PURE BENDING 2
1PURE BENDING 2
1.1 Problem definition
Determine the deflections and bending stresses at the middle of the carbon steel beam.
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 4.23, pg. 95.
The thirty inch high carbon structure is stressed at both ends by a constant line load. The following values are given:

Length of several chapter

Total length

Constant line load

Moment of Inertia

Max. fiberdistance

Modulus of Elasticity
Where:
Variable 
Description 
Unit 
Used Value 
Maximum stress 
lbs/ inchÂ² 
9836,066 

Bending Moment 
ft lbs 
6000000,0 

Section Modulus 
inchÂ³/cmÂ³ 
610,0/9996,10 
Moment of Inertia 
inch^{4}/cm^{4} 
9150,0/380853,25 

Max. fibre distance 
inch 
15,00 

Chapter length 
ft 
10,00 

Total length 
ft 
40,00 

Line load 
lbs/ ft 
10000,00 

Radius of curvature 
inch 
45750,00 

Modulus of Elasticity 
lbs/ inchÂ² 
30000000 

Deflection 
inch 
0,01574 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
The system consists of four equal long bars (l_{C}= 10 ft â‰™ 120 inch). For this model it necessary to generate a new profile (IPB30â€œ see figure 4) with the given moment of inertia of 9150,0 inch^{4}. The section parameters of the profile are written in the profile database (see figure 3).The beam is supported by two simple supports. At point B the torsion and axial displacement is fixed to avoid a singular system: At both sides, between end and boundary condition, constant line loads are applied. The line load were increased by a factor of 100 to increase the number of significant digits in the output. In the Lc Load1 the gravitational acceleration is not taken into account.
Figure 3: Section parameters
Figure 4: Declaration the axes of an I
profile
Figure 5: Input from the PROFDS.r2u
Figure 8: Results for the increased load
Figure 7: Î´ from the Load case 1
Figure 6: Sectional results (equivalent stress) a point C
1.4 Result comparisons
Value 
Length [inch] 
Reference (Timoshenko) [lbs/inchÂ²] 
Rohr2 [lbs/inchÂ²] 
Difference [%] 
480,0 
9836,07 
9836,1 
<0,01 
Table 2: Comparison of the stress at the middle of the system
Value 
Length [inch] 
Reference (Timoshenko) [inch] 
Rohr2 [inch] 
Difference [%] 
480,0 
0,15738 
0,15726 
<0,08 
Table 3: Comparison of the max. deflection
1.5 Conclusion
The results are perfectly matching the reference values.
1.6 Files
R010_inch.r2w
R010_mm.r2w
R2_stresses_10.xls
PROFDS.r2u
SIGMA Ingenieurgesellschaft mbH www.rohr2.com