REPORT Strength of the Material

 Student: Almir Becirspahic

       

 European Master Course in “ADVANCED SHIP DESIGN”

 

Ship Structure and Ship Production By

Prof. Ph. RIGO                

Liege, 2014

 Exercise  2.      Given  the  following  light  ship  condition,  determine  W  (T/m)  and  M  (T/m).  Draw  the  load  distribution,  shear  force  and  bending  moment  diagrams.              

       

     First  we  have  to  find  the  position  of  buoyancy  force.  So  we  will  find  the  center  of  gravity  for  the  draft.  We  rectangle  2,5x100  and  triangle  1x100,  so  we  get:      

! =!! ∙ !! =

50 ∙ 250+ 66,6 ∙ 50250+ 50 =

12500+ 3330300 = 52,7  !  

 After  that  we  can  calculate  buoyancy  force  with  density  of  water  1000  kg/m3  

 !! = 300 ∙ 16 ∙ 1000 = 4800  !    Equation  for  calculating  M  and  W,  moment  equation  is  around  center  (50m):      

!! = 0    ! ∙ 100+! ∙ 20− 4800 = 0  

!! = 0    !! ∙ 2,7−! ∙ 800 = 0    

! =!! ∙ 2,7800 =

4800 ∙ 2,7800 = 16,2  !/!  

 

! =4800−! ∙ 20

100 =480− 32,4

10 =447,610 = 44,7  !/!  

   When  we  have  M  and  W  we  will  divide  our  ship  in  20  parts  and  make  table  for  calculation  shear  force  and  bending  moment.            

M  

W  

3,5m  2,5m  

100m  

20m  

16m  

11m  

 Calculations  Table:        The   table   is   imported   from   the   program   numbers   witch   is   similar   to   excel.  Integrate  in  tabular  form  using  Trapezoidal  Rule,  with  spacing  5m.  Draft  equation,    T(x)  =  0.01  x  +  2.5    ;        NetLoad  =  (W+  M)  –  BUOYANCY  I’ve  made  correction  for  the  bending  moment  calculations  due  to  my  integration  method   that   becomes   not   so   accurate.   The   greater   is   the   polynomial   function  more  error  is  imputed  in  the  solutions.        

     When  we  have  our  data  in  the  table  we  can  plot  the  diagrams.                      

X Draft Buoyancy Load Net load dlt. SF SF Avg SF Avg BM BM Corr BM m m T/m T/m T/m T T T T m T m T m

1 0.00 2.50 40.00 44.76 4.76 23.80 0.00 0.00 0.00 0.00 0.00 0.00 2 5.00 2.55 40.40 44.76 4.36 21.80 21.80 10.90 54.50 54.50 -128.30 25.65 3 10.00 2.60 41.20 44.76 3.56 17.80 39.60 30.70 153.50 208.00 -135.05 72.95 4 15.00 2.65 42.00 44.76 2.76 13.80 53.40 46.50 232.50 440.50 -142.16 298.34 5 20.00 2.70 42.80 44.76 1.96 9.80 63.20 58.30 291.50 732.00 -149.64 582.36 6 25.00 2.75 43.60 44.76 1.16 5.80 69.00 66.10 330.50 1,062.50 -157.52 904.98 7 30.00 2.80 44.40 44.76 0.36 1.80 70.80 69.90 349.50 1,412.00 -165.81 1,246.19 8 35.00 2.85 45.20 44.76 -0.44 -2.20 68.60 69.70 348.50 1,760.50 -174.54 1,585.96 9 40.00 2.90 46.00 44.76 -1.24 -6.20 62.40 65.50 327.50 2,088.00 -183.72 1,904.28

10 45.00 2.95 46.80 44.76 -2.04 -10.20 52.20 57.30 286.50 2,374.50 -193.39 2,181.11 11 50.00 3.00 47.60 44.76 -2.84 -14.20 38.00 45.10 225.50 2,600.00 -203.57 2,396.43 12 55.00 3.05 48.40 44.76 -3.64 -18.20 19.80 28.90 144.50 2,744.50 -214.28 2,530.22 13 60.00 3.10 49.20 44.76 -4.44 -22.20 -2.40 8.70 43.50 2,788.00 -225.56 2,562.44 14 65.00 3.15 50.00 44.76 -5.24 -26.20 -28.60 -15.50 -77.50 2,710.50 -237.43 2,473.07 15 70.00 3.20 50.80 44.76 -6.04 -30.20 -58.80 -43.70 -218.50 2,492.00 -249.93 2,242.07 16 75.00 3.25 51.60 44.76 -6.84 -34.20 -93.00 -75.90 -379.50 2,112.50 -263.09 1,849.41 17 80.00 3.30 52.40 44.76 -7.64 -38.20 -131.20 -112.10 -560.50 1,552.00 -276.93 1,275.07 18 85.00 3.35 53.20 60.96 7.76 38.80 -92.40 -111.80 -559.00 993.00 -291.51 701.49 19 90.00 3.40 54.00 60.96 6.96 34.80 -57.60 -75.00 -375.00 618.00 -306.85 311.15 20 95.00 3.45 54.80 60.96 6.16 30.80 -26.80 -42.20 -211.00 407.00 -323.00 84.00 21 100 3.50 55.60 60.96 5.36 26.80 -0.00 -13.40 -67.00 340.00 -340.00 0.00 21 100 3.5 56.00 60.96 4.96

W 44.76 M 16.2

W+M

60.96

Net  Load,  Shear  Force  and  Bending  Moment  diagrams:      The  diagrams  drew   in   the  program  numbers  witch   is  similar   to  excel.  The   first  diagram  for  Net  Load  has  one  problem  in  the  point  80,  because  I  plotted  diagram  from   table   not   by   hand,   and   it   has   to   be   vertical.   So   only   consider   from   80   is  vertical.                                                                                      

-8.00

-6.00

-4.00

-2.00

0

2.00

4.00

6.00

8.00

0 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

-150.00

-112.50

-75.00

-37.50

0

37.50

75.00

112.50

0 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

0

600.00

1200.00

1800.00

2400.00

3000.00

10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

Net  Load  

Shear  Force  

Bending  Moment