Three Point Bending and Shaft Design

Section A
1. Three point bending is bending where a piece of metal is placed two supports and then a
point load is applied to the metal between the supported ends.
2. It provides values for Young’s modulus, E and flexural strength.
3. Hollow shaft is shaft with a through hole concentric with the external shaft diameter.
Solid shaft is that shaft without a through hole inside it.
4. Advantage and disadvantage of solid shaft
Advantage: are stronger than hollow shaft when subjected to bending.
Disadvantage: weighs more than hollow shaft.
5. Advantage and disadvantage of hollow shaft
Advantage: are lighter and stronger than solid shafts of the same length, external cross-
sectional radius and material.

Disadvantage: do not transfer more power; however, they have higher power to weight
ratio than solid shaft. It generates louder noises when subjected to bearing motion
compared to other shafts.
6. Applications of solid shaft
- Power transmission in propeller shafts
- As drives in almost all process pumps and circulators
7. Applications of hollow shaft
- Torque transmission in automatic power transmission applications;
- Used in high torque motors to provide high torque and precision at lowest weight.
8. Shaft cross-section selection:- Would select annular cross-section to ensure low weight,
high power transmission and low cost.
9. Shaft material.
Selected material is low carbon alloy steel with tensile strength of 700MPa and above for
generator rotor shaft (Mori, T. (2014). U.S. Patent No. 8,853,903. Washington, DC: U.S. Patent
and Trademark Office).

Aluminum alloy EN AW 6061/6060 material for precision shaft to be used with linear plain
bearings. Examples include ceramic coated aluminum precision shafts. (Choi, Y., Kim, D. U.,
Kang, B. Y., Park, D. K., Lee, D. J., Lee, S. W., & Shin, H. T. (2013). Forming of the precision
aluminum tube for a light weight propeller shaft. Journal of Mechanical Science and
Technology, 27(11), 3445-3449.)
Figure 1: Ceramic coated aluminum allow
shaft Figure 2: Aluminum alloy shaft
10. Finite element analysis of a structure is the analysis of a structure by hypothetically
subdividing into an assembly of small parts called elements assumed to be connected to one
another at joints called nodes.
11. Preprocessing is model preparation by defining problem. It includes: design of model,
creation of mesh, element selection, defining geometrical properties, selecting material,
defining constraints and boundary conditions and loads.
12. Post-processing refers to evaluation and interpretation of the results or review of the
results.
13. Degree of freedom is the number of independent coordinates a structure can move.
14. Reaction force is a force opposite and normal to any action force in accordance with
Newton’s Third Law of motion.
15. Reaction force should be equal and opposite action force.

16. Beam element is the linear one dimensional structural element, with dimensions in
horizontal longitudinal direction is longer than its two transverse directions.
17. Difference between beam and truss elements.
- Beams support loads when in shear and bending while trusses support loads in tension and
compression;
18. 2D beam element has 4 degrees of freedom.
Node 1 linear displacement along x axis u1 x
Node 1 linear displacement along y axis u1 y
Node 2 linear displacement along x axis u2 x
Node 2 linear displacement along y axis u2 y
19. Possible supports that can be applied to end of a 2D. Support and Degrees of freedom.
- Roller support – allows the beam to move horizontally. Common in bridges. 1 degree
of freedom, u1.
- Pinned support – rotational movement is allowed at the support, one degree of
freedom, rotation allowed.
- Fixed – No rotation or displacement allowed, zero degrees of freedom.
- Simple support – rotation and displacement allowed, two degrees of freedom,
displacement along x axis u1 and rotation about the support.