Exercise 2
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Transcript of Exercise 2
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