SOLUTIONS MANUAL
1
, CONTENTS
Chapter 1. Introduction 3
Chapter 3. Micromechanics of Unidirectional Composites 6
Chapter 4. Short-Fiber Composites 26
Chapter 5. Macromechanics Analysis of an Orthotropic Lamina 33
Chapter 6. Analysis of Laminated Composites 46
Chapter 7. Analysis of Laminated Plates and Beams 109
Chapter 8. Advanced Topics in Fiber Composites 124
Chapter 9. Performance of Fiber Composites: Fatigue,
Impact, and Environmental Effects 135
Chapter 10. Experimental Characterization of Composites 137
2
, Chapter 1
Introduction
1.3
3
, 1.4
My 1
, bh3 , Mh 6M
I
max
x
I 12 I 2 bh2
1
(a-1) “EI” of steel 210 GPa 0.1 0.0063 378 N m2
beam 12 m4
1
“EI” of 2024-T4 aluminum 73 GPa 0.1 h3m 378 N m2
beam 12 4
h = beam thickness for equivalent “EI” = 8.5 mm
6M
(a-2) Bending moment on steel ULT
beam: steel bh2
1
M 0.83 GPa 0.1 0.0062 498 N m
m 3
6
6M 6 498 N m
Aluminum ULT
0.41 GPa
beam Al 0.1h 0.1h2m
2
Beam thickness for equivalent strength: h 8.54 10 3 m 8.54 mm
(b-1) Weight of steel beam per unit length:
3
bh 10 cm 0.6 cm 7.8 gm/cm3 46.8 gm/cm
Weight of aluminum beam for equivalent “EI”:
1)
bh from part(a-
4
1
, CONTENTS
Chapter 1. Introduction 3
Chapter 3. Micromechanics of Unidirectional Composites 6
Chapter 4. Short-Fiber Composites 26
Chapter 5. Macromechanics Analysis of an Orthotropic Lamina 33
Chapter 6. Analysis of Laminated Composites 46
Chapter 7. Analysis of Laminated Plates and Beams 109
Chapter 8. Advanced Topics in Fiber Composites 124
Chapter 9. Performance of Fiber Composites: Fatigue,
Impact, and Environmental Effects 135
Chapter 10. Experimental Characterization of Composites 137
2
, Chapter 1
Introduction
1.3
3
, 1.4
My 1
, bh3 , Mh 6M
I
max
x
I 12 I 2 bh2
1
(a-1) “EI” of steel 210 GPa 0.1 0.0063 378 N m2
beam 12 m4
1
“EI” of 2024-T4 aluminum 73 GPa 0.1 h3m 378 N m2
beam 12 4
h = beam thickness for equivalent “EI” = 8.5 mm
6M
(a-2) Bending moment on steel ULT
beam: steel bh2
1
M 0.83 GPa 0.1 0.0062 498 N m
m 3
6
6M 6 498 N m
Aluminum ULT
0.41 GPa
beam Al 0.1h 0.1h2m
2
Beam thickness for equivalent strength: h 8.54 10 3 m 8.54 mm
(b-1) Weight of steel beam per unit length:
3
bh 10 cm 0.6 cm 7.8 gm/cm3 46.8 gm/cm
Weight of aluminum beam for equivalent “EI”:
1)
bh from part(a-
4
