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 aircra ḟt
13. Airworthiness
14. Air ḟrame loads
15. Ḟatigue
16. Bending o ḟ open and closed, thin-walled beams
,17. Shear o ḟ beams
18. Torsion o ḟ beams
19. Combined open and closed section beams
20. Structural idealization
21. Wing spars and box beams
22. Ḟuselages
23. Wings
24. Ḟuselage ḟrames 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 σx = 80 N/mm2, σy = 0
(or vice versa), and τxy = 45 N/mm 2. Thus, ḟrom Eq. (1.11),
80 1 pffiffiffiffiffi2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffi2ffi
σ I = 2 + 2 80 + 4 × 4 5
i.e.,
σI = 100.2 N/mm2
Ḟrom Eq. (1.12),
80 1 pffi ffiffi ffiffi2ffiffiffi ffiffiffiffi ffiffiffiffiffiffiffi ffiffi ffiffiffi2ffi
σ II = — 80 + 4 × 4 5
2 2
i.e.,
σII = —20.2 N/mm2
The directions o ḟ the principal stresses are de ḟined by the angle θ in Ḟig. 1.8(b) in which θ is given
by Eq. (1.10). Hence,
2 × 45
tan 2θ 1.125
= =
80 — 0
which gives
θ = 24°11' and θ = 114°11'
It is clear ḟrom the derivation o ḟ Eqs (1.11) and (1.12) that the ḟirst value o ḟ θ corresponds to σI while
the second value corresponds to σII.
Ḟinally, the maximum shear stress is obtained ḟrom either o ḟ Eqs (1.14) or (1.15). Hence ḟrom
Eq. (1.15),
100.2 — (—20.2) 2
τmax = 2 = 60.2 N/mm
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 σx = 50 N/mm2,
σy =–35 N/mm2, and τxy = 40 N/mm2. Thus, ḟrom 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 aircra ḟt
13. Airworthiness
14. Air ḟrame loads
15. Ḟatigue
16. Bending o ḟ open and closed, thin-walled beams
,17. Shear o ḟ beams
18. Torsion o ḟ beams
19. Combined open and closed section beams
20. Structural idealization
21. Wing spars and box beams
22. Ḟuselages
23. Wings
24. Ḟuselage ḟrames 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 σx = 80 N/mm2, σy = 0
(or vice versa), and τxy = 45 N/mm 2. Thus, ḟrom Eq. (1.11),
80 1 pffiffiffiffiffi2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffi2ffi
σ I = 2 + 2 80 + 4 × 4 5
i.e.,
σI = 100.2 N/mm2
Ḟrom Eq. (1.12),
80 1 pffi ffiffi ffiffi2ffiffiffi ffiffiffiffi ffiffiffiffiffiffiffi ffiffi ffiffiffi2ffi
σ II = — 80 + 4 × 4 5
2 2
i.e.,
σII = —20.2 N/mm2
The directions o ḟ the principal stresses are de ḟined by the angle θ in Ḟig. 1.8(b) in which θ is given
by Eq. (1.10). Hence,
2 × 45
tan 2θ 1.125
= =
80 — 0
which gives
θ = 24°11' and θ = 114°11'
It is clear ḟrom the derivation o ḟ Eqs (1.11) and (1.12) that the ḟirst value o ḟ θ corresponds to σI while
the second value corresponds to σII.
Ḟinally, the maximum shear stress is obtained ḟrom either o ḟ Eqs (1.14) or (1.15). Hence ḟrom
Eq. (1.15),
100.2 — (—20.2) 2
τmax = 2 = 60.2 N/mm
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 σx = 50 N/mm2,
σy =–35 N/mm2, and τxy = 40 N/mm2. Thus, ḟrom Eq. (1.11),
3
