protank dome roof

8/13/2019 Protank Dome Roof

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INTRODUCTION

A structural finite element analyses were performed on a dome roof structure. Details

of the geometry and dimensions of the structure were given by the client. This report presents

the deformation responses of the dome roof structure under several anticipated load cases.

The internal moment acted in the radial and ring rafters is calculated. The correspondingstresses developed in the plate and rafter materials are discussed in terms of equivalent von

Mises stress.

A. MODEL

The dome roof structure measures 33.0 m in diameter and 3.359 m high. It is divided

into four circular sections, each section is separated by compression ring. Series of radial

rafters are welded to the rings thus making up the skeletal structure of the dome. The skin of

the dome roof is fabricated from 8 mm-thick steel plates using welded lap joints. Detail

drawing of the roof is reproduced, as shown in FIGURE P1 of Appendix I.

Due to symmetrical nature of the dome roof structure geometry, loading andboundary conditions, only a quarter of structure was modeled. Two views of this symmetrical

part are illustrated in FIGURE A1. Plane 1-2 and plane 2-3 are symmetry planes. The lines

represent radial rafters, rings and lap joints of the roof plates.

Cross-sectional dimensions of critical structural members are listed in Table A1.

Table A1 Size of critical members

Member Size

Roof plate 8 mm-thick

Radial rafter (Section 2,3,4) 100 x 75 x 10 mm

Radial rafter (Section 1) 75 x 65 x 10 mm

Ring rafter (Section 1,2,3,4) 100 x 75 x 10 mm

Lap joint 50 mm wide

The model is discretized into finite elements and nodes for structural stress analysis using the

finite element method. Types of elements used in the analysis are:

Plate - S4R (4-node quadrilateral shell elements with reduced integration)Angle - B31 (2-node linear 3D beam elements)

Total number of elements = 114,207

Total number of nodes = 131,695


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The following properties of a typical structural steel is used for the analysis:

Youngs modulus, E = 190 GPa

Poissons ratio, v= 0.30

Shear modulus, G = 73 GPa

Density, = 7850 kg/m

-3

= 7.850 x 10

-9

tonnes/mm

-3

The calculated mass of the quarter model is 17.221 tonnes.

The added stiffness to the dome roof structure due to welded lap joint of the roof plates is

considered through its moment of inertia effects as follows:

2

4mm

8mm 1

50 mm

The boundary conditions imposed on the model are as follows:

Symmetry of radial planes:Each radial plane at both sides of model (plane 1-2 and plane 2-3) is constrained such that:

(a) No displacement is allowed normal to the symmetry planes(b) Only in-plane rotational displacement is allowed for the symmetry planes.

Base of dome roof:The base of the dome roof is constrained from vertical displacement during simulation of

fabrication condition (i.e. simply supported).

When the dome roof is in-place, the base is constrained from all displacements and rotations

(fixed condition).

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Section 3

Section 2

Section 1

Section 4

Radial

rafter

Ring

Apex

Base

(a)

Apex

Base

(b)

FIGURE A1 Geometry of the quarter model of the dome roof

structure: (a) isometric view and (b) side view of the model.

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B. LOADING

Two different loading configurations were simulated. Load case A1 represents

fabrication condition where the dome roof is assumed rested on a rigid platform. Only the

weight of the roof contributes to the loading. Load cases B1 through B6 represent the

assembled dome roof with different loading conditions expected during operation.

All load cases are summarized in Table B1. The following magnitudes are used:

Dead load (DL) due to self weight of the dome roof structure.

Live load (LL) is 1.20 kN/m2acting normal to the roof plates.

Point load (PL) is 2.94 kN (or 300 kg-mass) acting in the middle of each radial rafter.Wind load (WL) is 0.72 kN/m

2acting normal to the roof plates.

Table B1 - Loading matrix for the analysis.

LoadCase Configuration Description

A1 Fabrication DL

B1 DL

B2 DL+LL

B3 DL+PL

B4 DL+WL

B5 DL+LL+WL

B6

Assembled

DL+PL+WL

It is required that the calculated stresses do not exceed the allowable stress of thematerial at 144 MPa. It is noted that the yield strength of typical carbon steels rangesbetween 205 MPa (ASTM A283 Gr C) to 250 MPa (ASTM A36).

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C. RESULTS AND DISCUSSIONFabrication condition (Load Case A1)

The deformation of the dome roof due to the self weight is shown in terms of total

displacement, u and and vertical displacement, u2 as shown in FIGURE C1 and FIGURE C2,respectively. A lateral displacement of 4.01 mm (outwards) is calculated at the simply-

supported base of the dome roof. The maximum vertical displacement of the roof is 11.85

mm with the distribution as shown in FIGURE C2 (the negative sign in the figure indicates adownward displacement)

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FIGURE C1 Total displacement field of the dome roof due toself-weight during fabrication condition (Load Case A1)

FIGURE C2 The vertical displacement component of the domeroof due to self-weight during fabrication condition (Load Case A1)

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The corresponding stress distribution in the dome roof plates is expressed in terms ofvon Mises stress, as shown in FIGURE C3. The maximum calculated stress is 76.2 MPa

occurring at the constrained base of the dome roof. This gives a factor of safety of 1.89 (i.e.

144 MPa / 76.2 MPa).

The section moment in the rafters and ring structures are distributed as shown in

FIGURE C4 and FIGURE C5 for direction 1 and 2, respectively. The positive sense of the

bending moments, SM1, SM2 and SM3 about axis-1, axis-2 and axis-3, respectively areillustrated as follows:

2

1

SM3

SM2

SM1

3

The greatest magnitudes of moment in each coordinate direction for Load Case A1 are:

SM1 = -980.1 N.m

SM2 = 408.5 N.mSM3 = -17.5 N.m

These magnitudes occur for rafters in Section 4 of the dome roof, as shown in FIGURE C4.The corresponding von Mises stress distribution in the rafters and rings is shown in FIGURE

C6. A maximum stress of 43.8 MPa is predicted for rafters in Section 4 of the dome roof,

closest to the base region.

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FIGURE C3 von Mises stress distribution in the dome roof plates due

to self-weight during fabrication condition (Load Case A1)

FIGURE C4 Distribution of bending moment, SM1 in the rafters andrings about axis-1 due to self-weight of the dome roof during fabrication

condition (Load Case A1)

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FIGURE C5 Distribution of bending moment, SM2 in the rafters and

rings about axis-2 due to self-weight of the dome roof during fabrication


FIGURE C6 von Mises stress distribution in the rafters and rings

structure of the dome roof due to self-weight during fabrication


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Assembled condition

(Sample description for Load Case B6)

The vertical displacement of the dome roof due to the Load Case B6 (combination of

self-weight, point load and wind load) is shown in FIGURE C7. The maximum vertical

displacement of the roof is 2.02 mm occurring at the apex region (Section 1). No lateraldisplacement is allowed at the welded base of the dome roof.

The von Mises stress distribution in the dome roof plates is shown in FIGURE C8.The maximum calculated stress is 18.5 MPa occurring at the apex region of the dome roof.

This corresponds to a factor of safety of 7.78 (i.e. 144 MPa / 18.5 MPa).

The section moment in the rafters and ring structures are distributed as shown in

FIGURE C9 and FIGURE C10 for direction 1 and 2, respectively. The greatest magnitudes

of moment in each coordinate direction for Load Case B6 are:

SM1 = 336.0 N.mSM2 = -141.8 N.m

SM3 = 1.794 N.m

These typical magnitudes occur for rafters in Section 1 (closest to the apex) and Section 4

(closest to the fixed base) of the dome roof as shown in FIGURE C9 and FIGURE C10. Thecorresponding von Mises stress distribution in the rafters and rings is shown in FIGURE

C11. A maximum stress of 16.83 MPa is predicted for rafters in Section 1 of the dome roof.

It is worth noting that this rafter has smaller cross sectional area than other radial rafters.

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FIGURE C7 The vertical displacement component of the domeroof due to Load Case B6 (combination of self-weight, point load

and wind load)

FIGURE C8 von Mises stress distribution in the dome roof plates dueto Load Case B6

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FIGURE C9 Distribution of bending moment, SM1 in the rafters andrings about axis-1 due to Load Case B6

FIGURE C10 Distribution of bending moment, SM2 in the rafters and

rings about axis-2 due to Load Case B6

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FIGURE C11 von Mises stress distribution in the rafters and rings

structure of the dome roof due to Load Case B6

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The maximum vertical displacement, u2 (mm), and von Mises stress, Mises (MPa)experienced by the dome roof structure for the different loading cases considered are

summarized in Table C1. The distribution of von Mises stresses for other load cases is

compiled in Appendix II.

Table C1 Maximum displacement, stress and bending momentin the dome roof structure for different load cases

Plate RafterLoad

Case u2 (mm) Mises(MPa) Mises(MPa)

A1 -11.85 76.21 43.82

B1 -0.5203 4.66 6.60

B2 -1.074 9.59 13.57

B3 -1.831 17.27 16.51

B4 -0.8423 7.04 10.81

B5 -1.425 13.59 17.78

B6 -2.018 18.50 16.83

The largest downward vertical displacement, u2 = 11.85 mm is predicted for the Load

Case A1 because there is no lateral support at the base of the dome roof during the

fabrication condition. In the assembled condition (with fixed support at the base) thecombination of self weight, concentrated forces and wind load (Load Case B6) resulted in the

highest vertical displacement of 2.02 mm.

In all the loading conditions considered, the maximum von Mises stresses in the roof

plate is 76.21 MPa while the stress in the rafter is 43.8 MPa, both corresponding to the Load

Case A1. These magnitudes are well within the allowable stress of 144 MPa, specified for thesteel.

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CONCLUSIONS

1. Boundary conditions and loading corresponding to the fabrication condition of thedome roof structure resulted in the severest deformation and stresses. However, the

response of the material is within the specified allowable stress.

2. All loading cases considered for the assembled dome roof structure resulted insmaller magnitude of deformation and stresses when compared to that predictedduring fabrication of the structure.

3. Concentrated forces (300-kg mass each) applied to each radial rafter contributed tothe greatest effect on stresses in the rafter when compared with other types of load

(compare Load Case B3 with Load Cases B1, B2 and B4).

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APPENDIX I

FIGURE P1 - Drawing of the dome roof structure used in the analysis(see next page)

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APPENDIX II

Distribution of von Mises stresses in the dome roof structure for the remaining load cases B1,

B2, B3, B4 and B5

FIGURE P2 von Mises stress distribution in the dome roof plates due to

self-weight in the assembled condition (Load Case B1)

FIGURE P3 von Mises stress distribution in the dome roof plates due toself-weight and live load in the assembled condition (Load Case B2)

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self-weight and point loads in the assembled condition (Load Case B3)

FIGURE P5 von Mises stress distribution in the dome roof plates due toself-weight and wind load in the assembled condition (Load Case B4)

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self-weight, live load and wind load in the assembled condition (Load Case B5)

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protank dome roof

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