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 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/ 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 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: 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