HOOK`S LAW
1HOOK`S LAW
1.1 Problem definition
Verify the unit elongation of a straight beam under axial force to verify Hooks law.
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 1.2, pg. 5.
Carbon steel beam with given axial stress. The following parameter are given:

Modulus of Elasticity

Length of the cylindrical steel bar

Tensile Stress

Diameter
Where:
Variable 
Description 
Unit 
Used Value 
Displacement 
inch 
0,01250 

Elongation 
inch/ inch 
0,0005 

Tensile Stress 
lbs/ inchÂ² 
15000 

Modulus of Elasticity 
lbs/ inchÂ² 
30000000 

Length of the cylindrical steel bar 
inch 
25 

Force 
lbf 
11780,9725 

Cross section 
inchÂ² 
0,7854 

Diameter 
inch 
1 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
The ROHR2 model consists of a beam model which is twentyfive inch long, with an pipe dimension from 1 inch x 0,5 inch (diameter x wall thickness). An additional material called carbon steel was defined with following material property values:

Young's Modulus= 30 x 10^{6} lbs/ inchÂ²

Alfa T (68 Â°F)= 10,8 Î¼m/ m

Tensile Strength= 55 x 10Â³ lbs/ inchÂ²

Yield Strength= 30 x 10Â³ lbs/ inchÂ²
At the beambottom a normal force is estimated. The axialforce is 117810 lbf. The force at the lower end is raised by the factor 10, to increase the number of available digits in the output. This allows to determine the difference between the reference solution and the program ROHR2 with higher precision. The exact reference value for the solution is 11780,9725 lbf. In this example for the load case (Lc) the gravitational acceleration isn't taken into account.
Figure 2: Î´ from the Load case (Lc) Dead
Weight
Figure 1: Overview of the variables used
1.4 Result comparisons
Value 
Length [inch] 
Reference (Timoshenko) [inch] 
Rohr2 [inch] 
Difference [%] 
25 
0,0125 
0,0125 
<0,01 
Table 2: Comparison of the elongation at the lower end
1.5 Conclusion
The results are exact up to the limit of the given digits.
1.6 Files
R001_inch.r2w
R001_mm.r2w
R2_stresses_1.ods
MATDAT.r2u
SIGMA Ingenieurgesellschaft mbH www.rohr2.com