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. 910.
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/ inchÂ² 
10000 

Modulus of Elasticity 
lbs/ inchÂ² 
30000000 
Length of both bars 
inch 
180 

Force 
lbf 
5000 

Cross section 
inchÂ² 
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 selfdefined steel bar. The beam is made of carbon steel (cross section 0,5 inchÂ² â‰™ 3.2258 cmÂ²). 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: Î´ 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) [inchÂ²] 
Cross section (Rohr 2) [inchÂ²] 
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