BENDING MOMENT AND SHEARING FORCE DIAGRAMS
1 BENDING MOMENT AND SHEARING FORCE DIAGRAMS
1.1 Problem definition
Verify the uprising sectional results when a constant line load stresses a bar
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 3.22, pg. 86.
At a system with a negative line load and two boundary conditions are following parameters given:

Constant line load

Length stretch AB

Length stretch BC

Total length (stretch AC)
Where:
Variable 
Description 
Unit 
Used Value 
Sectional force _{AY} 
lbf 
670 

Sectional force _{BY1} 
lbf 
1730 

Sectional force _{BY2} 
lbf 
1600 

Bending Moment 
ft lbs 
3180 

Constant line load 
lbs/ ft 
400 

Length_{AB} 
ft 
6 
Length_{BC} 
ft 
4 

Total length 
ft 
10 
Table 1: Overview of the used variables
1.3 Model description (ROHR2)
Figure 3: Overview of the force vectors
This system was built of two unequal long beams. The first (stretch AB) is six feet and the second one (stretch BC) is four feet long. The profile which is used, is equal to the previous model. The ten feet long beam is supported at the point A with an anchor and at point B with an axial stop (Z direction is also blocked). The anchor does not block the bending moment (Mx). At the whole length, the structural section is submitted to a constant line load (400 lbs/ inchÃ‚Â²). Like in the last few examples an occasional load case is creaded, without gravity. The third point C is overhanging right next to point B and was defined without any support.
Figure 4: F_{xY}, Mb at every points of the system
1.4 Result comparisons
Value 
Length [ft] 
Reference (Timoshenko) [lbf; ft*lbs] 
Rohr2 [lbf; ft*lbs] 
Difference [%] 
10,0 
670,00 
666,7 
<0,52 

1730,00 
1733,3 
<0,19 

1600,00 
1600,0 
<0,01 

3180,00 
3200,0 
<0,63 
Table 2: Comparison of the sectional results
1.5 Conclusion
The results are really close to the reference. The results would be exactly in the limit of the given digits, if Mr. S. Timoshenko didn't round up the loads. It can be remarked, that the dimensions, lengths and materials are free selectable as they don't influence the results checked.
Figure 5: force curve by Timoshenko
Figure 6: moment curve by Timoshenko
1.6 Files
R008_inch.r2w
R008_mm.r2w
R2_stresses_8
SIGMA Ingenieurgesellschaft mbH www.rohr2.com