon steel beam, which are 10 inch long. In this example the bars have the cross section of 1 inchÂ² â‰™6,4516 cmÂ². It is implemented by setting the dimensions with diameter and wall thickness (28,7 mm x 13,6 mm). At the middle of the system it is fixed by a boundary condition (anchor). Following forcedirections are defined for several points in the ROHR2 model:

node A upwards with 10000 lbf

node 1 downwards with 5000 lbf

node 3 upwards with 5000 lbf

node B downwards with 10000 lbf
For this calculation, all loads are scaled, just to recognize the elongation at the ROHR2output. The applied factor is 1000. In this case the gravity is also disable, so the beam line mass is 0 lb/ ft.
Figure 3: Î´ from the Lc Dead
Weight
Figure 4: Rohr2 model with increased loads and
sectional results
1.4 Result comparisons
Value 
Length [inch] 
Reference (Timoshenko) [inch] 
Rohr2 [inch] 
Difference [%] 
10 
0.008333 
0,008326 
<0,09 
Table 2: Comparison of the total elongation for point A and B
Value 
Cross section (Timoshenko) [inchÂ²] 
Cross section (Rohr 2) [inchÂ²] 
Difference [%] 
1,0 
0,9999 
<0,01 
Table 3: Comparison of between required and used cross section
1.5 Conclusion
The results are close to the references by Timoshenko. The very small difference appear, only because of the cross section definition, which is not exactly defined enough. In ROHR2 you get at every end point (A, B) just the half displacement. So the user had to multiply the results of the program by a factor 2.
1.6 Files
R003_inch.r2w
R003_mm.r2w
R2_stresses_3.ods
SIGMA Ingenieurgesellschaft mbH www.rohr2.com