Design of Diving Board

Design of Diving Board__________________________________________________________________

1. History of Diving Board The sport of diving is hard to trace as it has been around as long as people have leapt from rocks and cliffs so it’s difficult to pinpoint an exact origin of the sport. A tomb constructed in 480 BC called “Tomba del Tuffatore” or “Tomb of the Diver” had a painting of a young man diving from a narrow platform on the roof of a burial plot just south of Naples. Visitors to Hawaii in the late 19th century would talk about the natives leaping, diving, and somersaulting from considerable heights from cliffs into the bottoms of waterfalls or deep pools. [2]

Tomba del Tuffatore [1]

2. Problem Statement A diving board is used for diving and can be considered a cantilever beam. Diving boards are commonly fixed by a hinge at one end (so they can be flipped up when not in use), and the other end usually hangs over a swimming pool.

A diving board is to be designed that can bear a maximum weight of 120 kg of a person standing on the edge of the board. Diving Board (Cantilever Beam)

3. Scope and Limitations The design of the diving board is carried out using the following basic concepts of solid mechanics only 

Deflection of Beam



Maximum Bending Stress



Maximum Shear Stress

The following assumptions are made     

The board is assumed to be horizontal. The weight of board is neglected. Vibrations caused by jumping are neglected. Concepts of fatigue are not considered. Most of the times boards are coated with non-slip material. Their effects are not taken into consideration.

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Design of Diving Board__________________________________________________________________

4. Strategy o o o o

The method of deflection of beams will be used to limit the amount of deflection and get an equation in terms of length and thickness Diving boards can be considered as long beams, so the second critical criteria would be to keep the maximum bending stress within the limit of allowable stress This approach will provide another equation in terms of length and thickness. For safety, it should be further checked that the maximum shear stress is within the limit of the allowable shear stress.

5. Design

5.1 Assumptions Some suitable assumptions are made For a person to stand easily on the board it should be 50 cm wide i.e.

Modulus of Elasticity =E= 70 GPa Maximum Shear Stress = τ = 69 MPa Yield Stress = σyield = 105 MPa

Width of board = b = 50 cm= 0.5 m Maximum deflection to be allowed is 5 cm i.e. Vmax = 5 cm = 0.05 m Most of the times, diving boards are made out of aluminium so as a starting point we will use properties of aluminium (AA1100). [3]

5.2

For bending stress, using a factor of safety at 2 σallow =

σyield F.S

=

σyield 2

=

105MPA = 2

52.5 MPa

For shear stress, using a factor of safety of 2 𝜏

𝜏

τallow = 𝐹.𝑆 = 2 = 34.5 MPa

Deflection of Beam

The moment equation in terms of x is given by

Deflection of Beam

M = - P𝑥 Relation between deflection and moment is given by 𝑑2 𝑣 𝐸𝐼 = −𝑃𝑥 𝑑𝑥 2

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Design of Diving Board__________________________________________________________________

Integrating with respect to x, and putting

Boundary Conditions used for a Cantilever beam utilize the fact that there is no deflection at the point of support (x=0)

5.3

𝑑𝑣

boundary conditions, at x= L, 𝑑𝑥= 0, v= 0 𝑣=

𝑃 ( −𝑥 3 + 3𝐿2 𝑥 − 2𝐿2 ) 6𝐸𝐼

Max, deflection occurs at x = 0 𝑉𝑚𝑎𝑥 =

𝑃 (𝐿3 ) 3𝐸𝐼

Putting Vmax = 0.05 m 𝐼=

0.5 ℎ3 12

We get L3 = 371644.5804h3 (1)

Maximum Bending Stress Maximum bending stress is given by σallow = −

𝑀𝑚𝑎𝑥 𝑐 𝐼

Maximum stress occurs at the outer edge of beam ℎ i.e. c= Therefore we 2 get 𝐿 = 3716.4458 ℎ2

(2)

Simultaneously solving (1) and (2) Bending Moment Diagram

5.4

ℎ = 19.345 𝑚𝑚 L = 1.39 𝑚

Shear Stress

For rectangular cross sections, 𝑉𝑚𝑎𝑥 ) 𝐴

τallow ≥ 1.5( 𝑉𝑚𝑎𝑥 ) 𝐴

1.5 (

= 0.183 MPa

Therefore, 𝑉𝑚𝑎𝑥 ) 𝐴

τallow ≥ 1.5(

OK Shear Force Diagram

Hence, all our requirements are fulfilled.

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Design of Diving Board__________________________________________________________________

6. Conclusion

Material: Aluminum (AA1100) Dimensions: L = 1.39m b = 0.5m h = 19.345m

Different concepts of mechanics of materials were used to design the diving board. The analysis gives out the height to be 19.345 mm and length to be 1.39m using aluminium. Keeping in view the assumptions it is safe to assume that dimensions calculated will keep the diving board in safe region. Any force less than or equal to 1176 N will not cause the board to break.

7. References [1] Tomba del Tuffatore figure. Retrieved from http://www.archive.archaeology.org [2] History of the Diving Board. (2014, September 19). Retrieved from http://www.sunplay.com/blog/fun-factfriday-history-diving-board/ [3] Properties of Aluminum AA1100. Retrieved from http://www.metalmensales.com/properties-ofaluminum.html

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