All 28 Chapters Covered
SOLUTIONS
,Table of contents
Part A: Fundamentals of Structural Analysis
1. Basic elasticity
2. Two-dimensional problems in elasticity
3. Torsion of solid sections
4. Virtual work and energy methods
5. Energy methods
6. Matrix methods
7. Bending of thin plates
8. Columns
9. Thin plates
10. Structural vibration
Part B: Analysis of Aircraft Structures
11. Materials
12. Structural components of aircraft
13. Airworthiness
14. Airframe loads
15. Fatigue
16. Bending of open and closed, thin-walled beams
,17. Shear of beams
18. Torsion of beams
19. Combined open and closed section beams
20. Structural idealization
21. Wing spars and box beams
22. Fuselages
23. Wings
24. Fuselage frames and wing ribs
25. Laminated composite structures
26. Closed section beams
27. Open section beams
28. Wing problems
, Solutions Manual
Solutions to Chapter 1 Problems
S.1.1
The principal stresses are given directly by Eqs (1.11) and (1.12) in which σ x ¼ 80 N/mm2, σ y ¼ 0
(or vice versa), and τxy ¼ 45 N/mm2. Thus, from Eq. (1.11),
80 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
σI ¼ + 802 + 4 452
2 2
i.e.,
σI ¼ 100:2 N=mm2
From Eq. (1.12),
80 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
σ II ¼ 802 + 4 452
2 2
i.e.,
σII ¼ 20:2 N=mm2
The directions of the principal stresses are defined by the angle θ in Fig. 1.8(b) in which θ is given by
Eq. (1.10). Hence,
2 45
tan2θ ¼ ¼ 1:125
80 0
which gives
θ ¼ 24°110 and θ ¼ 114°110
It is clear from the derivation of Eqs (1.11) and (1.12) that the first value of θ corresponds to σ I while the
second value corresponds to σ II.
Finally, the maximum shear stress is obtained from either of Eqs (1.14) or (1.15). Hence from
Eq. (1.15),
100:2 ð20:2Þ
τmax ¼ ¼ 60:2 N=mm2
2
and will act on planes at 45° to the principal planes.
S.1.2
The principal stresses are given directly by Eqs (1.11) and (1.12) in which σ x ¼ 50 N/mm2,
σ y ¼ –35 N/mm2, and τxy ¼ 40 N/mm2. Thus, from Eq. (1.11),
3
SOLUTIONS
,Table of contents
Part A: Fundamentals of Structural Analysis
1. Basic elasticity
2. Two-dimensional problems in elasticity
3. Torsion of solid sections
4. Virtual work and energy methods
5. Energy methods
6. Matrix methods
7. Bending of thin plates
8. Columns
9. Thin plates
10. Structural vibration
Part B: Analysis of Aircraft Structures
11. Materials
12. Structural components of aircraft
13. Airworthiness
14. Airframe loads
15. Fatigue
16. Bending of open and closed, thin-walled beams
,17. Shear of beams
18. Torsion of beams
19. Combined open and closed section beams
20. Structural idealization
21. Wing spars and box beams
22. Fuselages
23. Wings
24. Fuselage frames and wing ribs
25. Laminated composite structures
26. Closed section beams
27. Open section beams
28. Wing problems
, Solutions Manual
Solutions to Chapter 1 Problems
S.1.1
The principal stresses are given directly by Eqs (1.11) and (1.12) in which σ x ¼ 80 N/mm2, σ y ¼ 0
(or vice versa), and τxy ¼ 45 N/mm2. Thus, from Eq. (1.11),
80 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
σI ¼ + 802 + 4 452
2 2
i.e.,
σI ¼ 100:2 N=mm2
From Eq. (1.12),
80 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
σ II ¼ 802 + 4 452
2 2
i.e.,
σII ¼ 20:2 N=mm2
The directions of the principal stresses are defined by the angle θ in Fig. 1.8(b) in which θ is given by
Eq. (1.10). Hence,
2 45
tan2θ ¼ ¼ 1:125
80 0
which gives
θ ¼ 24°110 and θ ¼ 114°110
It is clear from the derivation of Eqs (1.11) and (1.12) that the first value of θ corresponds to σ I while the
second value corresponds to σ II.
Finally, the maximum shear stress is obtained from either of Eqs (1.14) or (1.15). Hence from
Eq. (1.15),
100:2 ð20:2Þ
τmax ¼ ¼ 60:2 N=mm2
2
and will act on planes at 45° to the principal planes.
S.1.2
The principal stresses are given directly by Eqs (1.11) and (1.12) in which σ x ¼ 50 N/mm2,
σ y ¼ –35 N/mm2, and τxy ¼ 40 N/mm2. Thus, from Eq. (1.11),
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