2145321 Air Struc I – Ex 1-1

2145321 Air Struc I – Ex 1-1

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

Stress-strain diagram

A uniaxial specimen has the cross sectional area of 100 mm² and 20 cm long. It is first subjected to the tensile load of 35 kN. This tensile load is removed. Then, a compressive force of 35 kN is applied and removed again.

1. Write down the loading history on the stress-strain diagram

2. Determine the residual permanent deformation after all loads are removed.

2145321 Air Struc I – Ex 1-2

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

Stress elements Fill in the blanks

MPa MPa MPa

x

y

xy













20 MPa 10 MPa

30 MPa

x y xy







 



 

1

1

1 1

MPa MPa MPa

x

y

x y













2

2

2 2

7 MPa 4 MPa 5 MPa

x y x y









 



0 MPa 5 MPa 4 MPa

x y xy













1 MPa 2 MPa 0 MPa

3 MPa 0 MPa 3 MPa

x y z xy yz xz















 







 1 MPa

2 MPa 3 MPa

0 MPa 5 MPa 0 MPa

x y z xy yz xz















 









2 MPa 3 MPa

6 MPa 4 MPa 0 MPa 5 MPa

x y z xy yz xz













 



 





 

2145321 Air Struc I – Ex 1-3

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

Stress-strain relationship

Given E = 200 GPa and  = 0.3, determine the unknown normal stress and strain components and sketch the deformed element.

Stress element (unit square) Plane stress Plane strain

x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























x

z x

z

MPa MPa MPa

y

y

























2145321 Air Struc I – Ex 1-4

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

2D stress/strain transformation

Determine the stress components when the xy axes are rotated by 30° CCW to x y  axes. Then, write down in answers in the blank stress element on the right. Then, find principal stresses and the maximum in-plane shear stress and average normal stress and their orientations

MPa MPa MPa

x

y

xy













° MPa MPa MPa

x

y

x y













 









1 1 2

2

MPa

° MPa

°

p

p

















max

1

MPa MPa

°

avg s













2145321 Air Struc I – Ex 1-5

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

3D stress/strain transformation

The state of stress at a point relative to an xyz coordinate system is

200 100 0

100 0 500 MPa

0 500 0



  

 

  

 

 

1. Determine the complete state of stress relative to the new coordinate system x y z

x 60^o 90^o

y 120 ^o 30^o 90^o z 90 ^o 90^o

2. Sketch the orientation of stress element in the new coordinate system with respect to xyz coordinate system and write down the stress components on each of element’s surface.

3. Determine the principle stresses.

4. Determine the principle directions.

2145321 Air Struc I – Ex 1-6

Assignment Date: Wednesday 15 August 2012 Submission Date: In class

Name ID No

Strain Rosette

If the 2D state of strain is _x  10 10 , 20 10 , 30 10^6 _y   ^6 _xy   ^6. The state of strain is measured from the 60°

strain rosette as shown. Determine the actual readings from the strain gauges.