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/ inch²	15000
	Modulus of Elasticity	lbs/ inch²	30000000
	Length of the cylindrical steel bar	inch	25
	Force	lbf	11780,9725
	Cross section	inch²	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 twenty-five 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 10⁶ lbs/ inch²

• Alfa T (68 °F)= 10,8 μm/ m

• Tensile Strength= 55 x 10³ lbs/ inch²

• Yield Strength= 30 x 10³ lbs/ inch²

At the beam-bottom a normal force is estimated. The axial-force 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: δ 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