Question

Rudolph is a male professional ballet dancer who is looking for a new house. He wants to purchase a typical residential house which will suit his budget and his lifestyle. Being a professional dancer is a regime not just a job, and this means that Rudolph needs to train and rehearse on a daily basis. Hence, Rudolph intends to practice his dance routines in the lounge room of his new house on a frequent basis. Rudolph is your auntie’s protégé, and since you are a qualified Structural Engineer, she has asked you to assist Rudolph in finding a suitable house. You have had a meeting with Rudolph and obtained information that will assist you in analysing suitable houses and this information effectively forms your specification for this ‘project’. As a part of the decision-making process, you need to determine the following: i. The area in mm2 which Rudolph’s feet take up on the floor. ii. The pressure Rudolph will place on the floor when he is practicing his pirouettes. iii. The work that the floor has to do to stop Rudolph’s leaps. iv. The Live Load Q as per the Limit State Design Method for Rudolph’s dance routines based on the assumed velocity of his movements and leaps. v. What type of house would you recommend that Rudolph purchase? Why? vi. Rudolph has found a renovated, Victorian architecturally-styled house in a location close to his work. It is a three-bedroom, one-bathroom house constructed with floor joists at 450 mm centres and bearers at 1.6 m centres. The large 4 m x 5 m lounge room with polished timber floor boards looks particularly promising. a. What would you anticipate the Live Load capacity of the house to be based on the floor joists and bearers? b. Is this house suitable for Rudolph to practice his dance routines? Why/ why not? Provide a detailed response based on floor live loads considerations as per AS 1170.1 (discussed in the Reading Material for this module) and your calculations. c. Based solely on the dance practice criteria, do you recommend that Rudolph purchase this house? Why/ why not? Provide a detailed response with a justification for your answer. Assumptions  Size of average male foot – 330 mm x 120 mm  Ball of male foot – 165 mm x 120 mm  Mass of average-sized male ballet dancer = 85 kg  Maximum velocity Rudolph can attain is 5.88* m/s and he attains this velocity in 4.5 seconds from a stopped position; generally, he can continue at this velocity of 5.88 m/s or greater for at least 20 seconds. Consider Rudolph’s movements in this regard in terms of a vehicle. [*This velocity assumes Rudolph is capable of running 100 m in approximately 17 seconds, this is well below the Olympic records of most contemporary male athletes (Usain Bolt of Jamaica achieved a distance of 100 m in 9.68 seconds at the Olympics).]  Rudolph’s leaps – 1.5 m above the ground and landing on the ball of one foot. Note:  Ballet dancers tend to be smaller and lighter than the average for their sex.  The information and assumptions provided in this question are simplified and would not necessarily be utilised and calculated in this manner for a real-world application. [Hint: Newton’s Laws of Motion would be useful to determine some of the required information.]

Answer 1

(i) The area in mm2 which Rudolph’s feet take up on the floor.

V= 5.88 m/s

t1 =4.5 sec

t2= 20 sec.

we have to calculate the distance from given velocity and time

S1= V*t = 5.88 *4.5 = 26.46 m

S2 =V*t = 5.88 *20 = 117.6 m

take the maximum distance as a length of the floor

L =117.6 m

now we have consider the sqare size of the floor so

Width of the floor will be same as a Length of the floor.

W= 117.6 m

We ahve to determine the floor area in mm2

A =L*W = 117.6 *117.6

= 13829.76 M2

A = 13829760000 mm2

(ii) The pressure Rudolph will place on the floor when he is practicing his pirouettes.

we have to find the pressure on the floor.

M =85 Kg .

we have to convert it in to weight

W = M*g

= 85 *9.8 = 833 Kg-m/s2 (N)

W =833 N

we have to find the Pressure P

so P = W/A = F/A . W=F = 833 N

A= 330 *120 mm2 = 39600 mm2

P =833/ 39600

P = 0.021 N/mm2

(iii) The work that the floor has to do to stop Rudolph’s leaps.

we have to find the work done.

Work Done = F*Distance

= 833 N* 1.5 m

= 1249.5 N-m