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Question 3

A thin composite strip is manufactured from GFRP with the following properties:

E1 = 130 GPa, E2 = 10 GPa, G12 = 4 GPa, 12 = 0.3 t = 0.3mm per ply

Xt = 1200 MPa Yt = 60 MPa S12 = 40 MPa

Xc = 800 MPa Yc = 80 MPa

The strip is manufactured from two plies. The upper ply is aligned at 45 and the lower ply is aligned

at -45 to the length direction of the strip. A tensile load of 100N is uniformly applied to the end of the

strip. The x-axis of the beam reference coordinate system is aligned with the length of the strip.

The strip and its loading are shown below:

i) Find each term of the [A B/B D] matrix of the laminate. (14 marks)

Assuming, which may or may not be correct, that the inverse of the [A B/B D] matrix calculated in

i) is as follows:

A B

B D

(Units in N, mm)

ii) Determine the strains (in the beam reference coordinate system) on the upper surface of the strip.

(5 marks)

Assuming, which may or may not be correct, that the answer for part ii) is as follows:

x 1250

y = -800 10-6

xy 1350

125 -80 0 0 0 225

-80 125 0 0 0 225

0 0 110 225 225 0

0 0 225 4500 -2500 00 0 225 -2500 4500 0

225 225 0 0 0 3500

10-6

-1

10 mm100 N

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iii) Using the maximum strain failure criterion, and ignoring the strains on the lower surface, determine

the failure load of the strip. (6 marks)

(Total 25 marks)

(PTO/ Page 4)

Question 4

A carbon fiber reinforced plastic laminate is manufactured from fiber and resin with the

following properties:

Fiber Resin

E1 = 280 GPa E2 = 14 GPa E = 4.5 GPa

G12 = 5 GPa 12 = 0.28 = 0.34

The fiber volume fraction has been measured as 0.65.

i) Neglecting the effects of different Poissons contractions, estimate the following elastic

properties of a unidirectional CFRP lamina: E1, E2, G12, 12. (6 marks)

ii) Adjust your estimates from i) to account for a void fraction of 2%. (4 marks)

Assume, which may or may not be correct, that the answers for ii) are as shown in the carpet

plot below:

A balanced and symmetric laminate comprising 0, 90, 45 plies is desired. It is required that

the number of 0 plies is equal to the number of 90 plies. Additionally it is required that the

apparent Poissons ratio of the laminate when loaded in the X-direction is approximately 0.23.

iii) Select one configuration of the thinnest laminate that meets these requirements. (4 marks)

iv) Estimate the apparent Poissons ratio of this laminate when loaded in the Y-direction, yx.

(2 marks)

v) Estimate the apparent Poissons ratio of this laminate when loaded at 45 to the X-direction. Very

briefly explain your method. (4 marks)

20% 040% 0

60% 0

80% 0

100% 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

.

0 10 20 30 40 50 60 70 80 90 100

% 45 Layers

xy

E1 = 132.0 GPaE

2= 10.8 GPa

G12

= 5.65GPa

12= 0.24

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vi) Derive an expression that gives the apparent Poissons ratio of a laminate loaded in the X-

direction. Explain the limitations in applicability of this equation and hence of carpet plots.

(5 marks)

(Total 25 marks)

(PTO/ Page 5)