Design and Analysis of High Pressure Door With Stiffened Plate

DESIGN AND ANALYSIS OF HIGH PRESSURE DOOR WITH STIFFENED PLATE

DEPARTMENT OF MECHANICAL ENGINEERING Page 1

1 INTRODUCTION

This paper examines several aspects of stiffened plate structure, with an emphasis on

application to the high pressure door system. A stiffened plate is formed of a flat deck plate

integrally stiffened with stiffeners in the longitudinal and in the transverse directions. The

stiffeners are attached to the bottom side of the door plate and have different stiffness in the

orthogonal directions which is sometimes called an eccentrically stiffened orthotropic plate.

1.1 Theory of stiffened plate

A thin steel plate is very flexible when it carries loads that act in the direction of its

normal but it is extremely stiff when the loads are applied within its plane. It is this rigidity

which engineer attempt to utilize when they design thin walled structure such as door, plate

girders, box girders and so on. This restraint can be provided by folding the plate along parallel

lines, which lie in the longitudinal direction, or restraining a plate is to provide longitudinal

stiffener, which are additional plate elements whose planes are inclined to that of the plate. Thus

the concept of a stiffened plate has been developed and now a stiffened plate panel forms the

basic building block of many thin steel structures. There are basically two types of stiffener

1] Open section stiffener 2] Closed cross section stiffener.

The stiffened panel with closed cross section as shown in figure 1(b) has considerably

greater resistance to twisting moments than single connected or so called open sections. Thus the

local distortions of closed cross sections are less and it has advantages for door because there is

less likelihood of cracking of the pavement under normal pressure load. Due to use of

intermediate transverse and longitudinal stiffeners serves a dual purpose; it increases an initial

buckling load and also enables the web to carry load in excess of initial buckling due to the so



called tension field effect. There are basically four methods are used for the design and analysis

of stiffened plate as given below.

1. Analysis of an equivalent grid or beam and plate system.

2. Solution of the differential equation from orthotropic plate theory.

3. Approximate solution from Energy Principle.

4. Approximate solution by FEM.

The solution of the problem discussed in this paper is obtained by using the differential equation

from orthotropic plate theory by Naviers method.



2. ANALYTICAL SOLUTION

A door having clean opening area 1200 x 2000 mm2 subjected to high pressure air of 0.1 N/mm2

provided that the maximum deflection of the bottom door plate should be limited to 10 mm.

Material selection:

Bottom door plate = M.S. (I.S. 2062), Stiffener = M.S. (I.S. 2062),

Yield stress of mild steel = = 250 N/ mm2

2.1 Case I: Door Plate without Stiffener

Door plate of high pressure door system is nothing but rectangular plate. This rectangular plate is

simply supported subjected to high pressure air. The maximum deflection of the door plate can

be founded by using Naviers equation

=

---2.1

Where, D=flexural rigidity=

() ---2.2

As the door plate material is mild steel, consider the following parameters.

= possions ratio = 0.3, h = Thickness of door plate = 5 mm, E = 210000 N/mm2

q = pressure load acting over door plate = 0.1 N/mm2, a = width of door plate = 1200 mm.

By using above values we can get the maximum deflection.

Wmax = 358.63 mm

2.2 Case II: Door plate with vertical stiffener

In case I, it was observed that the door plate without any stiffener leads to more

deflection than required. So it becomes necessary to use stiffeners to make door more rigid. It is

possible to consider two vertical C channels of closed cross-section stiffeners attached to the



bottom door plate. With the addition of these stiffeners it is possible to find out maximum

deflection for such stiffened plate with all edges are simply supported, by using Naviers

equation.

Maximum deflection of stiffened door plate is given by Naviers method

----2.3

For this high pressure door plate,

d = Spacing between the stiffener =492 mm, a = Width of the door plate=1200 mm.

b = Depth of the door plate=2000 mm, q = uniformly distributed press.=0.1N/mm2

I = M.I. of one stiffener about the mid-plane of bottom door plate=3865926.67 mm4

E = Modulus of elasticity of plate material=210000 N/mm2

E* = Modulus of elasticity of vertical stiffener material=210000 N/mm 2

= Possions ratio=0.3, h = Thickness of the bottom door plate= 5 mm.

By using the above parameters, we can get



Table 1. Values for case II

By using all the above values in equation (2.3), we obtained the maximum deflection.

W max = 15.78 mm

It can be observed that still the maximum deflection value for this case is more than

permissible limit (10 mm). Therefore it becomes necessary to provide the stiffener in horizontal

direction also.

2.3 Case III: Door plate with vertical and horizontal stiffener

The maximum deflection of the door plate is still more than 10mm; hence it is necessary to

provide horizontal stiffeners along with two vertical stiffeners, which results in different value of

flexural rigidity in X - directions as compared to case II.

For this door plate,

d1 = spacing between the stiffener in X-direction= 492mm

d2 = spacing between the stiffener in Y-direction=334 mm

I1= M.I. of one stiffener of closed C cross section about the mid plane of the bottom door

Plate =3865926.67 mm4



I2 = M.I. of one stiffener of rectangular cross section about the mid plane of the bottom door

Plate = 482291.66mm4

By using the above parameters, we can get

By using above values in equation (2.3), we obtained the maximum deflection.

Wmax= 6.61 mm

As the maximum deflection of the door plate of the high pressure door is reduced up to 6.61mm

which less than 10 mm (prescribed limit), it can be concluded that design is safe.



3 NUMERICAL VALIDATION

In this section, the Naviers method is validated by comparison against a detailed Finite

Element model. Design the door for maximum clean opening area 1200 x 2000 mm2 subjected to

pressurized air of 0.1 N/mm2 pressure, so that the deflection of the door plate is required to be

limited to 10 mm.

3.1 Case I: Door Plate without Stiffener

The bottom door plate without stiffener subjected to high pressure air shown in figure.5 (a) is

considered for FEA Analysis using ANSYS. This pressurized air is uniformly distributed over

the door plates inner surface. The bottom door plate model consist of 4 flat plates having 12

holes for passage of shooting bolts which provide support to the door plate. The thickness of

bottom door plate is 5 mm and that of flat plate is 10 mm, pressure load acting over door plate is

0.1 N/mm2, width of door plate over which air is acting 1200mm, Modulus of elasticity is

210000 N/mm2

As shown in figure.5 (b), the maximum deflection of door plate without any stiffener for given

pressure load condition obtained by finite element analysis using ANSYS is 229.87 mm.

3.2 Case II: Door plate with vertical stiffeners

As the maximum deflection obtained in case I is far more than the permissible value 10 mm. So

the stiffeners are provided for reducing the deflection and increase in strength of the door plate.

In this case, two closed cross section box type stiffeners in vertical direction are used. The



thickness of the vertical stiffener is 5 mm. This model is also subjected to same pressure

condition.

As shown in figure 6 (b), the maximum deflection of the door plate with vertical stiffeners

obtained by finite element analysis using ANSYS software is 13.45 mm.

3.3 Door plate with vertical and horizontal stiffeners

In this arrangement the bottom door plate is provided along with vertical and horizontal

stiffeners. This structure is nothing but like grid structure. In this model it is possible to

providing 15 horizontal stiffeners. Due to increased stiffeners it is possible to getting stronger

structure leading to reduction in deflection. The thickness of the horizontal stiffener is 10 mm.



As shown in figure 7(b), the maximum deflection of the door plate with vertical stiffener and

horizontal stiffeners obtained by finite element analysis using ANSYS software is 6.66 mm

which is desirable.



4. RESULTS AND DISCUSSION

It is possible to compare the maximum deflection obtained by analytical method and

finite element method. By comparison it is come to know that the results obtained by these two

methods are very close to each other. Table No.3 Comparison of deflection



5. CONCLUSION

The example presented in this paper demonstrates the practical application of stiffeners in

the design of door system. A high pressure door model is developed and correlated in this paper.

The model encompasses analytical representations of the door without stiffeners and with

vertical, horizontal stiffeners. As shown in table no.3 the deflections obtained by both the

methods are very close to each other. From the results obtained by all three steps it is proved that

the deflection of the door plate decreases, as the number of stiffeners are increases. Thus the

arrangement of the door plate having vertical as well as horizontal stiffeners can be used to get

the desired result.



REFERENCES

[1] W.H.Hoppann, Baltimore M.D. Bending of orthogonally stiffened plates

[2] NJ.HuffingtonTheo. determination of rigidity properties of orthogonally stiffened plate

[3] Stephen P. TimoshenkoTheory of plates and shells.

[4] K.Bhaskar Analysis of plates. pp 151-152 Narosa Publishing House, London 1999.

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Design and Analysis of High Pressure Door With Stiffened Plate