Report Rigo 4 Almir

Strength of the Material

Exercise 4.

Giventhe following light ship condition, determineW (T/m)and M (T/m). Make the long. system scantling of ship and find the

ultimate bending moment in case of sagging and hogging, by using two methods: Paik method and Rahman method.

Compare the results and comment why do you think the results are different?

Strength of the Material 1

4.5m

5.5m

W

M

20m

100m

B=16m

A

Section A-A

H=11m

A

Ship scantling

The scantling has done by longitudinal system. There is no transverse bulkheads considered on this exercises. The frames

and the girder are identical in dimensions, so that both elements share the load and support each other.

We adopt the following values in the exercise:

Frame Spacing: 2500 mm

Stiffener Spacing: 500 mm

Bottom Plate Thickness: 17 mm

Side Shell Thickness:

12 mm

Deck Plate Thickness: 10 mm

Bottom [mm]Bottom [mm] Side [mm]Side [mm] Deck [mm]Deck [mm] Girder & Frames [mm]Girder & Frames [mm]

HW 250 HW 200 HW 150 HW 500

TW 20 TW 10 TW 10 TW 20

HF 100 HF 100 HF 80 HF 200

TF 25 TF 15 TF 15 TF 20

Stiffener Dimensions


4.58

4 AGider

Gider

Section A-A

Neutralaxis


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Ultimat bending moment by Paik

Using the program developed in Fortran we got ultimat bending moment for case of Sagging and Hogging. The obtained

data are presented in the following table.

Results of Paik method - Deck PanelsResults of Paik method - Deck PanelsResults of Paik method - Deck Panels

Beta 1.7251 -

Lamda 0.4345 -

Yield strenght 250.0 N/mm2

Ultimate compressive strenght 187.3 N/mm2

Relative Iltimate strenght SULT/SY 0.749 -

Results of Paik method - Bottom PanelsResults of Paik method - Bottom PanelsResults of Paik method - Bottom Panels

Beta 1.0148 -

Lamda 0.2546 -




Results of Paik method - Side Shell (upper/lower)Results of Paik method - Side Shell (upper/lower)Results of Paik method - Side Shell (upper/lower)

Beta 1.4376 -

Lamda 0.3284 -




Results of Paik method - Ultimate bending momentsResults of Paik method - Ultimate bending momentsResults of Paik method - Ultimate bending moments

Fully plastic bending moment 1365752 kNm

G axis 2.7621 m

Fully plastic shear force 65386.8 kN

Neutral axis 4.527 m

SAGGING: Ultimate bending moment MU 1 114 864 kNm

MULT/MPlastic 0.8163

HOGGING: Ultimate bending moment MU 1 268 021 kNm

MULT/MPlastic 0.9284


Ultimat bending moment by progresive collaps analyses ( method of Rahman)

Using the program developed by Fortran of Rahmans method we consider also the value of lateral pressure and initial

imperfection. In the obtained result we can see what is the strength of the stiffener and what for the plate and we can know

what will buckle first. The results obtained from Rahmans method are presented in the following table:

Results of Rahman method - Deck PanelsResults of Rahman method - Deck PanelsResults of Rahman method - Deck Panels

Panel strenght when stiffenr is under compress. 240.80 N/mm2

Panel strenght when plate is under compress. 190.37 N/mm2


Ultimate compressive strenght (we take the smallest) 190.37 N/mm2


Results of Rahman method - Bottom panelsResults of Rahman method - Bottom panelsResults of Rahman method - Bottom panels






Results of Rahman method - Side ShellResults of Rahman method - Side ShellResults of Rahman method - Side Shell






Results of Rahman method - Ultimate bending momentsResults of Rahman method - Ultimate bending momentsResults of Rahman method - Ultimate bending moments

Fully plastic bending moment 1353000 kNm

SAGGING: Ultimate bending moment MU 987 269 kNm

MULT/MPlastic 0.729

HOGGING: Ultimate bending moment MU 1 233 157 kNm

MULT/MPlastic 0.911


Now we can present our data of progresive collaps ( in matlab program) in stress-strain relations for the case sagging and

hogging in the same diagram in order to see the difference. In the first diagram on the X-axis is mean strain and on the Y-axis

is applied strss in [N/mm2 or MPa]. In the second diagram on the X-axis is relation of applied strain/yield strain and on the Y-

axis is applied strss/yield stress. We can see the tree zones of the Rahmans method. First zone is stable zone, second one

is no-load shedding zone where the ultimate stress is reached and remain constant for some time, and the third zone is

postcolapse or load-sheding zone where we have decreasing of the stress. The yield stress is 250 [N/mm2].

In the next table we can see the comparison between results of Paik method and Rahman method, so we have:

Comparison between two methodsComparison between two methodsComparison between two methodsComparison between two methods

Description Paik Rahman Unit

Deck - Ultimate compressive strenght 187.3 190.37 N/mm2

Deck - Relative ultimate strenght SULT/SY 0.749 0.761 -

Bottom - Ultimate compressive strenght 224.2 201.67 N/mm2

Bottom - Relative ultimate strenght SULT/SY 0.897 0.8067 -

Side shell - Ultimate compressive strenght 204.9 191.24 N/mm2

Side shell - Relative ultimate strenght SULT/SY 0.82 0.765 -

SAGGING: Ultimate bending moment MU 1 114 864 987 269 kNm

MULT/MPlastic 0.8163 0.729

HOGGING: Ultimate bending moment MU 1 268 021 1 233 157 kNm

MULT/MPlastic 0.9284 0.911


Conclusion

The Paik method is based on the empirical formulation of the ultimate compressive strength of a stiffened panel as a function

of the plate slenderness and the column slenderness ratio and dont consider any effective with of plate. It takes into

account residual stress and initial imperfections but it is implicitly included in the relations and cannot be changed. This

method also doesnt include the lateral pressure.

Rahmans method is progressive collapse analysis which is based on approach of applied incremental curvature. The

ultimate compressive strength of a stiffened panel is determined according to Hughes method. This method takes into

account lateral pressure. The residual stress and initial imperfection are not included into the relation, in this method you

enter these values. In my case I assume 10% of residual stress and 0.001 for the initial imperfection.

The results that obtained from both methods are different. The Rahmans method gave us smaller results for the bending

moments and stiffened panels except for the deck where gave bigger value in comperison with Paik.

Comparison between two methodsComparison between two methodsComparison between two methodsComparison between two methodsComparison between two methodsComparison between two methods

Description Paik Rahman Diffe. Unit

Deck - Ultimate compressive strenght 187.3 < 190.3 3.07 N/mm2

Bottom - Ultimate compressive strenght 224.2 > 201.6 22.6 N/mm2

Side shell - Ultimate compressive strenght 204.9 > 191.2 13.7 N/mm2

SAGGING: Ultimate bending moment MU 1 114 864 > 987 269 127 595 kNm

HOGGING: Ultimate bending moment MU 1 268 021 > 1 233 157 34 864 kNm

If we look to the scanling we can see that the web plates on the deck are (150x15) that are shorter than the side or bottom

web plates. Now just to play little bit I will change the aspect ratio of web profile on the deck and side shell but keeping the

same section area. Instead of web dimension 150x15 I will put 225x10 for deck which is the same area and instead of

200x15 put 250x12 to be more slender. Also I will try to exclude the lateral pressure from the second method, so I will keep

it zero. Now start the both programs again and we got:

Comparison between two methodsComparison between two methodsComparison between two methodsComparison between two methodsComparison between two methodsComparison between two methods

Description Paik Rahman Diffe. Unit

Deck - Ultimate compressive strenght 195.71 > 195.75 0.04 N/mm2

Bottom - Ultimate compressive strenght 224.2 > 211.6 12.6 N/mm2

Side shell - Ultimate compressive strenght 208.3 > 203.8 4.5 N/mm2

SAGGING: Ultimate bending moment MU 1 145 427 > 1071 910 73 517 kNm

HOGGING: Ultimate bending moment MU 1 269 350 > 1 261 610 7740 kNm

Now we can see that obtained results are closer. As we can see that the lateral pressure can cause some difference in the

results how it is not included into Paiks method. Also we can see that when we change the aspect ratio of scantling by

keeping the same section area, both of methods response different on it. So it may happen that for some aspect ratio

obtained results are very close but for samo another ratio little far. Also the effective width is not included implicitly into the

Paiks method.

Anyhow the results have no significant difference and both methods are good. But seams that Rahmans method is little

more accurate and provide more informations than Paiks method.


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Report Rigo 4 Almir