WORKING STRESS

1 WORKING STRESS

1.1 Problem definition

Determinate the necessary cross section areas of the bars and deflections of the point B.


Figure 1: Model by Timoshenko




Figure 2:ROHR2 model






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 1.4, pg. 9-10.


A structure consisting of two equal carbon steel bars are submitted to a vertical force. The following parameters are given:

  • Angle of inclination

  • Modulus of Elasticity

  • Length of both bars

  • Stress

  • Force



Where:

Variable

Description

Unit

Used Value

Deflection

inch

0,12

Angle of inclination

deg

30

Length variation

inch

0,06

Stress

lbs/ inch²

10000

Modulus of Elasticity

lbs/ inch²

30000000

Length of both bars

inch

180

Force

lbf

5000

Cross section

inch²

0,5

Table 1: Overview of the variables used

1.3 Model description (ROHR2)

The ROHR2 model consist two equal beams which are 180 inch long with a self-defined steel bar. The beam is made of carbon steel (cross section 0,5 inch² ≙ 3.2258 cm²). At the middle a downward (-Z direction) vertical force (5000 lbf) is applied. Both bars are fixed at each end (Point 1,5). Additionally the points 1, B and 5 have the same boundary conditions (section moment MX isn't transmitted). As no acceleration due to gravity is to be considered, the line mass of the structural section is set to 0 lb/ ft.






Figure 3: Model with sectional results



1.4 Result comparisons



Figure 4: δ from the Lc Dead Weight





Value

Length

[inch]

Reference

(Timoshenko) [inch]

Rohr2 [inch]

Difference

[%]

180

0,012

0,012

<0,01

Table 2: Comparison of the deflection at point B


Value

Cross section

(Timoshenko) [inch²]

Cross section

(Rohr 2) [inch²]

Difference

[%]

0,5

0,5

<0,01

Table 3: Comparison of the cross section



1.5 Conclusion

The results are exact up to the limit of the given digits.

1.6 Files

R002_inch.r2w

R002_mm.r2w

R2_stresses_2.ods

SIGMA Ingenieurgesellschaft mbH www.rohr2.com