Design of Diving Board

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Design of Diving Board__________________________________________________________________

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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 its difficult to pinpoint an exact origin of the

sport. A tomb constructed in 480 BC called Tombadel Tuffatoreor Tomb of the Diverhad 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]

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.

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.

Tomba del Tuffatore [1]

A diving board is to be

designed that can bear a

maximum weight of 120 kgof

a person standing on the

edge of the board.

Diving Board (Cantilever Beam)


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4. Strategy

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

o 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

o This approach will provide another equation in terms of length and thickness.

o 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.

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]

Modulus of Elasticity =E= 70 GPa

Maximum Shear Stress = = 69 MPa

Yield Stress = yield = 105 MPa

For bending stress, using a factor of safety at 2

allow=yield

F.S=yield

=

MPA

= 52.5 MPa

For shear stress, using a factor of safety of 2

allow=

.=

= 34.5 MPa

5.2 Deflection of Beam

The moment equation in terms of x is

given by

M = - P

Relation between deflection and

moment is given by

=

Deflection of Beam


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Integrating with respect to x, and putting

boundary conditions, at x= L,

= 0, v= 0

=

6 ( + 3 2 )

Max, deflection occurs at x = 0

=

3()

Putting

Vmax= 0.05 m

=.

We get

L3= 371644.5804h3 (1)

5.3 Maximum Bending Stress

Maximum bending stress is given by

allow=

Maximum stress occurs at the outer

edge of beam

i.e.

Therefore we

get

= 3716.4458 (2)

Simultaneously solving (1) and (2)

5.4 Shear Stress

For rectangular cross sections,

allow 1.5(

)

1.5 (

) = 0.183 MPa

Therefore,

allow 1.5(

) OK

= 19.345

L = 1.39

c =

Bending Moment Diagram

Shear Force Diagram

Boundary

Conditions used for

a Cantilever beam

utilize the fact thatthere is no

deflection at the

point of support

x=0

Hence all our re uirements are fulfilled.


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6. Conclusion

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 fromhttp://www.archive.archaeology.org

[2] History of the Diving Board. (2014, September 19). Retrieved from http://www.sunplay.com/blog/fun-fact-

friday-history-diving-board/

[3] Properties of Aluminum AA1100. Retrieved from http://www.metalmensales.com/properties-of-

aluminum.html

Material:Aluminum (AA1100)

Dimensions:

L = 1.39mb = 0.5m

h = 19.345m

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Design of Diving Board