Materials Science and Engineering 4T03

Assignment 1 due the 25th February

You are a member of a rescue team employed by Titan Salvage to work on the wreck of Costa Concordia. Your objective is to design the cables used to tow away the boat (which is now floating) to the port where it will dismantled.

The overall mass of the boat is estimated to be 130,000 tons. If we assume a simple force balance of the following form: in which m is the mass of the weight (we assume we can neglect the weight of the cable), a the acceleration, W the weight due to gravity (9.8m/sec2) and F the force required to move the boat and R the resistance of the water to the boat motion.

a)The boat is floating, what can we assume for the value of W? (1pt)

b)We want to tow away the boat to the port of Gibraltar, some 1,500 kms away, in 5 days. At what velocity V should we travel? (1pt)

c)As a first step, we need roughly 1 hour to accelerate to full speed V while we are in calm waters (R=20,000 N). What is the value of a? (1pt)

d)What is the force F required to tow the boat to full speed? (1pt)

e)To design the cable capable to tow the boat we need to calculate the maximum stress applied to the cable. Calculate for a cable of 1, 2, 3, 4, 5 and 10cm this stress. (2pts)

f)What should be the strength of the cable? (2pts)

g)What is a model we can use to design the cable? (1pt)

h)In which mode will we use this model? (1pt)

i)We have several materials at our disposal as illustrated in the table below:

Material / Matrix strength (MPa) / Matrix cost
($/kg) / Reinforcement strength (MPa) / Reinforcement cost ($/kg)
A / 4 / 15 / 800 / 1000
B / 8 / 50 / 600 / 600
C / 2 / 100 / 1,000 / 2000

Calculate the volume fraction of reinforcement for each composite and the 5 diameters(3pts)

j)Which materials make the most practical sense from a property perspective? From a cost perspective? From both perspectives? (3pts)

k)Let’s consider the two ideal packing arrangements of long fibers. For the material of choice, calculate in both case the distance center to center between fibers, and the distance edge to edge between fibers for a fiber radius equal to a tenth of the cable’s. (4pts)