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