Problem 1: Stress analysis of a lamina using experimental data from a strain rosette

The strain rosette used to measure failure strains at a point yielded the following ratio between

the strains in the lamina coordinate axes:

&1= n₂/₁2=0

E2

The lamina was loaded by tensile stresses and ₂.

Compare the results obtained by the maximum stress, Tsai-Hill and Tsai-Wu criteria to

determine the failure stress. Which of these criteria prescribed the safest stress combination?

&c

Eb

60°

Y

60°

30°

QU

X

45⁰

Figure 1. Typical strain gauge rosettes (eFunda.com).

(a)/nNotes:

The ratio of strains: See Table 1 for your variant.

Material: See Tables 2 and 3 for your variant.

Table 1. The strain ratio measured in the lamina at failure.

Variant 1

n

Variant 10

1.3

n

1.5

Variant 19

1.4

n

2

1.1

11

1.6

20

0.75

3

1.2

12

1.15

4

0.8

13

0.7

5

2.0

14

0.5

6

1.7

15

1.5

7

0.6

16

1.2

8

0.9

17

0.4

9

0.75

18

1.6

1/nTable 2: Material in Problem 1 (see Table 3 for properties)

Var.

1

Material 1

Var.

10

Material 1

Var.

Material

19

1

2

1

11

1

20

1

3

1

12

1

4

2

13

2

5

2

14

2

6

2

15

2

7

3

16

3

8

3

17

3

9

3

18

3/nTable 3. Composite materials for problems 1 and 2 (material number in your variant refers to the

material in Table 1.1 below)

From

Table 1.1 Typical properties of unidirectional composites

E.J. Barbero, "Introduction to Composite Materials"

Density (

Longitudinal Model E

Tven Mode GP

Inplane Shear Modulus G₁ GP

P's Radio

Longitudinal Tessile Strength F₁, [MPa]

Transverse Tensile Strength PMP

Inplane Shear Strength (MP

Longitudinal Compressive Strength F₁, [MPa]

Transverse Compressive Strength F (MP)

elaminar Shear Strength (For Fy) [MPa]

Longitudinal Tessile Strain 3, 1963

Longitudinal CTE o [10/C)

Transverse CTE [10/

Longitudinal moisture

Transserse mistare expansice P

Fiber Volume Fract V

Void Content V. []

Fiber Misalignment

Material number

E-Glass S-Class

Epoxy Epoxy

2.076

12

55

30

0

55

16

0.2

60

82-85SBASERE

0.19 0.28

10:20 1630

40

60

630

140

60

23

37

Jalalalalalalal

16

60

6.90

140

80

29

32

02

60

2

*** 982-30*****338-3822M

E-Glas Kevlar

Epery

ophtal

Polyester

1.85

113

40

40

357

24

6.5

3.53

1.380

75.8

5.5

934

13800

34.5

441

586.0

138.0

48.69

1.8

-1.0

60

0.01

02

60

4

Carbo Carbon/ Carbon Carbon

Epoxy Epoxy Epey

ASA/35-6 T80/1960-2 1551 ASAPCE

PEEK

1.58

142

10.3

7.2

0.27

1830

57

71

1096

228

1.29

-49

27

0

02

60

n

1558

19

5.14

0.3

2608

168

0.0095

0.321

151

9.0

5.6

0.3

L64

57.3

DI

1.6

138

102

5.7

0.3

2000

85

186

1360

400

150

1.45

0.5

30

61

6

2

Carbo

Polid

ASU

Avi

Note: Carbon/epoxy, Kevlar/epoxy and boron/epoxy (to a smaller extent) are used in aerospace

applications, while less expensive glass/epoxy and glass/polyester are preferred by shipbuilders

and in civil engineering.

110

83

37

63

1000

0.5