Lesson 4 2 Weight Shifts Additions and Removals

Lesson 4. 2 Weight Shifts, Additions and Removals WL G 1 G Z Z 11 Z B

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

Vertical Weight Shifts GG 1 = KG 1 - KGo M GG 1 KGo G 1 G 1 G 1 G G G 11 B KG 1

KG 1 = (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

KG 1 = (Wo x KGo) ± (w x kg) Wf 25 T M Wo = 2000 T 30 FT G 1 G 1 G 1 G G 1 12 FT B KG 1 ?

45 T M Wo = 3400 T 8 FT G 15. 5 FT 33 FT B 17 T

KG 1 = (Wo x KGo)±(w 1 xkg 1)±(w 2 xkg 2) Wf WHERE; w 1&2 = Weights Shifted kg 1&2 = Distances Shifted Wo = Original Displacement KGo = Original Height of G Wf = Final Displacement ± = + if shift up/- if shift down

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

Vertical Weight Additions M G 1 G B

Vertical Weight Additions GG 1 M M M 1 1 G M M 11 GG 11 GG BB 11 B BB KG KGo 1

KG 1 = (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

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

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

M MMM M M G G G BB BBB KK K K KK CLCC LC LCL L Z B 1 BB 111

M G 11 G G G 11 1 G G 11 G Z Z 1 1 Z Z 111 Z B 1 K CL

M G 1 G T Z 1 Z

Sin O = OPP HYP WHERE; OPP = GT HYP = GG 1 Sin O = GT GG 1 O REDUCTION IN RIGHTING ARM GT = GG 1 x Sin O G T

RIGHTING ARMS (FT) KG 1 = 19. 8 FT KGA = 19 FT 5 GT = GG 1 x Sin O Sin 0° = 0 Sin 30°= 0. 5 4 GT 0°=. 8 FT x 0 = 0 FT GT 30°=. 8 FT x. 5 =. 4 FT Sin 90°= 1. 0 GT =. 8 FT x 1 =. 8 FT 90° 3 2 FINAL CURVE. 4 FT X 1 0 X -1 0 10 20 30 40 50 . 8 FT X 60 70 ANGLE OF INCLINATION - DEGREES 80 90

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

Horizontal Weight Shifts M G G G G 2 G 222222 GG 2 B

GG 2 = w x d Wf WHERE; w = Weight Shifted d = Distance shifted Wf = Final Displacement

Horizontal Weight Shifts M GG 2 = w x d Wf Wo = 3000 T G G G G 2 G 222222 GG 2 34 T B 24 FT

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

Horizontal Weight Additions and Removals M GG 2 = w x d Wf G G G 22222 GG 2 B

GG 2 = w x d Wf WHERE; w = Weight Added or Removed d = Distance Added/Removed from Centerline Wf = Final Displacement

Horizontal Weight Additions and Removals M GG 2 = w x d Wf Wo = 4500 T G G G 22222 B GG 2 28 FT 50 T

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

Cosine Correction MM M M M Z G G G GG G G 2222222 B B B B BBB 1 B 1 B 111

M G G 2 Z Z 2

M G P G 2 Z Z 2

REDUCTION IN RIGHTING ARM G O WHERE; ADJ = GP HYP = GG 2 Cos O = GP GG 2 GP = GG 2 x Cos O P Cos O = ADJ HYP G 2

RIGHTING ARMS (FT) KGA = 19 FT KG 1 = 19. 0 FT GG 2 =. 9 FT 5 GP = GG 2 x Cos O Cos 0° = 1. 0 Cos 60°= 0. 5 4 GP 0°=. 9 FT x 1 = 0. 9 FT GP 60°=. 9 FT x. 5 =. 45 FT Cos 90°= 0 GT =. 9 FT x 0 = 0 FT 90° 3 2 FINAL CURVE. 45 FT X 1 X. 9 FT 0 X Angle of List -1 0 10 20 30 40 50 60 70 ANGLE OF INCLINATION - DEGREES 80 90

RIGHTING ARMS (FT) 5 ORIGINAL CURVE CORRECT FOR KG 1 4 3 FINAL CURVE 2 N O I T C E CORR SINE COSINE C O 1 RRECTION 0 -1 0 10 20 30 40 50 60 70 ANGLE OF INCLINATION - DEGREES 80 90

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