Use of Symmetry in Structures Shatha Taha.pptx

1. Use of Symmetry in
Structures
Reflective symmetry
Shatha E.Taha
Supervised by: Dr. Gassan Masabha

2. Types of symmetry
• Reflective (mirror)
• Skew
• Axial
• Cyclic
Reflective symmetry Skew symmetry
Cyclic symmetry Axial symmetry

3. How does Reflective Symmetry achieve?
A correspondence in:
▪ Size, Shape, and position of loads.
▪ material properties (E , Poisson's ratio)
▪ boundary conditions that are on opposite sides of a dividing line or plane

4. No symmetry in geometry No symmetry in load and
boundary conditions
symmetry
No symmetry in geometry, load and material
properties
symmetry

5. Example:

6. Solution:
1) Find the plane of reflective symmetry
2) Forces in the plane of symmetry are reduced
by half
3) Cross-sectional Area of elements in the plane
of symmetry is reduced by half
4) Vertical roller hinges must be installed on
nodes in the plane of symmetry

7. Reduced Structure :
 Number of nodes = 4
 Number of elements = 6
 𝐴 = 3 ∗ 10−4 𝑚2
 𝐸 = 70 𝐺𝑃𝑎
 𝐹𝑦2 = −50 𝑘𝑁
 𝐹𝑦4 = −50 𝑘𝑁
 𝐹𝑥2 = 0 𝑘𝑁
• Nodes coordinates:
 Node 1 ( 0 , 0 )
 Node 2 ( 0 , 3 )
 Node 3 ( 3 , 0 )
 Node 4 ( 3 , 3 )

8. Sample Calculation :
stiffness matrix for element 1
 Node 1 ( 0 , 0 )
 Node 2 ( 0 , 3 )

9. Sample Calculation :
Global stiffness matrix

10. Sample Calculation :
Global stiffness matrix

11. Sample Calculation :

12. Sample Calculation :

13. Analysis Using (ABAQUS) Software

14. Hand Calculation VS. Software
Node 𝑭𝒙 ( 𝒌𝑵 ) 𝑭𝒚 (𝒌𝑵 ) 𝑼𝒙 (𝒎) 𝑼𝒚 (𝒎)
1
H.C 40.531 100 0 0
S 40.5330 100 0 0
2
H.C 0 -50 0.00135275 -0.00849561
S 0 -50 0.00135244 -0.00849524
3
H.C 9.469 0 0 -0.0136755
S 9.46695 0 0 -0.0136724
4
H.C -50 -50 0 -0.01638101
S -50 -50 0 -0.0163773
Element
#
1 2 3 4 5 6
Stress
(MPa)
H.C – 198 0 44.6 -31.6 -191 -63.1
S – 199.71 2.04715 44.6218 -33.1045 -190.72 -60.0538

15. Thank you!