1. Weight Shifts, Additions and Removals
Lesson 4.2
Weight Shifts, Additions and Removals B WL G1 Z1 G Z

2. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horiz Weight Additions / Removals 6. Cosine Correction 7. Example Problem

3. Vertical Weight Shifts
GG1 = KG1 - KGo G B M G1 G1 G1 G1
GG1
KG1 G1 G1 G1
KGo

4. KG1 = (Wo x KGo) ± (w x kg) Wf WHERE; w = Weight Shifted
kg = Distance Shifted
Wo = Original Displacement
KGo = Original Height of G
Wf = Final Displacement
± = + if shift up/- if shift down

5. KG1 = (Wo x KGo) ± (w x kg) Wf 30 FT 25 T M Wo = 2000 T G1 G1 G1 G1 G1B

6. 45T
Wo = 3400 T M
8 FT
33 FT G
15.5 FT B
17T

7. WHERE; w1&2 = Weights Shifted
KG1 = (Wo x KGo)±(w1xkg1)±(w2xkg2) Wf
WHERE; w1&2 = Weights Shifted
kg1&2 = Distances Shifted
Wo = Original Displacement
KGo = Original Height of G
Wf = Final Displacement
± = + if shift up/- if shift down

8. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem

9. Vertical Weight AdditionsM B G

10. Vertical Weight AdditionsM B G G1 M1 B1 M B G G1 M1 B1 M B G G1 M1 B1 M B G G1 M1 B1
GG1
KGo
KG1

11. KG1 = (Wo x KGo) ± (w x kg) Wf WHERE; KGo = Original Height of G
Wo = Original Displacement
± = + if addition/- if removal
w = Weight Added/Removed
kg = Distance Keel to "g" of wt
Wf = Final Displacement

12. 42 FT
16 TONS
Wo = 2000 TONS
KGo = 12 FT
ADD

13. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem

14. Z CL K B G M B1 CL K B G M B1 CL K B G M B1 CL K B G M B1 CL K B G M

15. Z Z1 Z1 Z Z Z1 Z Z1 Z1 Z Z1 Z Z1 Z Z G G1 G1 G M G G1 G G1 G1 G G1 GB1 K CL

16. Z1 Z G1 G M T

17. G1 G T Sin O = OPP HYP WHERE; OPP = GT O HYP = GG1 Sin O = GT GG1
REDUCTION IN
RIGHTING ARM
GT = GG1 x Sin O

18. KGA = 19 FT KG1 = 19.8 FT GT = GG1 x Sin O1 -1 2 3 4 5 10 20 30 40 50 60 70 80 90
ANGLE OF INCLINATION - DEGREES
RIGHTING ARMS (FT)
KGA = 19 FT
KG1 = 19.8 FT
GT = GG1 x Sin O
Sin 0° = 0 Sin 30°= 0.5 Sin 90°= 1.0
GT0°= .8FT x 0 = 0 FT
GT30°= .8FT x .5 = .4 FT
GT90°= .8FT x 1 = .8 FT
FINAL CURVE X
.8 FT X
.4 FT X

19. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem

20. Horizontal Weight ShiftsM G G2 G2 G G2 G G G2 G2 G2 G2 G2
GG2 B

21. GG2 = w x d Wf WHERE; w = Weight Shifted d = Distance shifted
Wf = Final Displacement

22. Horizontal Weight Shifts
GG2 = w x d Wf M
Wo = 3000 T G G2 G2 G2 G G2 G G G2 G2 G2 G2
GG2 B
34 T
24 FT

23. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem

24. Horizontal Weight Additions and Removals
GG2 = w x d Wf B M G G2 G2 G2 G2 G2
GG2

25. GG2 = w x d Wf WHERE; w = Weight Added or Removed
d = Distance Added/Removed from Centerline
Wf = Final Displacement

26. Horizontal Weight Additions and Removals
GG2 = w x d Wf B M G
Wo = 4500 T
50 T G2 G2 G2 G2 G2
GG2
28 FT

27. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem

28. Cosine Correction B B1 M G G2 B B1 M G G2 B B1 M G G2 B B1 M G G2 B B1Z G G2 G2 G G G2 G G2 B

29. Z Z2 M G2 G

30. Z Z2 M G2 G P

31. P G G2 O Cos O = ADJ WHERE; HYP ADJ = GP HYP = GG2 Cos O = GP GG2
REDUCTION IN RIGHTING ARM G2 G P O
Cos O = ADJ
HYP
WHERE;
ADJ = GP
HYP = GG2
Cos O = GP
GG2
GP = GG2 x Cos O

32. KGA = 19 FT KG1 = 19.0 FT GG2 = .9 FT GP = GG2 x Cos O1 -1 2 3 4 5 10 20 30 40 50 60 70 80 90
ANGLE OF INCLINATION - DEGREES
RIGHTING ARMS (FT)
KGA = 19 FT
KG1 = 19.0 FT
GG2 = .9 FT
GP = GG2 x Cos O
Cos 0° = 1.0 Cos 60°= 0.5 Cos 90°= 0
GP0°= .9FT x 1 = 0.9 FT
GP60°= .9FT x .5 = .45 FT
GT90°= .9FT x 0 = 0 FT
FINAL CURVE X
.9 FT X
.45 FT X
Angle of List

33. ORIGINAL CURVE 1 -1 2 3 4 5 10 20 30 40 50 60 70 80 90
ANGLE OF INCLINATION - DEGREES
RIGHTING ARMS (FT)
CORRECT FOR KG1
FINAL CURVE
SINE CORRECTION
COSINE CORRECTION

34. CLASS TOPICS
1. Vertical Weight Shifts 2. Vertical Weight Additions/Removals 3. Sine Correction 4. Horizontal Weight Shifts 5. Horizontal Weight Additions/Removals 6. Cosine Correction 7. Example Problem