1. L02 - Load and stress analysis
302315
L02 - Load and stress analysis

2. Identify critical cross sections Principle stress determination
Load analysis
Assume materials to be homogeneous and isotropic
Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD
Load termination
Based on the load distribution, determine what cross sections of the part are most heavily loaded.
Identify critical cross sections
(SFD, BMD)
Determine the stress distribution over the cross section of interest. Locate the highest of applied and combine stresses
Stress determination
identify state of stress at a points of interest
Stress element
Calculate the principal stresses and maximum shear stress
Principle stress determination
Calculate the critical deflection of the part
Critical Deflection
Failure criteria

3. Crimping tool-static loading

4. FBD
Link3
Link4
Link2

5. 15 varibles; 13 equations
1) F12x + F32x = 0
2) Fh + F12y + F32y = 0
3) RhFh + (R12xF12y - R12yF12x) + (R32xF32y – R32yF32x) = 0
4) F23x + F43x = 0
5) F23y + F43y = 0
6) (R23xF23y – R23yF23x) + (R43xF43y – R43yF43x) = 0
7) Fc4x + F34x + F14x = 0
8) Fc4y + F34y + F14y = 0
9) (Rc4xFc4y – Rc4yFc4x) + (R34xF34y – R34yF34x) + (R14xF14y – R14yF14x) = 0
Link2
Link3
Link4
10) F32x - F23x = 0
Given
11) F32y - F23y = 0
12) F43x - F34x = 0
13 varibles; 13 equations
13) F43y - F34y = 0

6. Cross product Mz= (RxFy-RyFx) Moment = R x F (+) i (-) j (+) k Rx RyRz Fx Fy Fz
M = Mxi + Myj + Mzk i j k Rx Ry Rz Fx Fy Fz i j k Rx Ry Rz Fx Fy Fz i j k Rx Ry Rz Fx Fy Fz
Mxi = (RyFz-RzFy)i
Myj = - (RxFz-RzFx)j
Mzk = (RxFy-RyFx) k
In 2 - D
(+) i
(-) j
(+) k Rx Ry Fx Fy
Mx= 0
Mz= (RxFy-RyFx)
My = 0

7. Assignment AS01

8. Solving system of linear equations
Inverse matrix
Cramer’s rule
Gaussian elimination

9. solution Force geometric data 1 Fh 0.236 kN Rh -111.76 mm 2 F12x 6.732
R12x
35.56 3
F12y
-1.695
R12y
1.27 4
F32x
-6.732
R32x
55.88 5
F32y
1.459
R32y
2.032 6
F23x
R23x
-15.24 7
F23y
-1.459
R23y
3.302 8
F43x
R43x
15.24 9
F43y
R43y
-3.302 10
F34x
R34x
4.064 11
F34y
R34y
19.304 12
F14x
1.969
R14x
-4.064 13
F14y
-0.390
R14y 14
Fc4x
-8.701
Rc4x
11.43 15
Fc4y
1.849
Rc4y
8.636 16
Fc1x
8.701
Rc1x 17
Fc1y
-1.849
Rc1y 18
F21x
R21x 19
F21y
1.695
R21y 20
F41x
-1.969
R41x 21
F41y
0.390
R41y
solution

10. matrix

11. Link 3 – compression load

12. Link 4 – bending load

13. Combine load

14. Load Static load dynamic load Impact load Vibration Beam load Type
Load termination
Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD
dynamic load
Impact load
Vibration
Beam load
Type
location
direction
Time-variation
Magnitude
concentrate
force
duration
distribute
continuation
torque
uniform
moment
non-uniform

15. Stress analysis
Column and Beam

16. Identify critical cross sections Principle stress determination
Stress analysis
Assume materials to be homogeneous and isotropic
Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD
Load termination
Based on the load distribution, determine what cross sections of the part are most heavily loaded.
Identify critical cross sections
(SFD, BMD)
Determine the stress distribution over the cross section of interest. Locate the highest of applied and combine stresses
Stress determination
identify state of stress at a points of interest
Stress element
Calculate the principal stresses and maximum shear stress
Principle stress determination
Calculate the critical deflection of the part
Critical Deflection
Failure criteria
Calculate Von Mises effective stress at each selected point based on the principal stresses
Trial on a material
Compute safety factor based on tensile yield strength of that material
DUCTILE MATERIALS
Calculate Coulomb-Mohr effective stress at each selected stress element based on its principal stresses
Compute safety factor based on ultimate tensile strength of that material
BRITTLE MATERIALS

17. Stress component
sxx txy txz
tyx syy tyz
tzx tzy szz
sxx txy
tyx syy

18. transformation stress

19. Normal stress
The plane at which zigma is max, shear stress is zero

20. SHEER STRESS
The plane at which shear stress is max,

21. Principal stress

22. Mohr’s circle 2-D https://youtu.be/WOCFY4gnTyk
3-D

23. Assignment
Dynamic load
Stress in Beam

24. Dynamic loading Fx = max Fy = may Mz = Izz dynamic analysis
Fz = maz
Mx = Ixx – (Iy-Iz)yz
My = Iyy – (Iz-Ix)zx
Mz = Izz – (Ix-Iy)xy
2-D in x-y plane
Fx = max
Fy = may
Mz = Izz

25. caSE : Link 4 STRESS IN BEAM

26. Shear stress
SFD – Sheer force diagramj

27. Stress due to bending
BMD – Bending moment diagramj