Assignment 4

Problem 1: (15 Marks)

Determine if the Following Statements are True or False, why?

a) Adding plies to a laminate will always increase the axial stiffness, Ex or Ey, in either

the X or Y direction (see the lecture note for chapter 4)

b) For mechanical loading, the [A] matrix is independent of stacking sequence

c) For a balanced laminate, the D16 and D26 terms are always zero

d) The axial stiffness Ex of a (90)10 laminate is greater than the axial stiffness Ex of a

(90)4 laminate

e) A symmetric laminate will always have the same value for D11 and D22

Problem 2: (25 Marks, problem 1 in page 387 of the textbook)

A laminated [0/90/0/90]s carbon/epoxy beam is 1 mm thick and 20mm wide, and has

0.125mm thick plies. The lamina properties are ( )

1

( )

2

( )

12

( )

12

180GPa 1700MPa

10GPa 1400MPa

7GPa 40MPa

0.28 230MPa

L

L

T

T

E s

E s

G s

s

a) Determine the flexural modulus for the beam.

b) How could the flexural modulus be improved without changing the ply materials, the

number of plies, or the ply orientations?

c) Using the maximum stress criterion for each ply, determine the magnitude of the

maximum allowable bending moment that the beam can withstand. Which ply fails first?

d) What type of analysis would be required if the ply orientations are [+45/90/-45/0]s?

Problem 3: (20 Marks, problem 6 in page 388 of the textbook)

By expanding the [A] matrix in terms of ply stiffness show that a “balanced” cross-ply

laminate having equal numbers of 0 and 90o plies is not necessarily quasi-isotropic.

Problem 4: (20 marks, problem 7 in page 388 of the textbook)

A [-60/0/60] laminate and a [0/45/90] laminate both consists of 1.0 mm-thick plies

having the following properties: E1=181GPa; E2=10.3GPa; G12=7.17GPa; v12 =0.28.

Calculate Aij for both [-60+//60+] and [/45+/90+] laminates as a function of the

orientation to determine which, if any, of the laminates is quasi-isotropic.

Problem 5: (20 Marks, problem 4 in page 388 of the textbook)

Determine the stiffness matrix for a [+45/-45] anti-symmetric laminate consisting of

0.25mm-thick unidirectional AS/3501 carbon/epoxy plies.

(The due date for this assignment is at 10am 26 October)