ANALYSIS OF SEMI CIRCULAR-ARCH TRUSES USING I-DEAS

MOHD.RIZAL BIN LIASFakulti Kejuruteraan Mekanikal & PembuatanKolej Universiti Teknologi Tun Hussein Onn

(KUiTTHO)

ABSTRACT

With the emenrgence of high-speed computer system and other manufacturing

technologies, computational engineering for complex are made reality for many branches of engineering. The computation of circular arches trusses structure, in this study is based on mathematical model through simulation and is used to study the structure itself. .Development of computational engineering had enable increased realism, improved efficiency, reliability and quality control, and integration of methods to acquire more accurate simulation. The simulation using I-DEAS software had being applied to simulate the structure with various of different load being applied. The objectives of this study is to compare the result within simulated result to the manual calculation based on the same method of mathematical solution. Failure analysis is also being performed to determine the reliability of the structure, with application of major failure theories and also the result of determining the maximum load and critical point of the structure, due to perform a safety factor as a long term of the structure in used. As the scope of this studies is an analysis to the rooftop structure at Studio Music KUiTTHO within the usage of finite element approach method with a several type of load applied to the structure. With result of 28000 N of load can be applied to the structure and mean error of 3% or 97 % of efficiencies, this study, is succeed in performing objective of the whole study cases generally.

1.0 INTRODUCTION

In the field of mechanical engineering, conventional analysis, such as the use of stress-strength interface curves relating material life to applied stress, become intractable when the structure is complex, or when it is composed of many different materials which do not lend themselves to direct analysis. A realistic test of a large object such as a roof trusses frame cannot be done without going to the expensive of building the structure . Structural analysis is important before structures are being designed. Understanding of member's reaction while the burden is being imposed is extremely important. For structure of trusses, the analysis purpose is to find internal ability that is shouldered by structure including self weight. Method that regularly been used to receive internal ability of member is through calculation by human being or using computer analysis. Method of analysis by human being will only suitable if the structures are not big and difficult. But if structures that are big and difficult, the use of computer is needed. At this time really there is many software that is in market to analyze and design such as Staad Pro, I-DEAS, TB Stress and others. In progress of using the computer, the user must understand about how to provide data correctly and understand the decision that is printed. Any mistake in analyzing data can cause the structure fail. .

2.0 LITERATURE REVIEW

2.1: Introduction to Roof Trusses

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Roof trusses can be categorized into 2 type of main structure, one made by timber or steels[1]. Building a structure without internal support and the outsider with a mast-pillar 12 m, economically most suite with used of steel structure system or known as roof trusses structure system[9]. In this modern era, there’s a lot of roof structure design such as the arches trusses design[7]. Like cables, the arches can be used to reduce the bending moments in long span structure.[1].

2.2 Load React to the Trusses

Mostly, an axial load is the only load that react to the trusses.[8] Burden that reacts towards structure consist of live load and dead load. Dead is load that acts retainly and matching throughout structural life also acting doesn't remain (temporarily) from its position and also value. Live loads are load that will be able to move from its position and the value is not fixed.[8]

2.3: Finite Element Approach to the Trusses

The finite element analysis is an idea that realized a physical system into discretization of mathematical model and the interpretation of numerical result.[]. A typical plane truss structure consist only two-forces member in FEA subjected in direct tension or compression.[2] In a truss, it is required that all load and reactions are applied only at joints and that all members are connected together at their ends by frictionless pin joints[3]These methods use the fundamentals of static, become tedious when applied to the large scale statically indeterminate truss structure.[3].

2.3.1: Element Stiffness Matrix

The element stiffness matrices are assembled in the usual manner to obtain the structural stiffness matrix.

... (1)

.. (2)

... (3)

... (4)

In order to simulate a 2 D trusses, Equation (1) will be used with Equation (2) and Equation (3) indicated of global stiffness matrix solution, Equation (4).

2.3.2 Stress Calculation

Expressions for the element stresses can be obtained by noting that a truss element in local coordinates is a simple two-forces member thus, the stress in a truss element is given by :

... (5)

... (6)

2

Once the displacement are determined by solving Equation (4) the stresses can be

recovered from Equation (6).

3.0 METHODOLOGY

3.1 Manual Calculation

Manual calculation of this studies is done in the same method of Finite Element Analysis with the matrix solving calculation using ( Band Solver 2D Truss Analysis-Gauss Elimination) with 6 major steps: (a) Idealization of the physical system.(b) Discretization of the mathematical model. (c) Application of the finite element process (d) Solution of the equations (e) Evaluation of stresses (f) Interpretation of numerical result

3.2 Simulation Using I-DEAS

Simulation using I-DEAS (Fig 4.14)is perform with the same method as manual calculation. Load from 5kN-30kN(Fig 3.1)were applied to the trusses in orderly 5kN .Result were obtained in 3 different ways(displacement X and Y, planar stress of element) and plotted into graph and table element-stress and displacement-nod.

3.3 Comparison Analysis

Comparison analysis is done in statistical method using Microsoft Office 2003 with calculation of mean error and std deviation.

3.3 Failure Analysis.

Failure analysis is perform using Safety factor of 1 with 3 major failure theorem based on true plastics deformation analysis of steel: (a) Von Misess –Henchky (b) Max. Normal (c) Max.Shear.

4.0 RESULT AND DISCUSSION

4.1 Result of Studies

Result were obtained in 3 different way with various of load From 5kN-30kN and plotted into graph and tables as shown in Fig 4.1-4.12

4.2 Discussion of Comparison Analysis

Based on comparison analysis between manual calculation and I-DEAS simulation the overall mean errors of this studies between both is approximately to 3% or 97 of efficiencies with std deviation of 3.11 from the true data.

4.3 Discussion of Maximum Load For Trusses

Maximum load for trusses is determined by safety factor of 1 and the validation of the theorem based on 3.2 is the theorem of Von Misess with the result of load can be applied of 28000N or 28kN and react at the element 31 at node 14.(Fig.4.13)5.0 CONCLUSION

The entire result was overall fulfilled the objective of study where is for get the

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comparison analysis from manual calculation to the I-DEAS simulation for the Semi Circular Arches Roof Trusses and determine the maximum load that can be perform by the structure intestinally. As an arrangement of Data-step of analysis and with result obtained of 28000 N of load can be applied to the structure and mean error of 3% or 97 % of efficiencies, this study, conclude is succeed in performing objective of the whole study cases generally..

6.0 REFERENCE

1. Askenazi, V.A.a.A., Building Better Products with Finite Element Analysis. First ed. 1999, Santa FE,USA: Onword Press

2. Breikopf, M.K.a.P., Finite Element Method In Structural Mechanic. Translation Edition ed. 1993, West Sussex, England: Ellies Horwood.

3. D.Belegundu, T.R.C.a.A., Introduction to Finite Element In Engineering. Third Edition ed. 2003, New Jersey: Prentice Hall.

4. Engel, I., Structural Steel In Architecture and Building Technology. First ed. 1988, Englewood Cliff, New Jersy: Prentice Hall.

5. Mat, N.Z.B.C., Analisis Kerangka Kereta Formula SAE Menggunakan Simulasi I-DEAS, in Fakulti Kejuruteraan Mekanikal. 2003, KUiTTHO.

6. Mc Cormac, J., Structural Steel Design. 1992: Ed.Harper Colin.7. P.Timoshenko, J.M.G.d.S., Mekanik Bahan. Edisi ketiga ed. 1990, Skudai:

Universiti Teknologi Malaysia.8. Shahrin Mohammad, A.A.S., Mohd Ismail, Redzuan Abdullah.,

Rekabentuk Struktur Keluli. 1 ed. 2001: Dewan Bahasa Dan Pustaka.9. Tat, F.C., Rekabentuk Kekuda Bumbung, in Fakulti Kejuruteraan Awam.

1999, Universiti Teknologi Malaysia: Skudai.

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Figure 3.1: Load Applied To the structure

Elemen Melawan Tegasan(manual)

-200

-150

-100

-50

0

50

100

0 10 20 30 40 50 60

Elemen

Teg

asan

(N/m

m2)

Nod Melawan Anjakan X(manual)

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35

Nod

Anj

akan

X (m

m)

Figure 4.1: Stress Result of 20000N(Manual) Figure 4.2: Displacement X of 20000N (Manual)

Nod Melawan Anjakan Y (manual)

-12

-10

-8

-6

-4

-2

0

2

0 5 10 15 20 25 30 35

Nod

Anj

akan

Y (m

m)

Elemen Melawan Tegasan (IDEAS)

-400

-300

-200

-100

0

100

200

0 10 20 30 40 50 60

Elemen

Tega

san

(N/m

m2 )

Figure 4.3: Displacement X of 20000N (Manual)

Figure 4.4: Stress Result of 20000N (I-DEAS)

5

Nod Melawan Anjakan X (I-DEAS)

-4

-3

-2

-1

0

1

2

0 5 10 15 20 25 30 35

Nod

An

jak

an X

(m

m)

Nod melawan Anjakan Y (I-DEAS)

-16

-14

-12

-10

-8

-6

-4

-2

0

2

0 5 10 15 20 25 30 35

Nod

Anj

akan

Y (m

m)

Figure 4.5: Displacement X of 20000N (I-DEAS)

Figure 4.6: Displacement Y of 20000N(I-DEASl)

Elemen Melawan Tegasan(manual)

-400

-300

-200

-100

0

100

200

0 10 20 30 40 50 60

Elemen

Teg

asan

(N

/mm

2)

Nod Melawan Anjakan X (manual)

-5

-4

-3

-2

-1

0

1

2

0 5 10 15 20 25 30 35

NodA

njak

an X

(mm

)

Figure 4.7: Stress Result of 30000N(Manual)

Figure 4.8: Displacement X of 30000N(Manual)

Nod Melawan Anjakan Y(manual)

-20

-15

-10

-5

0

5

0 5 10 15 20 25 30 35

Nod

An

jak

an Y

(mm

)

Elemen Melawan Tegasan (I-DEAS)

-600

-400

-200

0

200

0 10 20 30 40 50 60

Elemen

Teg

asan

(N

/mm

2)

Figure 4.9: Displacement Y of 30000N(Manual)

Figure 4.10: Stress Result of 30000N(I-DEAS)

Nod Melawan Anjakan X (I-DEAS)

-6

-4

-2

0

2

4

0 5 10 15 20 25 30 35

Nod

An

jak

an X

(m

m)

Nod Melawan Anjakan Y (I-DEAS)

-25

-20

-15

-10

-5

0

5

0 5 10 15 20 25 30 35

Nod

Anj

akan

Y(m

m)

Figure 4.11: Displacement X of 30000N (I-DEAS)

Figure 4.12: Displacement Y of 30000N (I-DEAS)

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Figure 4.13: Result Of Maximum Load For the Trusses

Figure4.14: Simulation Using I-DEAS

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