STRESS AND STRAIN PRODUCED IN A BAR BY ITS OWN WEIGHT
1STRESS AND STRAIN PRODUCED IN A BAR BY ITS OWN WEIGHT
1.1Problem definition
Verify the total elongation and cross section area of a vertical prismatical bar at axial force and of dead weight.
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 1.5, pg. 15.
Steel beam with given axial stress. The following listed values are used:

Load at lower end

Length

Working Stress

Density

Modulus of Elasticity
Where:
Variable 
Description 
Unit 
Used Value 
Total elongation 
inch 
2,5271 

Length of the prismatic beam 
feet/ inch 
720/ 8640 

Working Stress 
lbs/ inchÂ² 
10000 

Modulus of Elasticity 
lbs/ inchÂ² 
30000000 

Load 
lbf 
70000 

Cross section 
inchÂ² 
9,2722 

Density 
lbs/ ftÂ³ 
490 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
The ROHR2 model consists of a 720 feet long carbon steel beam. The only parameter necessary for this test case is the cross section which is given by Timoshenko as9,27 inchÂ² â‰™ 59,82 cmÂ². In the model an equivalent pipe dimension of 88 mm x 38,3 mm (diameter x wall thickness) is taken. The loads applied in thisexample is a point load at the lower end (2) of 70000 lbf and dead load. In the load case (Lc) dead load the gravitational acceleration is taken into account.
Figure 2: Rohr2 model with sectional results
(displacements)
Figure 3: Î´ from the Lc Dead Weight
1.4 Result comparisons
Value 
Length [inch] 
Reference (Timoshenko) [inch] 
Rohr2 [inch] 
Difference [%] 
8640 
2,5271 
2,5260 
<0,05 
Table 2: Comparison of the elongation at the lower end
Value 
Cross section (Timoshenko) [inchÂ²] 
Cross section (Rohr 2) [inchÂ²] 
Difference [%] 
9,2722 
9,2691 
<0,04 
Table 3: Comparison between demand and used cross section
1.5 Conclusion
The results are very close to the reference by Timoshenko. The small difference is due to the number of digit entered for the cross section. The results precision is excellent.
1.6 Files
R004_inch.r2w
R004_mm.r2w
R2_stresses_4.ods
SIGMA Ingenieurgesellschaft mbH www.rohr2.com