1. Ch. 2: Fundamental of Structure
Aircraft is a structure
Structures provide aerodynamic properties
Challenge: weight must minimum
Structural strength vs weight
Solid Mechanics
How a solid object resists/supports load ?
Solid ?
Conservations ?

2. Elasticity Ability to bounce back Aircraft has limited elasticity
Stress & Strain

3. Elasticity

4. Stress Strain Measure of force intensity  = F/A Units !!
Five Types Of Stress
Tension
Compression
Bending force
Torsion
Shear force
Strain
Measure of deformation
Units ?
 = /L

6. Stress & Strain
Measure of force intensity

7. Example 2.1 A prismatic bar with rectangular cross section (20mmx40mm)
and length, L=2.8m is subjected to an axial tensile force 70 kN.
The measured elongation of the bar is =1.2mm. Calculate the
tensile stress and strain in the bar.

8. Sign Conventions/Notation of Stresses
Stress at a point (A) on a plane of a body has the components of;
1 direct stress, 
2 shear stresses, 
x : direct stress in the direction of x axis
xy : shear stress  x: the plane, y: the direction
On each plane, there are 2 equal; but opposite stresses
In the x axis direction; +ve & tensile
In the –ve x axis direction; -ve & compression

9. State of Equilibrium
Stresses on opposites faces are differ & stated in Taylor’s series;

10. State of Equilibrium
Stresses on opposites faces are differ & stated in Taylor’s series;
X, Y, Z are force per unit area.

11. Plane Stress Aircraft structural components  thin metal sheet
Stress across thickness  negligible

12. Stresses on Inclined Plane
The chosen of axes system is arbitrary
So need to examine stresses on other planes

13. Stresses on Inclined Plane

14. Example 2.2
A cylindrical pressure vessel has an internal diameter of 2m and is fabricated from 20mm thick plate. The pressure inside the vessel is 1.5N/mm2, and the vessel is also subjected to axial tensile load of 2500kN. Determine the direct and shear stresses on a plane inclined at an angle of 60o to the axis of the vessel. Determine also the maximum shear stress.

15. Example 2.3
A cantilever solid beam, circular cross section supports a compressive load of 50kN applied to its free end at a point 1.5m below a horizontal diameter in the vertical plane of symmetry together with a torque of 1200Nm. Calculate the direct and shear stresses on a plane inclined at 60o to the axis of the cantilever at a point on the lower edge of the vertical plane of symmetry.
Sixma bending=My/I. I is 2nd moment of area, for circle=pai *d^4/64

16. Stop 20/09/2012

17. Principles Stress : direct (normal)
The stress on the inclined plane is max/min when
Differentiate n w.r.t ,
2 solutions at  and +/2
Principal stress (max)
Sixma bending=My/I. I is 2nd moment of area, for circle=pai *d^4/64
Principal stress (min)

18. Principles Stress : shear
The stress on the inclined plane is max/min when
Differentiate  w.r.t ,
2 solutions at  and +/2
The plane of max shear stress  at 45o to principal plane
Principal stress (max)
Sixma bending=My/I. I is 2nd moment of area, for circle=pai *d^4/64
Principal stress (min)

19. Stress on Mohr’s Circle
Stress on inclined plane;
Sixma bending=My/I. I is 2nd moment of area, for circle=pai *d^4/64

20. Strain Force causes the body to deform : strain
Direct strain : due to direct stress
Shear strain: due to shear stress
Points P & Q deformed to P’ & Q’ the normal strain are,

21. Shear Strain Shear strain components are;
Rigid body motion ; a body undergoes displacement without inducing strains.

22. Example 2.3
Consider a 2-D body (a unit square ABCD) in xy plane. After deformation, four corners points move to A’, B’, C’ and D’ respectively. Assume the displacement in the x and y direction are given by u=0.01y and v=0.015x respectively. Obtain the deformed coordinates, normal strain and shear strain.

23. Principal Strain The principal strains are given by,
The principal strains can be determined graphically by using Mohr’s circle for strain

24. Stress-Strain Relation
6 components stress;
6 components strains;
For plane stress, we have
E is Young’s modulus
 is Poisson’s ratio
G is modulus of rigidity

25. Stress-Strain : Example 2.4

26. Stress-Strain : Example 2.5