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/ inch²

10000

Modulus of Elasticity

lbs/ inch²

30000000

Load

lbf

70000

Cross section

inch²

9,2722

Density

lbs/ ft³

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 inch² ≙ 59,82 cm². 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 1: Rohr2 model with sectional results (equivalent stress)



Figure 2: Rohr2 model with sectional results (displacements)





Figure 3: δ 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) [inch²]

Cross section

(Rohr 2) [inch²]

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