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

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 GG1 = KG1 - KGo G B M G1 G1 G1 G1 GG1 KG1 G1 G1 G1 KGo

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

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

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

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

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 B G

Vertical Weight Additions M 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

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

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

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

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

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 G B1 K CL

Z1 Z G1 G M T

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

KGA = 19 FT KG1 = 19.8 FT GT = GG1 x Sin O 1 -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

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 G2 G2 G G2 G G G2 G2 G2 G2 G2 GG2 B

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

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

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 GG2 = w x d Wf B M G G2 G2 G2 G2 G2 GG2

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

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

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 B B1 M G G2 B B1 M G G2 B B1 M G G2 B B1 M G G2 B B1 Z G G2 G2 G G G2 G G2 B

Z Z2 M G2 G

Z Z2 M G2 G P

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

KGA = 19 FT KG1 = 19.0 FT GG2 = .9 FT GP = GG2 x Cos O 1 -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

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

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