Skywalk Report

SKYWALK – ANALYSIS AND DESIGN A PROJECT REPORT Submitted by

BARASKAR M. A. BHADBHADE S. M. CHINTA C. A. INAMDAR N. J. RAGHATATE A.M. in partial fulfillment for the award of the degree of

BACHELOR OF TECHNOLOGY in

CIVIL ENGINEERING

COLLEGE OF ENGINEERING, PUNE – 411005 MAY 2009

Final Year Project Report

Abstract

ABSTRACT In this final year project, a steel skywalk structure is analyzed and designed using conventional and finite element approach. Analysis based on stiffness method has been carried out using analysis and design software ‘STAAD.Pro-05’ and the results obtained are verified by manual calculations. The skywalk design is as per the clauses and norms specified by ‘IS 800-1982’. Finite element model of the same is formulated and analyzed using ‘ANSYS-10’ and the results are compared with stiffness analysis and experimental testing. A scaled model of skywalk structure is prepared to a scale of 1:10 using mild steel. The experimental model is tested under static loads and simulated wind loads for various load combinations. Free vibration analysis of the model is carried out to determine its natural frequency and other important parameters influencing its behavior under dynamic loads. Purpose of the project is validation of software models by comparing the results with experimental observations. The obtained numerical results are comparable in terms of strains and stresses developed in individual members. The variations in some of the experimental results may be attributed to practical limitations involved in testing procedures. The validated software models are further used in parametric study which includes formulation of interaction charts. Interaction charts depicting variation of modulus of section of individual members against span are plotted. The charts can be used to design an individual member with optimum modulus of section. The appropriateness of these charts can be verified by software analysis and manual calculations. However, these charts are restricted to the shape and form of the skywalk structure considered in this project.

i


Acknowledgement

ACKNOWLEDGEMENT The authors would like to thank their project guide, Prof. Balkrishna M. Dawari, for his guidance and advice rendered to them throughout the course of the final year project. The authors are also grateful for the patience and understanding that Prof. Dawari has shown throughout the course of the project. The authors would also like to express their gratitude to officials associated with R & D, Dighi for their extended support in the experimental testing of the scaled model. The authors would like to thank especially Mr. Giridhar Singh, Mr. Ramdas and Mr. Irfan for their valuable guidance. The authors are also thankful to Mr. Prashant Raskar, Design Engineer, R&D, ISMT for helping them in formulation of finite element model using ANSYS software. The authors would like to extend their appreciation to Mumbai Metropolitan Region Development Authority (MMRDA) for providing them all the necessary data related to the project. The authors are grateful to the officials of Strudcom Consultants (Monarch) for their guidance throughout the project. The authors also acknowledge all those who have helped them during the course of their project in one way or another.

ii


Table of Contents

TABLE OF CONTENTS

PAGE NO.

ABSTRACT

i

ACKNOWLEDGEMENT

ii

LIST OF FIGURES

v

LIST OF TABLES

viii

LIST OF SYMBOLS

ix

CHAPTER ONE – INTRODUCTION

1

1.1 Background

1

1.2 Objectives

9

1.3 Problem Definition

9

1.4 Scope

10

CHAPTER TWO – LITERATURE REVIEW

12

2.1 Background

12

2.2 Stiffness Method

20

2.3 Finite Element Method

20

CHAPTER THREE – MODELING METHODOLOGY

23

3.1 Analytical Model

23

3.2 STAAD Pro Model

25

3.3 ANSYS Model

33

3.4 Experimental Model

41

CHAPTER FOUR – TESTING METHODOLOGY

45

4.1 Preliminary Testing

45

4.2 Model Testing

55

4.3 Free Vibration Analysis

71

iii


Table of Contents

CHAPTER FIVE – RESULTS AND DISCUSSIONS

77

5.1 Validation

77

5.2 Interpretation

79

5.3 Discrepancies

79

CHAPTER SIX – PARAMETRIC STUDY

80

6.1 Objective

80

6.2 Skywalk Structure – Parametric Study

80

6.3 Interaction Charts

81

6.4 Sample Verification

90

6.5 Significance of Interaction Charts

90

6.6 Limitations of Interaction Charts

90

CHAPTER SEVEN– CONCLUSIONS AND

91

RECOMMENDATIONS 7.1 Conclusions and Recommendations

91

REFERENCES

92

INDEX

iv


List of Figures

LIST OF FIGURES

PAGE NO.

Figure 1.1: Skyway

01

Figure 1.2: Typical scene in any metropolitan city

03

Figure 1.3: Plan and Section

10

Figure 1.4: Perspective

11

Figure 2.1: Truss

14

Figure 2.2: Deconstruction

15

Figure 2.3: Displacement Vector

17

Figure 2.4: Stiffness Matrix

18

Figure 2.5: Stiffness Matrix with known Data

18

Figure 2.6: FEM-Concept

22

Figure 3.1: Beam 3D Element

34

Figure 3.2: Material Model Interface Initial Screen

35

Figure 3.3: Sample output window showing mass and other properties

38

Figure 3.4: Mode 1 (Deformed + Undeformed shape)

39

Figure 3.5: Direct Stress Contour of dead load + wind load

40

Figure 3.6: Combined Stress Contour of dead load + wind load

40

Figure 3.7: Skywalk Model in Working Stage

42

Figure 3.8: Completed Skywalk Model

42

Figure 4.1: Tension Test – Stress vs. Strain

46

Figure 4.2: Torsion Test – Torque vs. Angle

48

Figure 4.3: DPT – Purlin and Roof Joint

52

Figure 4.4: DPT – Primary and Secondary Beam Joint

52

Figure 4.5: Buckling Load Test Assembly

54

Figure 4.6: Typical Strain Gauge

56

Figure 4.7: Wheatstone Bridge Circuit

56

Figure 4.8: Working of a Strain Gauge

58

Figure 4.9: Strain Gauge

59

Figure 4.10: Strain Gauge Package and Strain Gauge Color Coding

60

Figure 4.11: PFL – 30-11 Strain Gauge Test Data

61

v


List of Figures

LIST OF FIGURES

PAGE NO.

Figure 4.12: Explanation of Strain Gauge Test Data

61

Figure 4.13: Surface Preparation –Dry Abrading

62

Figure 4.14: Surface Preparation –Wet Abrading

63

Figure 4.15: Application of Adhesive

63

Figure 4.16: Curing and Pressing

63

Figure 4.17: Raising the Gauge Leads

64

Figure 4.18: Bonding Connecting Terminals

64

Figure 4.19: Soldering the Gauge Leads

64

Figure 4.20: Soldering Extension Lead Wires

65

Figure 4.21: Location of Strain Gauges

66

Figure 4.22: Strain Reading Equipment

66

Figure 4.23: Test Setup for Static Load Test

67

Figure 4.24: Wind Load Simulation

69

Figure 4.25: Load Combination - LL (100kg) + WL (10kg)

69

Figure 4.26: Test Setup for Free Vibration Test

72

Figure 4.27: FFT Graph – Iteration 1 Accelerometer 1

73


73


73


74


74


74


75


75


75

Figure 6.1: Parametric Study

80

Figure 6.2: Curved Beam Zx

82

Figure 6.3: Curved Beam Zy

82

Figure 6.4: Curved Beam Zz

82

Figure 6.5: Primary Beam Zx

83

vi


List of Figures

LIST OF FIGURES

PAGE NO.

Figure 6.6: Primary Beam Zy

83

Figure 6.7: Primary Beam Zz

83

Figure 6.8: Primary Column Zx

84

Figure 6.9: Primary Column Zy

84

Figure 6.10: Primary Column Zz

84

Figure 6.11: Straight Plate Girder Zx

85

Figure 6.12: Straight Plate Girder Zy

85

Figure 6.13: Straight Plate Girder Zz

85

Figure 6.14: Secondary Column Zx

86

Figure 6.15: Secondary Column Zy

86

Figure 6.16: Secondary Column Zz

86

Figure 6.17: Inclined Roof Member Zx

87

Figure 6.18: Inclined Roof Member Zy

87

Figure 6.19: Inclined Roof Member Zz

87

Figure 6.20: Parabolic Member Zx

88

Figure 6.21: Parabolic Member Zy

88

Figure 6.22: Parabolic Member Zz

88

Figure 6.23: Inclined Strut Zx

89

Figure 6.24: Inclined Strut Zy

89

Figure 6.25: Inclined Strut Zz

89

vii


List of Table

LIST OF TABLES

PAGE NO.

Table 1.1: Proposed Skywalks in and around Mumbai

06

Table 3.1: Design Data

23

Table 3.2: Maximum Stresses in STAAD Pro Analysis

32

Table 3.3: Maximum Stresses in ANSYS Analysis

41

Table 3.4: Comparison of Member in Actual Structure and Prototype

43

Table 3.5: Comparison of Section Modulus in Actual Structure and Prototype

43

Table 4.1: Strain Gauge Specification

59

Table 4.2: Specifications of PFL – 30-11

59

Table 4.3: Micro-Strains for ten Loading Combinations

70

Table 4.4: Test Data for Free Vibration Analysis

72

Table 5.1: Stresses in different Structural Members for Live Load = 400kg

77

Table 5.2: Stresses in different Structural Members for Wind Load = 10kg

78

Table 6.1: Comparison of Section Modulus and Moment of Inertia

90

viii


List of Symbols

LIST OF SYMBOLS Fy = yield strength of steel bt=

bc =

maximum permissible bending stresses in tension and compression

Z = section modulus I = moment of inertia tw = thickness of web h = depth of beam v

= shear stress

λ = slenderness ratio for the column which is the ratio of effective length of column to minimum radius of gyration. ac

= maximum permissible axial stresses in compression.

Le = effective length of the column depending on the end conditions of the column. rmin = minimum radius of gyration. E = modulus of elasticity G = modulus of rigidity Y = deflection Vb = basic wind speed Pz = design wind pressure Vz = design wind speed m = member number Qm = vector of member's characteristic forces, which are unknown internal forces. Km = member stiffness matrix which characterises the member's resistance against deformations. qm = vector of member's characteristic displacements or deformations. Qm = vector of member's characteristic forces caused by external effects R = vector of nodal forces, representing external forces applied to the system's nodes. K = system stiffness matrix, which is established by assembling the members' stiffness matrices km. r = vector of system's nodal displacements that can define all possible deformed configurations of the system subject to arbitrary nodal forces R.

ix


Chapter 1 - Introduction

CHAPTER ONE – INTRODUCTION 1.1 BACKGROUND 1.1.1 SKYWAY In an urban setting, a skyway, catwalk, or skywalk is a type of pedestrian walkway consisting of an enclosed or covered bridge between two buildings. This protects pedestrians from the weather. These skyways are usually owned by businesses, and are therefore not public spaces (compare with sidewalk). Skyways usually connect on the second or third floor, though they are sometimes much higher, as in PETRONAS TOWERS (though this skyway is often referred to as a sky bridge). The space in the buildings connected by skyways is often devoted to retail business, so areas around the skyway may operate as a shopping mall. Non-commercial areas with closely associated buildings,

such

as

university campuses,

can

often

have

skyways

and/or tunnels connecting buildings.

Figure 1.1: Skyway Many of the early forms of these structures were provided to cross limited-access highways in areas that were built up and lacked intersections. By allowing pedestrians and bicycles to cross over the highway, these bridges were viewed as low-cost alternatives to intersections. In the 1999, Las Vegas, Nevada began a major effort to install pedestrian bridges at major intersections along the Las Vegas Strip, to reduce traffic congestion and improve pedestrian safety. 1



As the traffic increased, there was greater need for structures that would assist people to cross road without any risk and interfering the traffic. Thus gradually skywalks were evolved from skyways primarily for pedestrian traffic. Besides pedestrian safety and convenience, the chief reasons assigned by urban planners for skywalk development are decrease of traffic congestion, reduction in vehicular air pollution and separation of people from vehicular noise. A number of cities (for example, Spokane, Washington) have given intricate analysis to skywalk systems employing computer models to optimize skywalk layout (Carbon monoxide dispersion analysis in downtown Spokane, ESL Inc., Sunnyvale, (1973)).

1.1.2 NEED FOR SKYWALK 1. Limited Land Availability In an over populated country like India, there is always limited land available for roads, and as such we can’t afford to provide sufficient space for pedestrians in crowded areas. Hence the Maharashtra Government has decided to implement the Skywalk project in Mumbai.

2. Increased risk to Pedestrians In India, the most neglected social aspect is the pedestrian safety. Adequate weightage has not been given during the planning and implementation of urban infrastructure. To understand the gravity of this situation, consider a survey conducted in 2001accounting for accidental deaths in the United States. More than 6,000 pedestrians are killed by cars and trucks every year, one-seventh of all the people who die in traffic accidents; but 99 percent of the Federal transportation safety money is spent on improvements for drivers and passengers, not people walking, says a study released by advocates of pedestrians. The risk of a pedestrian's being killed by a car or truck is roughly double the risk of homicide by a stranger with a gun, the study found, and even in New York, the traffic death risk is three times larger than the risk from guns. In addition, 110,000 pedestrians are injured every year in traffic accidents. From this survey, we can imagine the number

2



of deaths in India, as in India the traffic scene is even worse and does not have proper transportation facilities.

3. Traffic Metropolitan cities always face the problem of ever increasing traffic and India, being a developing country, this problem is more severe. Due to huge traffic, pedestrians face lot of problems and hence there is a need for skywalk.

.

Figure 1.2: Typical scene in any metropolitan city

1.1.3 SUITABILITY OF SKYWALK 1. Economical construction Since the duration of construction is much less as compared to underground subways, skywalks often prove to be an economical choice. The problems faced during construction of subways such as those related with groundwater and the geotechnical properties of the soil increase the overall cost of the project. In case of skywalks, the dependability of total cost of the project on these factors is minimum. 2. Easy and fast construction In construction of skywalk, mostly pre-fabricated steel members are used which can be easily assembled on the site using welded and bolted connections. This results in saving of precious time.

3



3. Minimum disturbance to ongoing traffic The fast rate of construction of skywalk as compared to the underground subways causes minimum obstruction to the ongoing traffic. 4. Element of beautification plan of a city Elevated steel structures add a pleasing effect to the skyline of a crowded city. 5. Pedestrian safety Skywalks alienate the pedestrian traffic from the vehicular traffic, thereby safeguarding the pedestrians. It is found that the deaths caused due to accidents have been substantially reduced with the introduction of elevated pedestrian crossings.

1.1.4 CURRENT SCENARIO MMRDA i.e. Mumbai Metropolitan Region Development Authority has planned 50 Skywalks in Mumbai to tackle the traffic problems.

Cost Estimates Total estimated cost is about Rs.450 crores.

Implementing Agencies Out of 50 nos. of skywalks proposed to be constructed, construction of 18 nos. will be nder undertaken by MSRDC.

Implementing Agencies Before finalizing detailed project report i.e. before preparing GAD; local people, corporators, MLAs, MPs from that area are being contacted to understand their views, suggestions, concurrence etc.PMC for these works have been finalized and they are asked to coordinate with other concerned departments, like MCGM, Railways etc.

4



The alignment and designs To be finalized considering various factors like,

1. Dispersal/entry points at strategic locations 2. Underground utilities and minimum number of structures affected 3. Available road widths 4. Proximity of adjacent buildings 5. No. of trees, large and small size, getting affected 6. Provision of shops on the sky walk, if any, on one side or both the sides or on upper deck with a view to provide easy pedestrian movement

7. Speed of construction 8. Operation & maintenance, etc. Present Status 1. Project Management Consultants (PMC) for project preparation, designing and supervision work is finalized by MMRDA.

2. First skywalk from Bandra Station to Kalanagar Junction has been already completed, inaugurated by the Hon’ble Chief Minister on 24/6/2008 and immediately opened for public use after inauguration.

3. Tenders for 2 nos. of skywalks have been finalized and work is expected to start shortly.

4. The actual construction of balance skywalks is planned to start from October 2008 and is targeted to be completed within a time period of 6 months.

5. MSRDC has also finalized GADs for three skywalks and tenders for the same will be invited shortly. For balance sky walks, PMCs will be finalized very soon.

5



Present Status: Sr. No. 1

Mumbai CST

2

Sandhurst Road

Skywalk connecting from (South side of) MSRDC Hankok Bridge (at the West side of track) to the platform No.1 & 2 of the Station. (3.66 meters width x 100 meters long)

3

Chinchpokali

Skywalk connecting existing Railway’s MSRDC Foot Over Bridge to Ambedkar Road at the East Side of Station.(4.88 meters wide x 200 meter long)

4

Parel

Skywalk connecting East & West side of MSRDC the Station (with landing at all platforms 4.88 meters wide x 120 meters long)

Station

Implementing Agency Construction of Subway (instead of MSRDC Skywalk due to surface space constraint) at Chhatrapati Shivaji Terminus Station. (20 meters wide x 500 meter long) Scope of Works

Skywalk (at Mumbai end) connecting existing Railway’s Foot Over Bridge to Ambedkar Road (at East Side).(4.88 meter wide x 200 meters long) 5

Kurla

6

Vidyavihar

7

Kanjurmarg

Skywalk connecting existing Railway’s MSRDC Foot Over Bridge of Kurla Station to Lokmanya Tilak Terminus Station & Railway’s Foot Over Bridge of Tilak Nagar Station to Lokmanya Tilak Terminus Station (4.88 meters wide x 1300 meters long) Skywalk connecting existing Railway’s middle Foot Over Bridge (of East Side) to Nehru Nagar. (4.88 meters wide x 150 meters long) Skywalk connecting East & West side of MMRDA the Station and with existing Railway’s Foot Over Bridge (Under construction).(4.88 meters wide x 150 meters long) Skywalk connecting existing Railway’s MMRDA Foot Over Bridge (at Mumbai end) to the West side of L.B.S. Marg.(4.88 meters wide x 200 meters long) 6


8

Bhandup

9

Mulund

10

Thane

11

Koper

12

Kalyan

13

Reay Road

14

Sewri

15

Vadala Road

16 17 18

Borivali (W) Borivali Virar (West)

19 20 21 22 23


Skywalk connecting existing Railway’s MMRDA Foot Over Bridge to L.B.S. Marg. (3.66 meters wide x 350 meters long) Skywalk connecting East & West with MMRDA existing Railway’s Foot Over Bridge (at Mumbai end). (4.88 meters wide x 100 meters long) Skywalk (towards Kalyan end) MMRDA connecting West side Flyover [of Station Area Traffic Improvement Scheme (SATIS)] to Sant Tukaram Road (at East end) & also connecting with existing Railway’s Foot Over Bridge. Skywalk connecting existing Railway’s MMRDA Foot Over Bridge to East end & also landing towards Dombivili side through underpass of Diva- Vasai Flyover.(3.66 meters wide x 200 meters long) Skywalk connecting existing Railway’s MMRDA Foot Over Bridge (Under Construction) to Valli Peer Road (Kalyan Station Road at West end) and also to Kolsawadi side (at East end).(4.88 meters wide x 250 meters long) MSRDC

Virar (East) Bandra (East) Bandra (East)

Skywalk across D’Mello Road (at Kurla end) a landing at all Platforms.(3.66 meters wide x 100 meters long) Skywalk connecting Railway’s Foot Over Bridge to Public Foot Over Bridge (of D’Mello Road). (3.66 meters wide x 100 meters long) Skywalk across ‘P’ D’Mello Road & connecting existing Railway’s Foot Over Bridge of the Station (at Kurla end) (4.88 meters wide x 125 meters long) Platform No.8 to R.O.B.- BMC Platform No. 7 to PF No. 6 and East side Platform No.1 from South West Booking office to M.S.R.T.C. Bus Terminus. From existing F.O.B. to L.C. No.40. BA Local station to BDTS station BA Local station to Kalanagar

Bandra (West) Nallasopara

Construction of Sky walk Construction of Sky walk

MMRDA MSRDC

7

MSRDC

MSRDC

MMRDA MMRDA MMRDA MMRDA MMRDA MMRDA



24 25 26 27 28

Vasai Road Ambernath Goregaon Vileparle Kandivali

Construction of Sky walk Construction of Sky walk Construction of Sky walk Construction of Sky walk Construction of Sky walk

MSRDC MSRDC MSRDC MSRDC MSRDC

29

LowerparelConstruction of Sky walk Currey road walkway Masjid station Construction of Sky walk area CST to Construction of Sky walk Churgegate

MSRDC

Naigaon Grantroad Dadar – Ranade Rd. Dadar – Towards Kabutarkhana

Construction of Sky walk Construction of Sky walk Construction of Sky walk

MSRDC MSRDC MMRDA

Construction of Sky walk

MMRDA

36

Dadar - East


MMRDA

37

Dadar - Eastwest connector Chembur Ghatkopar Andheri (E) Andheri (W)


MMRDA

Construction of Sky walk Construction of Sky walk Construction of Sky walk Construction of Sky walk

MMRDA MMRDA MMRDA MMRDA MMRDA

44

Andheri Construction of Sky walk Telegali Malad - Construction of Sky walk Laljipada,MLR Dahisar (E) Construction of Sky walk

45

Dahisar (W)


MMRDA

46 47

Mira Road Bhayander


MMRDA MMRDA

48 49

Santacruz (E) Santacruz (W)


MMRDA MMRDA

50

Ulhasnagar


MMRDA

30 31 32 33 34 35

38 39 40 41 42 43

Table 1.1: Proposed skywalks in and around Mumbai 8

MSRDC MSRDC

MMRDA MMRDA



1.2 OBJECTIVE The objectives of Final Year Project are: 1. Validating the finite element model of the skywalk structure with the help of stiffness method and experimental model. 2. Preparing a model to a scale of 1:10 in mild steel and testing the same for various load combinations. 3. Formulating interaction charts using parametric study.

1.3 SCOPE In this final year project, analysis and design of a steel skywalk has been undertaken using stiffness method and finite element method. The stiffness analysis is carried out using STAAD Pro. 2005 and the results are compared with conventional manual calculations. The finite element model is formulated using ANSYS 10 with the help of linear beam 3D element. A scaled model of the proposed structure is prepared to a scale of 1:10 using mild steel and welded connections. The same is tested under static loads and simulated wind loads in varying combinations and proportions. Free vibration analysis of the model is carried out to determine its natural frequency and other important parameters influencing its behavior under dynamic loads. Validation of software models is done by comparing the stresses and strains of individual members at various locations with those obtained from experimental testing. On due validation, a parametric study is undertaken to formulate interaction charts for individual members.

9



1.4 PROBLEM DEFINITION Dimensions of the skywalk: 1. Length = 1 km 2. Width = 7 m 3. Height = 7+5 m 4. c/c distance between columns = 12 m Amenities: 1.-Shops (size= 2.85 x 1.85 m) 2.-Seating arrangement

Figure 1.3: Plan and Section 10



Figure 1.4: Perspective

11


Chapter 2 - Literature Review

CHAPTER TWO – LITERATURE REVIEW 2.1 BACKGROUND The final year project involves analysis and design of a steel skywalk based on two different approaches. The first one includes conventional method of analysis, i.e. stiffness method depicted through manual calculations and also through software analysis. The second approach uses the finite element method to analyze the steel structure. Finite element analysis is carried out using ANSYS 10 by considering linear beam 3D element as the basic element.

2.2 STIFFNESS METHOD 2.2.1 History Between 1934 and 1938 A. R. Collar and W. J. Duncan published the first papers with the representation and terminology for matrix systems that are used today. Aeroelastic research continued through World War II but publication restrictions from 1938 to 1947 make this work difficult to trace. The second major breakthrough in matrix structural analysis occurred through 1954 and 1955 when professor John H. Argyris systemized the concept of assembling elemental components of a structure into a system of equations. Finally, on Nov. 6 1959, M. J. Turner, head of Boeing’s Structural Dynamics Unit, published a paper outlining the direct stiffness method as an efficient model for computer.

2.2.2 Member stiffness relations A typical member stiffness relation has the following general form,

Qm = km.qm + Qom

(1)

where m = member number m.

Qm = vector of member's characteristic forces, which are unknown internal forces. 12



km = member stiffness matrix which characterises the member's resistance against deformations.

qm = vector of member's characteristic displacements or deformations. Qom = vector of member's characteristic forces caused by external effects (such as m

known forces and temperature changes applied to the member while q = 0). m

If q

m

are member deformations rather than absolute displacements, then Q are

independent member forces, and in such case (1) can be inverted to yield the socalled member flexibility matrix, which is used in the flexibility method. System stiffness relation For a system with many members interconnected at points called nodes, the members' stiffness relations such as Eq.(1) can be integrated by making use of the following observations: m

The member deformations q can

be expressed in terms

of system nodal

displacements r in order to ensure compatibility between members. This implies that r will be the primary unknowns. m

The member forces Q help to the keep the nodes in equilibrium under the nodal forces R. This implies that the right-hand-side of (1) will be integrated into the righthand-side of the following nodal equilibrium equations for the entire system:

R = K.r + Ro

(2)

Where,

R = vector of nodal forces, representing external forces applied to the system's nodes. K = system stiffness matrix, which is established by assembling the members' stiffness m

matrices k . = vector of system's nodal displacements that can define all possible deformed configurations of the system subject to arbitrary nodal forces R.

Ro= vector of equivalent nodal forces, representing all external effects other than the nodal forces which are already included in the preceding nodal force vector R. This vector is established by assembling the members' Qom.

13



2.2.3 Solution The system stiffness matrix K is square since the vectors R and r have the same size. In addition, it is symmetric because km is symmetric. Once the supports' constraints are accounted for in (2), the nodal displacements are found by solving the system of linear equations (2), symbolically:

r = K-1.(R - Ro)

(3)

Subsequently, the members' characteristic forces may be found from Eq.(1) where qm can be found from r by compatibility consideration.

2.2.4 The direct stiffness method It is common to have Eq.(1) in a form where qm and Qom are, respectively, the memberend displacements and forces matching in direction with r and R. In such case, K and R can

be

obtained

by

direct

summation

of

the

members'

matrices km and Qom. The method is then known as the direct stiffness method.

2.2.5 Example Breakdown The first step when using the direct stiffness method is to identify the individual elements which make up the structure.

Figure 2.1: Truss

14



Once the elements are identified, the structure is disconnected at the nodes, the points which connect the different elements together.

Figure 2.2: Deconstruction Each element is then analyzed individually to develop member stiffness equations. The forces and displacements are related through the element stiffness matrix which depends on the geometry and properties of the element. A truss element can only transmit forces in compression or tensi tension. on. This means that in two dimensions, each node has two degrees of freedom (DOF): horizontal and vertical displacement. The resulting equation contains a four by four stiffness matrix.

A frame element is able to withstand bending moments in addition tto o compression and tension. This results in three degrees of freedom: horizontal displacement, vertical displacement and in-plane plane rotation. The stiffness matrix in this case is six by six.

15



Other elements such as plates and shells can also be incorporated into the direct stiffness method and similar equations must be developed.

Assembly Once the individual element stiffness relations have been developed they must be assembled into the original structure. The first step in this process is to convert the stiffness relations for the individual elements into a global system for the entire structure. In the case of a truss element, the global form of the stiffness method depends on the angle of the element with respect to the global coordinate system (This system is usually the traditional Cartesian coordinate system).

(for a truss element at angle β) After developing the element stiffness matrix in the global coordinate system, they must be merged into a single “master” or “global” stiffness matrix. When merging these matrices together there are two rules that must be followed: compatibility of displacements and force equilibrium at each node. These rules are upheld by relating the element nodal displacements to the global nodal displacements.

16



Figure 2.3: Displacement Vectors The global displacement and force vectors each contain one entry for each degree of freedom in the structure. The element stiffness matrices are merged together by augmenting or expanding each matrix in conformation to the global displacement and load vectors.

(for element (1) of the above structure) Finally, the global stiffness matrix is constructed by adding the individual expanded element matrices together.

17



Solution Once the global stiffness matrix, displacement vector and force vector have been constructed, the system can be expressed as a single matrix equation.

Figure 2.4: Stiffness Matrix For each degree of freedom in the structure, either the displacement or the force is known.

Figure 2.5: Stiffness Matrix with Known Data After inserting the known value for each degree of freedom, the master stiffness equation is complete and ready to be evaluated. There are several different methods available for evaluating a matrix equation including but not limited to Cholesky decomposition and

18



the brute force evaluation of systems of equations. If a structure isn’t properly restrained, the application of a force will cause it to move rigidly and additional support conditions must be added. The method described in this section is meant as an overview of the direct stiffness method. Additional sources should be consulted for more details on the process as well as the assumptions about material properties inherent in the process.

2.2.6 Applications The direct stiffness method was developed specifically to effectively and easily implement into computer software to evaluate complicated structures that contain a large number of elements. Today, nearly every finite element solver available is based on the direct stiffness method. While each program utilizes the same process, many have been streamlined to reduce computation time and reduce the required memory. In order to achieve this, shortcuts have been developed. One of the largest areas to utilize the direct stiffness method is the field of structural analysis where this method has been incorporated into modeling software. The software allows users to model a structure and, after the user defines the material properties of the elements, the program automatically generates element and global stiffness relationships. When various loading conditions are applied the software evaluates the structure and generates the deflections for the user.

19



2.3 FINITE ELEMENT METHOD 2.3.1 History The

finite-element

method (FEM)

originated

from

the

need

for

solving

complex elasticity and structural analysis problems in civil and aeronautical engineering. Its development can be traced back to the work by Alexander Hrennikoff (1941) and Richard Courant (1942). While the approaches used by these pioneers are dramatically different, they share one essential characteristic: mesh discretization of a continuous domain into a set of discrete sub-domains, usually called elements. Hrennikoff's work discretizes the domain by using a lattice analogy while Courant's approach divides the domain into finite triangular subregions for solution of second order elliptic partial differential equations (PDEs) that arise from the problem of torsion of a cylinder. Development of the finite element method began in earnest in the middle to late 1950s for airframe and structural analysis and gathered momentum at the University of Stuttgart through the work of John Argyris and at Berkeley through the work of Ray W. Clough in the 1960s for use in civil engineering. By late 1950s, the key concepts of stiffness matrix and element assembly existed essentially in the form used today and NASA

issued

request

for

proposals

for

the

development

of

the

finite

element software NASTRAN in 1965. The method was provided with a rigorous mathematical foundation in 1973 with the publication of Strang and Fix's An Analysis of The Finite Element Method, and has since been generalized into a branch of applied mathematics for numerical modeling of physical systems in a wide variety of engineering disciplines, e.g., electromagnetism and fluid dynamics.

2.3.2 Introduction to FEM The finite element method (FEM), sometimes referred to as finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Simply stated, a boundary value problem is a mathematical problem in which one or more dependent variables must satisfy a 20



differential equation everywhere within a known domain of independent variables and satisfy specific conditions on the boundary of the domain. Boundary value problems are also sometimes called field problems. The field is the domain of interest and most often represents a physical structure. The field variables are the dependent variables of interest governed by the differential equation. The boundary conditions are the specified values of the field variables (or related variables such as derivatives) on the boundaries of the field. Depending on the type of physical problem being analyzed, the field variables may include physical displacement, temperature, heat flux, and fluid velocity to name only a few. The general techniques and terminology of finite element analysis will be introduced with reference to Figure 2.6. The figure depicts a volume of some material or materials having known physical properties. The volume represents the domain of a boundary value problem to be solved. For simplicity, at this point, we assume a two-dimensional case with a single field variable Φ (x, y) to be determined at every point P(x, y) such that a known governing equation (or equations) is satisfied exactly at every such point. Note that this implies an exact mathematical solution is obtained; that is, the solution is a closed-form algebraic expression of the independent variables. In practical problems, the domain may be geometrically complex as is, often, the governing equation and the likelihood of obtaining an exact closed-form solution is very low. Therefore, approximate solutions based on numerical techniques and digital computations are most often obtained in engineering analyses of complex problems. Finite element analysis is a powerful technique for obtaining such approximate solutions with good accuracy. A small triangular element that encloses a finite-sized sub-domain of the area of interest is shown in Figure 2.6. That this element is not a differential element of size (dx × dy) makes this a finite element. As we treat this example as a two dimensional problem, it is assumed that the thickness in the z direction is constant and z dependency is not indicated in the differential equation. The vertices of the triangular element are numbered to indicate that these points are nodes. A node is a specific point in the finite element at which the value of the field variable is to be explicitly calculated. Exterior nodes are 21



located on the boundaries of the finite element and may be used to connect an element to adjacent finite elements. Nodes that do not lie on element boundaries are interior nodes and cannot be connected to any other element. The triangular element of Figure 2.6 has only exterior nodes.

1 P(x, y)

Figure 2.6: FEM- Concept If the values of the field variable are computed only at nodes, how are values obtained at other points within a finite element? The answer contains the crux of the finite element method: The values of the field variable computed at the nodes are used to approximate the values at non-nodal points (that is, in the element interior) by interpolation of the nodal values. For the three-node triangle example, the nodes are all exterior and, at any other point within the element, the field variable is described by the approximate relation Φ (x, y) = N1(x , y) Φ1 + N2(x , y) Φ2 + N3(x , y) Φ3 where Φ1 , Φ2 ,Φ3 are the values of the field variable at the nodes, and N1, N2, and N3 are the interpolation functions, also known as shape functions or blending functions. The interpolation functions are most often polynomial forms of the independent variables, derived to satisfy certain required conditions at the nodes. The major point to be made here is that the interpolation functions are predetermined, known functions of the independent variables; and these functions describe the variation of the field variable within the finite element. 22


Chapter 3 - Modeling Methodology

CHAPTER THREE – MODELING METHODOLOGY 3.1 ANALYTICAL MODEL 3.1.1 Manual Analysis & Design Design is done as per IS 800-1984, IS:875-(part 1,2&3), IS:1893(part 1)-2002 Data considered: DESCRIPTION

PARTICULARS

LOCATION

MUMBAI

ZONE

IV

SOIL STRATA

250 kN

STEEL

Fy 250

CONCRETE

25 MPa

BASIC WIND SPEED

44 m/s

COLLISION LOAD

HARD STRATA

Table 3.1: Design Data

3.1.2 Sample Design (Beam) 3.1.2.1 Data Max. Shear Force

= 87.33KN

Max. Bending Moment

=341.285KN-m

3.1.2.2 Design Laterally supported beam bt=

bc =

0.66 fy

= 0.66*250 =165 MPa

23



Step 1: Z required = Moment/

bc

=341.285*106/165 =2769.69*103 Select section ISMB 600 @122.6 Kg/m Zxx = 3060.4 h = 600 mm

Zyy = 252.5 tw = 12 mm

Step 2: Check for stress: bc,cal

= M / Zxx = 341.285*106/ 3060.4*103 = 111.52 MPa <

bc=

165 MPa

…….. OK

Check for shear: Shear stress = Shear force/ h x tw v =87.33x10^3/ 600 x 12 =12.32 MPa Permissible value of shear stress. v = 0.4 x fy =0.4 x 250 =100 MPa > v cal

……. O.K

Check for deflection : Y max

= (5/384)(wl^4/EI) =11.4mm

Y allowable= Span/325 =3000/325 =36.92 mm > Ymax

……..O.K

24


1.1


STAAD Pro MODEL

3.2.1 Input File (Excerpt) STAAD SPACE START JOB INFORMATION ENGINEER DATE 08-Jan-09 END JOB INFORMATION INPUT WIDTH 79 UNIT METER KN JOINT COORDINATES 1 0 0.7 0; 2 0.0875 0.6564 0; 3 0.175 0.627 0; 4 0.2625 0.61 0; 5 0.35 0.6 0; - - - - - - - - - - - - - - - - - - - - - - 155 0.239828 0.614405 0; 156 0.46007 0.614385 0; MEMBER INCIDENCES 1 1 2; 2 2 3; 3 3 155; 4 4 5; 5 5 6; 6 6 156; 7 7 8; 8 8 9; 9 9 10; 10 10 11; - - - - - - - - - - - - - - - - - - - - - - 210 153 109; 211 154 112; 212 155 4; 213 156 7; DEFINE MATERIAL START ISOTROPIC STEEL E 2.05e+008 POISSON 0.3 DENSITY 76.8195 ALPHA 1.2e-005 DAMP 0.03 ISOTROPIC CONCRETE E 2.17185e+007 POISSON 0.17 DENSITY 23.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY INDIAN 34 TO 37 59 TO 62 73 TO 76 87 TO 90 120 122 124 126 128 130 132 134 136 138 25



140 142 144 146 148 150 152 154 156 158 PRIS YD 0.006 ZD 0.006 9 TO 16 63 TO 71 77 TO 85 91 TO 99 101 TO 109 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 183 TO 187 192 PRIS YD 0.01 ZD 0.02 72 86 100 110 159 161 163 165 167 169 171 173 175 177 179 181 188 TO 190 191 PRIS YD 0.012 ZD 0.006 160 162 164 166 168 170 172 174 176 178 180 182 204 TO 208 209 PRIS YD 0.032 ZD 0.02 1 TO 8 111 TO 118 210 TO 213 PRIS YD 0.02 ZD 0.032 20 TO 25 27 TO 32 46 TO 57 PRIS YD 0.015 193 TO 200 PRIS YD 0.01 201 203 PRIS YD 0.02 ZD 0.01 MEMBER PROPERTY INDIAN 33 PRIS YD 0.032 58 PRIS YD 0.032 CONSTANTS BETA 18 MEMB 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 MATERIAL STEEL ALL SUPPORTS 32 66 FIXED *____________________________________________________________________* DEFINE WIND LOAD *Vz = k1xk2xk3xVb *Vb = 44 m/s, k1=1.0, k2=1.05,(Terrain Category 1, *Class A, height <20 m), k3=1.0 *Vz = 1x1.05x1x44 = 46.2 m/s *Pz = 0.0006Vz^2 = 1.28 kN/m2 TYPE 1 INT 1.28 HEIG 13 *____________________________________________________________________* DEFINE 1893 LOAD *ZONE FACTOR FOR ZONE NO:3 =0.16 26



*IMPORTANCE FACTOR = 1.0 *SOIL TYPE - HARD SOIL *STRUCTURE TYPE - 2 STEEL STRUCTURE *DEPTH OF FOUNDATION = 3.0 M *RESPONSE REDUCTION FACTOR = 5(FOR STEEL MOMENT RESISTENT FRAME) ZONE 0.16 RF 5 I 1 SS 1 DT 3 *_____________________________________________________________________* *

*** BY SEISMIC COEFFICIENT METHOD ***

*____________________________________________________________________* SELFWEIGHT *MEMBER WEIGHT DUE TO DEAD LOAD MEMBER WEIGHT 160 166 172 178 UNI 0.145 162 168 174 180 204 TO 209 UNI 0.1025 164 170 176 182 UNI 0.0875 34 59 73 87 UNI 0.015 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 UNI 0.00203 *____________________________________________________________________* *MEMBER WEIGHT DUE TO LIVE LOAD 160 166 172 178 UNI 0.0725 162 168 174 180 204 TO 209 UNI 0.05125 164 170 176 182 UNI 0.04375 34 59 73 87 UNI 0.0075 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 UNI 0.00413 LOAD 1 LOADTYPE Seismic TITLE EQX 1893 LOAD X 1 LOAD 2 LOADTYPE Seismic TITLE EQZ 1893 LOAD Z 1 *___________________________________________________________________* 27



LOAD 3 LOADTYPE Dead TITLE DL *DEAD WEIGHT OF SLAB= 0.1X25=2.5 KN/SQ.M. (Assuming 100mm THK. Slab) *FLOOR FINISH LOAD = *SERVICE LOAD

=

=1.5 KN/SQ.M. =1.0 KN/SQ.M.

************ TOTAL SLAB LOAD=5.0 KN/SQ.M. SELFWEIGHT Y -1 MEMBER LOAD 160 166 172 178 UNI GY -0.145 162 168 174 180 204 TO 209 UNI GY -0.1025 164 170 176 182 UNI GY -0.0875 34 59 73 87 UNI GY -0.015 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 UNI GY -0.00203 *___________________________________________________________________* LOAD 4 LOADTYPE Live TITLE LL MEMBER LOAD 160 166 172 178 UNI GY -0.145 162 168 174 180 204 TO 209 UNI GY -0.1025 164 170 176 182 UNI GY -0.0875 34 59 73 87 UNI GY -0.015 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 UNI GY -0.00826 *___________________________________________________________________* LOAD 5 LOADTYPE Live TITLE COLLISION LOAD IN X-DIRECTION MEMBER LOAD 33 CON GX -25 0.1 *NORMAL VEHICLE COLLISION LOADS ON SUPPORTS OF BRIDGES *** TABLE-7, CLAUSE 225.3.1,

IRC:6-2000

LOAD 6 LOADTYPE Live TITLE COLLISION LOAD IN Z-DIRECTION MEMBER LOAD 33 CON GZ -25 0.1 *NORMAL VEHICLE COLLISION LOADS ON SUPPORTS OF BRIDGES 28


*** TABLE-7, CLAUSE 225.3.1,


IRC:6-2000

*___________________________________________________________________* LOAD 7 LOADTYPE Wind TITLE WL ON SLOPING ROOF MEMBER LOAD 124 126 134 136 144 146 154 156 UNI Y 0.043 37 62 76 90 120 122 128 130 132 138 140 142 148 150 152 158 UNI Y 0.0491 LOAD 8 LOADTYPE Wind TITLE WL ON PARRABOLLIC ROOF MEMBER LOAD 9 TO 16 63 TO 70 77 TO 84 91 TO 98 101 TO 108 UNI GX 0.0036 LOAD COMB 12 (DL+LL) 3 1.0 4 1.0 LOAD COMB 13 (DL+LL+COLLISION LOAD IN X-DIRECTION) 3 1.0 4 1.0 5 1.0 LOAD COMB 14 (DL+LL+COLLISION LOAD IN Z-DIRECTION) 3 1.0 4 1.0 6 1.0 LOAD COMB 16 DL+WL+1.2COLLISION LOAD IN X-DIRECTION 3 1.0 7 1.0 5 1.0 LOAD COMB 17 DL+WL+1.2COLLISION LOAD IN Z-DIRECTION 3 1.0 7 1.0 6 1.0 LOAD COMB 18 DL+LL+EQX 3 1.0 4 1.0 1 1.0 LOAD COMB 19 DL+LL-EQX 3 1.0 4 1.0 1 -1.0 LOAD COMB 20 DL+LL+EQZ 3 1.0 4 1.0 2 1.0 LOAD COMB 21 DL+LL-EQZ 3 1.0 4 1.0 2 -1.0 LOAD COMB 22 DL+EQX 3 1.0 1 1.0 LOAD COMB 23 DL-EQX 3 1.0 1 -1.0 LOAD COMB 24 DL+5EQX 29



3 1.0 2 1.0 LOAD COMB 25 DL-EQX 3 1.0 2 -1.0 LOAD COMB 26 DL+WL ON SLOPING ROOF 3 1.0 7 1.0 LOAD COMB 27 DL+WL ON PARRABOLLIC ROOF 3 1.0 8 1.0 LOAD COMB 31 DL+WL ON SLOPING ROOF+1.2COLLISION LOAD IN XDIRECTION 3 1.0 7 1.0 5 1.0 LOAD COMB 32 DL+WL ON PARRABOLLIC ROOF+1.2COLLISION LOAD IN XDIRECTION 3 1.0 8 1.0 5 1.0 LOAD COMB 36 DL+WL ON SLOPING ROOF+1.2COLLISION LOAD IN ZDIRECTION 3 1.0 7 1.0 6 1.0 LOAD COMB 37 DL+WL ON PARRABOLLIC ROOF+1.2COLLISION LOAD IN ZDIRECTION 3 1.0 8 1.0 6 1.0 PERFORM ANALYSIS PRINT STATICS CHECK PARAMETER 1 CODE INDIAN DFF 500 MEMB 34 59 73 87 160 162 164 166 168 170 172 174 176 178 180 182 204 205 TO 209 DFF 325 MEMB 1 TO 16 20 TO 25 27 TO 33 46 TO 58 63 TO 72 77 TO 86 91 TO 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159 161 163 165 167 169 171 173 175 177 179 181 183 TO 201 203 210 TO 213 DFF 250 MEMB 37 62 76 90 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 FYLD 250000 ALL CHECK CODE ALL 30



PARAMETER 2 CODE INDIAN STEEL TAKE OFF ALL FINISH STAAD.Pro CODE CHECKING - (ISA ) ***********************

3.2.2 Output File (Excerpt) ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED) MEMBER FX

TABLE

MY

RESULT/ CRITICAL COND/ MZ

RATIO/

LOADING/

LOCATION

============================================================ 1 PRI SMAT PASS IS-7.1.1(A) 0.45 C 0.00 2 PRI SMAT PASS IS-7.1.1(A) 0.45 C 0.00 3 PRI SMAT PASS IS-7.1.1(A) 0.45 C -0.01 4 PRI SMAT PASS IS-7.1.1(A) 0.03 C 0.00 5 PRI SMAT PASS IS-7.1.1(A) 0.14 C 0.00 6 PRI SMAT PASS IS-7.1.1(A) 0.10 C 0.00 7 PRI SMAT PASS IS-7.1.1(A) 0.41 C -0.02 8 PRI SMAT

(INDIAN SECTIONS) 0.038 13 -0.01 0.10 (INDIAN SECTIONS) 0.038 13 -0.01 0.00 (INDIAN SECTIONS) 0.043 19 0.01 0.07 (INDIAN SECTIONS) 0.066 16 -0.02 0.00 (INDIAN SECTIONS) 0.083 16 0.03 0.09 (INDIAN SECTIONS) 0.111 16 0.04 0.02 (INDIAN SECTIONS) 0.046 14 0.00 0.09 (INDIAN SECTIONS) 31


PASS IS-7.1.1(A) 0.41 C -0.02 9 PRI SMAT PASS IS-7.1.2 0.01 T -0.02 STAAD SPACE


0.050 14 0.00 0.00 (INDIAN SECTIONS) 0.305 17 0.01 0.00 -- PAGE NO. 14

ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED) MEMBER FX

TABLE

MY

RESULT/ CRITICAL COND/ MZ

RATIO/

LOADING/

LOCATION

============================================================= Maximum Combined Stress (MPa)

Member

Loading Combination

Compressive

Tensile

Compressive

Tensile

Primary Column

19.68

20.23

DL + WL on

WL on Sloping

Sloping Roof

Roof

Secondary Column

76.14

75.94

WL on Sloping

DL + WL on

Roof

Sloping Roof

Curved Beam Member

8.38

8.17

DL + LL - EQX

Load Transfer Member

35.78

18.19

DL + LL + EQZ

Secondary Beam

10.22

19.7

Primary Beam

17.06

3.12

DL + LL - EQX

Purlin

4.41

31.63

DL + LL + EQZ

Parabolic Roof Member

11.2

20.42

DL + LL - EQZ

Inclined Strut

13.05

24.83

DL + LL + EQZ

WL on Sloping Roof WL on Sloping Roof

WL on Sloping

DL + LL -

Roof

EQX WL on Sloping Roof EQZ DL + WL on Sloping Roof WL on Sloping

Table 3.2: Maximum Stresses in STAAD Pro Analysis

32

Roof



3.3 ANSYS MODEL 3.3.1 Introduction ANSYS is an engineering simulation software provider founded by software engineer John Swanson. It develops general-purpose finite element analysis and dynamics software. These are general-purpose finite element modeling packages for numerically solving mechanical problems, including static/dynamic structural analysis (both linear and non-linear), heat transfer and fluid problems, as well as acoustic and electromagnetic problems.

3.3.2 Purpose The basic purpose of introducing ANSYS analysis in this project is to determine the stress contours. The stress contours thus obtained are used for locating the critical positions on the experimental model to paste the strain gauges.

3.3.3 Building the Sky Walk Model Building a finite element model requires more of your time than any other part of the analysis. First, you specify a job name and analysis title. Then, you use the PREP7 preprocessor to define the element types, element real constants, material properties, and the model geometry.

3.3.3.1 Specifying a Job name and Analysis Title This task is not required for an analysis, but is recommended.

3.3.3.2 Defining Units The ANSYS program does not assume a system of units for your analysis. Except in magnetic field analysis, you can use any system of units so long as you make sure that you use that system for all the data you enter. (Units must be consistent for all input data.)

33



3.3.4 Defining Element Types The ANSYS element library contains more than 150 different element types. Each element type has a unique number and a prefix that identifies the element category: BEAM4, PLANE77, SOLID96, etc. The element type determines, among other things: 1 The degree-of-freedom set (which in turn implies the discipline - structural, thermal, magnetic, electric, quadrilateral, brick, etc.) 2 Whether the element lies in 2-D or 3-D space. BEAM4, for example, has six structural degrees of freedom (UX, UY, UZ, ROTX, ROTY, ROTZ), is a line element, and can be modeled in 3-D space and hence we have used this particular element for sky walk analysis.

3.3.4.1 BEAM4 Element Description BEAM4 is a uniaxial element with tension, compression, torsion, and bending capabilities. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. Stress stiffening and large deflection capabilities are included. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analysis.

Figure 3.1: Beam 3D Element 34



3.3.5 Defining Element Real Constants Element real constants are properties that depend on the element type, such as crosssectional properties of a beam element. From the preliminary testing we have identified all such properties.

3.3.6 Defining Material Properties Most element types require material properties. Depending on the application, material properties can be linear or nonlinear. As with element types and real constants, each set of material properties has a material reference number. The table of material reference numbers versus material property sets is called the material table. ANSYS identifies each set with a unique reference number.

3.3.7 Material Model Interface ANSYS includes an intuitive hierarchical tree structure interface for defining material models. A logical top-down arrangement of material categories guides you in defining the appropriate model for your analysis. For this particular project material models selected are structural, linear, isotropic and elastic. These properties will further govern the stress developments in model.

Figure 3.2: Material Model Interface Initial Screen 35



3.3.8 Creating the Model Geometry Once you have defined material properties, the next step in an analysis is generating a finite element model - nodes and elements that adequately describes the model geometry. This is the most interesting part of the analysis. For this skeletal structure we decided to go with coordinate system. With the help of available coordinates, lines and splines we generated a 2-D model. Later with the copy command the same is copied and pasted at 4 different places at interval of 30cm and are joined by purlins and primary beams. Once we are ready with model then the struts are added.

3.3.9 Meshing From the available meshing elements a simple line meshing is chosen for the skeletal structure. The meshing is done along length of member and the size of meshed element is 3 cm. A simple process explained as follows is used for meshing. Using the mesh attributes command the lines i.e. structural members are selected. These members are then meshed using the mesh command. Modified meshing is used to refine the mesh if required.

3.3.10 Applying Loads and Obtaining the Solution In this step, you use the SOLUTION processor to define the analysis type and analysis options, apply loads, specify load step options, and initiate the finite element solution. You also can apply loads using the PREP7 preprocessor.

3.3.11 Defining the Analysis Type and Analysis Options You choose the analysis type based on the loading conditions and the response you wish to calculate. In this project we have performed two types of analysis. One is the regular static analysis to determine the stresses and the other is modal analysis to determine the natural frequency of the structure.

36



3.3.12 Applying Loads The word loads as used in ANSYS documentation includes boundary conditions (constraints, supports, or boundary field specifications) as well as other externally and internally applied loads. Loads in the ANSYS program are divided into six categories: 1.

DOF Constraints

2.

Forces

3.

Surface Loads

4.

Body Loads

5.

Inertia Loads

6.

Coupled-field Loads

You can apply most of these loads either on the solid model (keypoints, lines, and areas) or the finite element model (nodes and elements). In this case we needed to apply three different loads and load combinations. Apart from the gravity load the other loads considered are the live load and the wind load, acting in the upward direction. The model is then analyzed for only (dead load), (dead load + live load) and (dead load + wind load) loading combinations. These are the critical load combinations in our case and hence the FEM analysis for these load cases is done. Boundary Conditions: All the six degrees of freedom were constrained at the base of both the columns, i.e. Column base is assumed to be rigid. Dead Load: Once the material properties and dimensions are provided, the software by default calculates the dead load and corresponding stresses. The dead load from the given data is observed to be 47.195 kg. Live Load: Live load to the structure is 5 kN/m2 as per IS 875- PART II. This load is then multiplied by width of the structure to get the uniformly distributed load along length. Further this load is multiplied by the length of element and then divided by number of nodes (42) to get the force at each node. This load is then applied to the model and the analysis is carried out.

37



Wind Load: Uplift action of the wind is considered in this case to get the possible critical case. Wind forces per node are directly obtained from STAAD Pro 2005 and are applied in ANSYS. To get the worst effect strictly only dead load was considered along with upward wind load.

Figure 3.3: Sample output window showing mass and other properties

3.3.13 Initiating the Solution To initiate solution calculations, use either of the following: Command(s): SOLVE GUI:

Main Menu> Solution> Solve> Current LS Main Menu> Solution> solution_method

When you issue this command, the ANSYS program takes model and loading information from the database and calculates the results. Results are written to the results 38



file (Jobname.RST, Jobname.RTH, Jobname.RMG, or Jobname.RFL) and also to the database. The only difference is that only one set of results can reside in the database at one time, while you can write all sets of results (for all substeps) to the results file.

3.3.14 Reviewing the Results Now we are done with the analysis process and the final step is to view the results. As mentioned earlier 2 types of analysis are performed whose results can be obtained as followsModal Analysis: Read Results – First Set – Plot Controls – Animate – Mode Shapes Mode 1 (Deformed + Undeformed Shape) Natural Frequency: 5.219 Hz

Figure 3.4: Mode 1 (Deformed + Undeformed Shape) Static Analysis: General Postprocess – Element Table – Plot Element Table . In element table we get axial, bending and combined stresses.

39



Figure 3.5: Direct Stress contour of dead load + wind load

Figure 3.6: Combined Stress contour of dead load + wind load

40



Maximum Combined Stress

Loading

(MPa)

Combination

Primary Column

-15.2

DL + LL

Secondary Column

-69

DL + LL

Curved Beam Member

-14

DL + LL


-22.5

DL + LL

Secondary Beam

15

DL + LL

Primary Beam

43

DL + LL

Purlin

-13

DL + LL


-12

DL + WL

Inclined Strut

16

DL + WL

Member

Table 3.3: Maximum Stresses in ANSYS Analysis

3.4 EXPERIMENTAL MODEL 3.4.1 Introduction A scaled-down model of the structure is prepared within the practical limits for experimental purposes. The scale chosen is 1:10. The model is prepared using mild steel with welded connections. Material testing is carried out to confirm the actual material properties, thereby eliminating any assumptions. The material properties worked out are as follows: Modulus of Elasticity = 2.01*105 MPa Modulus of Rigidity = 7.90*105 MPa

41



Figure 3.7: Skywalk Model in Working Stage

Figure 3.8: Completed Skywalk Model

3.4.2 Scaling Procedure The scale of model is 1:10. This scale is selected by keeping into consideration all the practical difficulties that might arise during modeling. It is ensured that the smallest member of the structure would be modeled with appropriate scaled dimensions and would not be very slender. Thus the member with least dimensions, i.e. purlin became the governing criterion for selection of scale. The members of original structure with original dimensions are scaled down individually. Modulus of section is calculated of the individual member and then it is scaled down to 1:10. Now, for the scaled modulus of section appropriate solid section is selected. The solid sections readily available in the market are selected. If hollow sections are used, though the model weight would have decreased considerably, the member sizes for the same scale would be very large. Hence, keeping in mind practical limitations, the solid sections are used.

42



Following table gives one to one correspondence of actual and scaled member sections: MEMBER

ACTUAL STRUCTURE

MODEL

Purlin

ISMC 100

RECT 6X6 mm

Parabolic roof member

ISMB 300

RECT 10X20 mm

Secondary floor beams

ISMB 250

RECT 6X12 mm

Primary floor beams

ISMB 600

RECT 20X32 mm

Curved beam

ISMB 600

RECT 20X32 mm

Secondary column section

PIPE 0.5 mφ, 12mm Thk.

ROD 15 mmφ

Primary column section


ROD 34mmφ

Inclined struts


ROD 10mmφ

DESIGNATION

Table 3.4: Comparison of Members in Actual Structure and Model

MODULUS OF MEMBER

SECTION (ACTUAL

DESIGNATION

STRUCTURE) cm3

MODULUS OF SECTION (1:10 SCALED MODEL) cm3

Purlin

37.3

0.108

Parabolic roof member

573.6

1.667

Secondary floor beams

410.5

0.864

Primary floor beams

4882.4

5.461

Curved beam

4882.4

5.461

Secondary column section

54.79

0.249

Primary column section

3741.4

6.560

Inclined struts

49.9

0.051

Table 3.4: Comparison of Section Modulus in Actual Structure and Model

43



3.4.3 Limitations Few practical difficulties were faced during preparation of scaled model. Following practical limitations are taken into consideration: 1. Solid steel members readily available in market are used which are selected as close to the required modulus of section as possible. This has led to some discrepancies in ideal and scaled model. 2. To facilitate the bending of the curved members, like the parabolic roof member and the curved beam, the members were bent about the weaker axis which let to the interchange of the major and minor axes as compared to that of the idealized scaled model. 3. For the actual structure the joints would be welded together using a weld size of 8 mm. However, to scale down the weld size is not feasible in the model. Hence the joints, which are the most critical points in the actual structure, were found to have greater weld strength in the model. 4. The base of the structure is made completely rigid by welding it to a channel section. In the proposed structure pile foundations are provided which are assumed to be rigid.

44


Chapter 4 - Testing Methodology

CHAPTER FOUR – TESTING METHODOLOGY 4.1 PRELIMINARY TESTING 4.1.1 Tension Test The tension test on the material to be used for the preparation of the model is carried out on the UTM (600 kN capacity). References: 1.

IS 1608- 1972 Method for tensile testing of steel products.

2.

IS 432-1966

3.

IS 2854- 1964 Method of test for determining modulus of elasticity.

Mild steel and medium tensile steel bars.

Test Requirements: The cross sectional area shall be determined from the arithmetic mean of two measures of the diameter at right angles to each other. Gauge length shall be made on the test piece at (5*dia.) mm length. Procedure: 1. Determine the mean diameter of the specimen, mark gauge length on it. 2. Fix the specimen in the tension grip of the machine and adjust the position of the crosshead, so that the specimen is held tight. 3. Attach extensometer to the specimen, at the central position, start the pumping unit and apply load gradually. 4. Record the load and corresponding elongation at regular intervals. Remove the extensometer. 5. Record further elongation on a scale, fix to the UTM observe neck formation and failure of the specimen. 6. Plot the graph of stress vs. strain and calculate modulus of elasticity of the material.

45



Observation: 1. Diameter of the specimen: 12 mm 2. Gauge length: 60 mm 3. Elongated length: 70 mm

Graph:

Figure 4.1: Tension Test – Stress vs. Strain Result: Modulus of elasticity of the material, E= 2.01 * 105 MPa

46



4.1.2 Torsion Test The torsion test on the material to be used for preparation of the model is carried out on torsion testing machine. References: 1. IS 1717- 1971 Method of simple torsion testing of steel wire. Test Requirements: Length of the specimen= 10* dia. Ends are squared for gripping in the machine. Gauge length is measured as ungripped length of circular parts. Procedure: 1. Measure the sectional diameter of the specimen, adjust the supports for the required span and place it symmetrically. 2. Adjust for zero when the specimen is in the right position, carry out initial adjustment of the lever so that the pointer coincides with zero. 3. Apply the torque gradually and adjust the scale for rotation so as to coincide the pointer. 4. Note down the values of load and the corresponding angular rotation. Continue the procedure until the specimen fails. 5. Record the torque at failure of specimen and also its appearance and developed cracks. 6. Plot the graph of load vs. deflection and calculate the value for modulus of rigidity. Observation: 1. Diameter of the specimen= 11.1 mm 2. Polar moment of inertia= 1402.69 mm4

47



Graph:

Figure 4.2: Torsion Test – Torque vs. Angle Result: Modulus of rigidity of the material, G= 7.9 * 104 MPa.

4.1.3 Shear Test The shear test on the material to be used for preparation of the model was carried out on universal testing machine (10- ton capacity). References: 1. IS 5242- 1972 Method of test for determination of shear test of metals.

48



Procedure: 1. Measure diameter of specimen. Place it in testing accessory of UTM such that it is subjected to shearing along one plane for single shear failure and two planes for double shear. 2. Place the shear attachment between middle and lower cross heads of UTM. 3. Place the specimen in cutters and apply the load such that the rate of separation of cross heads at any moment shall not be greater than 10mm/min. Observation: 1. Diameter of specimen: 12 mm 2. Cross sectional area: 113.1 mm2 3. Single shear load: 45.96 kN 4. Double shear load: 88.20 kN Result: 1. Single shear stress: 406.37 MPa 2. Double shear stress: 779.84 MPa

4.1.4 Strength of Weld Test The scaled model is prepared using welded connections. The connections are the most critical positions defining the structural behavior of the model under application of loads. Hence, strength of weld test is carried out to determine the failure load for a welded joint. Connections mark an important point for effective load transfer. Good joint transfers the load safely without any deformation while a poor joint might lead to local failure. When two members with varying cross sections are welded together, smooth load transfer does not take place leading to undesirable stress concentration at this juncture. In the scaled model, such a critical location is the connection between parabolic roof member and secondary beam. Hence, study of the same has been carried out.

49



Procedure: 1. A welded connection between parabolic roof member (10 mm X 20 mm) and secondary beam (6 mm X 12 mm) is used as the test specimen. 2. The specimen is fixed in UTM(600 kN capacity) and gradual tensile force is applied. 3. Failure load for the specimen is noted down. Observation: 1. Breaking load, specimen I = 29.32 kN 2. Breaking load, specimen II = 35.00 kN Result: Average breaking load = 32 kN By knowing the strength of the weld, the structure can be loaded carefully so as to avoid any local failure.

4.1.5 Dual Penetration Test Welded connections being of critical importance, they are checked for defects and irregularities by ‘Dual Penetration Test (DPT) ‘.DPT was carried out to check strength and quality of all welded joints. Test Assembly: It consists of three different kinds of sprays, manufactured by ‘DYEGLO, Pune’. 1. Cleaner (CL01) 2. Red Penetrant (RP81) 3. Developer (RD01)

50



Procedure: 1. Initially, the metal surface is cleaned with a dry cloth. The Cleaner spray is used for pre-cleaning the surface. Avoid direct spraying of Cleaner on test surface, spray on cloth to clean the surface. 2. Apply the Red Penetrant on the dried surface. Hold the can at a distance of 7”-9” while spraying so as to get a uniform and thin coating. 3. Recommended dwell time is 5-15 minutes. 4. Clean the surface using Cleaner to remove excess Penetrant. 5. Apply the Developer on the surface. Hold the can at a distance of 7”-9” while spraying so as to get a uniform and thin coating. 6. Recommended dwell time is 3-7 minutes. 7. Observe the welded joint for any appreciable defects like cracks, depressions or porous voids.

Result: No appreciable damage is observed as shown in the figures. This confirms the good quality and high strength of the welded joints.

51



Figure 4.3: DPT – Purlin and Roof Joint

Figure 4.4: DPT – Primary and Secondary Beam Joint

52



4.1.6 Buckling Load Test Buckling load test is carried out to determine buckling load and failure load of the Yshaped column. This test is useful in determining the maximum load the structure can handle during actual testing without undergoing any permanent failure. Buckling load is determined through testing and also using Euler’s theory. Euler’s Theory: CASE I: Length of the entire column is considered Assume fy = 250 MPa Length of Column,

L = 0.61 m

Effective Length,

Le = 1.2 * 0.61 = 0.732 cm

Cross sectional area: A1 = Π*(32)2 / 4 = 804.24 mm2 A2+ A3 = 2*Π*(15)2 / 4 = 352.42 mm2 rmin = (I/A)0.5 = 3.75 mm λ = Le/ rmin = 73.2/ 3.75 = 19.52 σac = 148 N/mm2

…from IS 800- 1984.

Hence the load on the column, P = Area * Stress = 353.42 * 148 = 52.3 kN. CASE II: Length of the secondary column is considered Length of Column,

L = 0.26 m

Effective Length,

Le = 1.2 * 0.26 = 31.2 cm

λ = Le/ rmin = 31.2/ 3.75 = 8.32 σac = 150 N/mm2

…from IS 800- 1984.

53



P = Area * Stress = 353.42 * 150 = 53 kN. Euler’s critical load: Pe = Π2*E*I/ Le2 = (Π2 * 2 * 105 * 4970.09) / (2*73.22) = 70.34 kN. Test Assembly: 1. The specimen consists of a Y-shaped column resembling the one that supports the scaled model with a horizontal member at the top to facilitate application of compressive load. 2. The specimen is placed in the UTM (600 kN capacity). Dial gauges, five in number, are connected to the specimen in order to measure the deflection in the specified direction. 3. Compressive load is applied at a constant rate and the deflection in the dial gauges is noted. 4. The failure load for the setup is determined.

Figure 4.5: Buckling Load Test Assembly

54



Observation: Buckling load for the specimen (Test) = 50.23 kN Result: The maximum safe load that the column can carry: 1. Buckling load for the specimen (Test) = 50.23 kN 2. Buckling load for the specimen (Euler’s Theory) = 52.30 kN

4.2 MODEL TESTING 4.2.1 Static Load Testing The scaled model is tested under various static loads and loading combinations for better understanding of behavior of the steel structure. Basic loads consist of: 1. Dead Load 2. Live Load 3. Simulated Wind Load Using these loads, the structure is loaded in varying combinations and the strains developed at fifteen different locations are recorded. Strain gauges are used for the same.

4.2.1.1 Strain Gauge - Introduction A Strain gauge is a sensor whose resistance varies with applied force. It converts force, pressure, tension, weight, etc., into a change in electrical resistance which can then be measured. The strain gauge has been in use for many years and is the fundamental sensing element for many types of sensors, including pressure sensors, load cells, torque sensors, position sensors, etc.

55



The majority of strain gauges are foil types, available in a wide choice of shapes and sizes to suit a variety of applications. They consist of a pattern of resistive foil which is mounted on a backing material. They operate on the principle that as the foil is subjected to stress, the resistance of the foil changes in a defined way.

Figure 4.6: Typical Strain Gauge The strain gauge is connected into a Wheatstone Bridge circuit with a combination of four active gauges (full bridge), two gauges (half bridge), or, less commonly, a single gauge (quarter bridge). In the half and quarter circuits, the bridge is completed with precision resistors.

Figure 4.7: Wheatstone Bridge Circuit The complete Wheatstone Bridge is excited with a stabilized DC supply and with additional conditioning electronics, can be zeroed at the null point of measurement. As stress is applied to the bonded strain gauge, a resistive change takes place and balances the Wheatstone Bridge. 56



This results in a signal output, related to the stress value. As the signal value is small, (typically a few mill volts) the signal conditioning electronics provides amplification to increase the signal level to 5 to 10 volts, a suitable level for application to external data collection systems such as recorders or PC Data Acquisition and Analysis Systems. Most manufacturers of strain gauges offer extensive ranges of differing patterns to suit a wide variety of applications in research and industrial projects. They also supply all the necessary accessories including preparation materials, bonding adhesives, connections tags, cable, etc. The bonding of strain gauges is a skill and training courses are offered by some suppliers. There are also companies which offer bonding and calibration services, either as an in-house or on-site service. If a strip of conductive metal is stretched, it will become skinnier and longer, both changes resulting in an increase of electrical resistance end-to-end. Conversely, if a strip of conductive metal is placed under compressive force (without buckling), it will broaden and shorten. If these stresses are kept within the elastic limit of the metal strip (so that the strip does not permanently deform), the strip can be used as a measuring element for physical force, the amount of applied force inferred from measuring its resistance. Such a device is called a strain gauge. Strain gauges are frequently used in mechanical engineering research and development to measure the stresses generated by machinery. Aircraft component testing is one area of application, tiny strain-gauge strips glued to structural members, linkages, and any other critical component of an airframe to measure stress. Most strain gauges are smaller than a postage stamp, and they look something like this:

57



Figure 4.8: Working of a Strain Gauge A strain gauge's conductors are very thin: if made of round wire, about 1/1000 inch in diameter. Alternatively, strain gauge conductors may be thin strips of metallic film deposited on a no conducting substrate material called the carrier. The latter form of strain gauge is represented in the previous illustration. The name "bonded gauge" is given to strain gauges that are glued to a larger structure under stress (called the test specimen) The task of bonding strain gauges to test specimens may appear to be very simple, but it is not. "Gauging" is a craft in its own right, absolutely essential for obtaining accurate, stable strain measurements. It is also possible to use an unmounted gauge wire stretched between two mechanical points to measure tension, but this technique has its limitations. Typical strain gauge resistances range from 30 Ohms to 3 k Ohms (unstressed). This resistance may change only a fraction of a percent for the full force range of the gauge, given the limitations imposed by the elastic limits of the gauge material and of the test specimen. Forces great enough to induce greater resistance changes would permanently deform the test specimen and/or the gauge conductors themselves, thus ruining the gauge as a measurement device. Thus, in order to use the strain gauge as a practical instrument, we must measure extremely small changes in resistance with high accuracy. The strain gauge used at the time of experimentation has following specifications:

58


Main Test


Materials

Metal,Mortar

Materials Operating

Backing Materials

- to +80°C -20

Temperature Compensation

Element

+10 to +80°C

range Bonding adhesive

Strain limit

CN,RP-2

Polyester Cu-Ni Ni alloy foil 2% (20000×10-6)

Fatigue life at

1×106

room temp.

(±1500×10-6)

Table 4.1: Strain Gauge Specifications

Single element (G.F. 2.1 approx.) 0.11mm2PVC Lead wire pre-attached pre Total resistance per meter: 0.32Ω

Figure 4.9: Strain Gauge

TML PFL-30-11

Type

PFL30-11

Gauge length (mm)

30

Gauge Backing Backing Lead wire Resistance width length width pre(Ω) (mm) (mm) (mm) attached

Type name of lead wire

Paralleled 1m Paralleled 3m Paralleled 5m 3-wire wire 3m 3-wire wire 5m

-1L -3L -5L -3LT -5LT

2.3

40

7

120

Table 4.2: Specifications of PFL-30-11

59



Figure 4.10: Strain Gauge Package and Strain Gauge Color Coding

60



Figure 4.11: PFL-30-11 Strain Gauge Test Data

Figure 4.12: Explanation of Strain Gauge Test Data 61



4.2.1.2 Bonding of Strain Gauges Bonding of strain gauges is done in following steps: 1. Preparation: The following items are required for bonding and wire connection: strain gauges, bonding adhesive, connecting terminals, test specimen, solvent, cleaning tissue, soldering iron, solder, abrasive paper, marking pencil, scale, tweezers, extension lead wire, polyethylene sheets and nippers. 2. Positioning: Roughly determine the location on the test specimen where the strain gauge is to be located. 3. Surface Preparation: Before bonding, remove all grease, rust, paint etc. from the bonding area. Sand an area somewhat larger than the bonding area uniformly and finely with an abrasive paper. This process is known as ‘dry abrading’.

Figure 4.13: Surface Preparation-Dry Abrading 4. Fine cleaning: Clean the bonding area with industrial tissue paper or cloth soaked in a small amount of industrial solvent such as acetone. Continue cleaning until a new tissue or cloth comes away completely free of contamination. Following the surface preparation, be sure to attach the gauge before the surface becomes contaminated or gets covered with an oxidizing membrane. This process is also known as ‘wet abrading’ Initially the surface was cleaned using acid solution. To neutralize the surface, this step was followed by cleaning using a base. The surface should appear smooth after wet abrading. 62



Figure 4.14: Surface Preparation-Wet Abrading 5. Applying bonding adhesive: Drop the proper amount of adhesive onto the back of the gauge base. Usually one drop of adhesive will suffice, but you may increase the number of drops as per the size of the gauge. Use the adhesive nozzle to spread the adhesive thinly and uniformly over the back surface. Sometimes a special adhesive known as ‘accelerator’ is used to accelerate the process of bonding of the strain gauges.

Figure 4.15: Application of Adhesive 6. Curing and pressing: Place the gauge on the guide mar, place a polyethylene sheet onto it and press down on the gauge constantly using your thumb or a gauge pressing device. This should be done quickly as the curing process is completed very fast. The curing time varies according to the gauge, test specimen, temperature, humidity and pressing force. Curing time under normal circumstances is 20-60 sec.

Figure 4.16: Curing and Pressing

63



7. Raising the gauge leads: After curing completely, remove the polythene sheet, and raise the gauge leads with a pair of tweezers.

Figure 4.17: Raising the Gauge Leads

8. Bonding connecting terminals: Position the proper size connecting terminals adjacent to the bonded gauge. A distance of 3-5 mm generally allows for easier wiring later.

Figure 4.18: Bonding Connecting Terminals

9. Soldering the gauge leads: Wrap the gauge leads around the connecting terminal wires. Solder the junction area with a little slack in the gauge leads, taking care to prevent excessive tension during measurement.

Figure 4.19: Soldering the Gauge Leads

64



10. Soldering extension lead wires: Solder an extension lead wire to the terminal wires on the other side of the connecting terminals. Clip off any excess extension lead wire with a pair of clippers.

Figure 4.20: Soldering Extension Lead Wires

4.2.1.3 Location of Strain Gauges From the stress contours obtained in ANSYS analysis, fifteen critical locations are identified as follows: 1. Primary column: 3cm from top 2. Secondary column: 3 cm from bottom 3. Secondary column: 3 cm from bottom 4. Load transferring member: 3.7cm from bottom 5. Curved beam: centre of the beam on the underside 6. Central primary beam: centre of entire span on the underside 7. Central primary beam: centre of second span at the top 8. Right primary beam: centre of entire span on the underside 9. Secondary beam: 8cm from face of right primary beam 10. Parabolic roof member: 7.5cm from second lower purlin 11. Parabolic roof member: at centre of uppermost span 12. Purlin: 7cm from face of secondary beam on the lowermost purlin 13. Inclined strut: center 14. Inclined strut: center 15. Inclined strut: center

65



Figure 4.21: Locations of Strain Gauges

Figure 4.22: Strain Reading Equipment 66



4.2.2 Live Load Skywalk being a public structure, higher values of live load are chosen as per IS-875 (PART II). Live load considered during analysis is 5 kN/m2. This pressure intensity is converted to equivalent load using the whole deck area of the model. The calculation resulted into maximum 400 kg load to be applied during testing.

4.2.2.1 Loading Combinations For application of live load, 20 kg iron weights are used. Live load is applied in following increments: 1. LL = 100 kg 2. LL = 200 kg 3. LL = 300 kg 4. LL = 400 kg

Figure 4.23: Test Setup for Static Load Test

67



4.2.3 Wind Load Simulation Taking into consideration practical difficulties, wind load is simulated and converted into equivalent point load so as to achieve simplicity during testing. The most critical case, i.e. uplift of straight portion of the roof is taken into consideration. The wind intensity is converted into equivalent point load for each of the four panels. Procedure for the same can be illustrated as follows: For one sub panel of 0.3m X .14m, WL = 0.049 kN/m

… according to IS-875 (PART III)

For one single panel (30 cm width), L = 0.049 * (0.3) = 0.0147 kN Total load on each span (panel) = 6 * 0.0147 = 0.09 kN

… six sub panels

= 9 kg For a reaction frame and string arrangement, load that is to be applied at the straight end of the string is, T = 9/sin θ where, θ = angle between string and the model roof

4.2.3.1 Test Assembly For uniform application of simulated wind load, a steel mesh is fixed at various points to the model roof using binding wires. Introduction of steel mesh ensures smooth and uniform transfer of point load to the roof members without undergoing any deformation. An inextensible string is fixed at the center of each panel to the steel mesh. The string is carried over a reaction frame and weights are attached to the straight portion of the string. Two kg iron weights are used for loading which are assembled together in gunny bags.

68



Figure 4.24: Wind Load Simulation

Figure 4.25: Load Combination - LL (100 kg) + WL (10 kg)

69



4.2.3.2 Loading Combinations Following load combinations are considered during testing: 1. WL = 10 kg 2. WL = 15 kg 3. LL = 100 kg + WL = 10 kg 4. LL = 300 kg + WL = 15 kg 5. LL = 400 kg + WL = 15 kg

4.2.4 Observations [ Sign Convention: Positive – Tensile, Negative – Compressive] LL=

LL= 200

LL= 100

LL=

LL=

LL= 300

LL=

LL= 400

WL=

WL=

100

kg +

kg +

200

300

kg +

400

kg +

10

15 kg

kg

WL=15kg

WL=10kg

kg

kg

WL=15kg

kg

WL=15kg

kg

[1] Strain

-2

46

30

-4

-4

46

-5

48

35

[2] Strain

-23

-483

-302

-79

-118

-522

-170

-587

-316

[3] Strain

32

492

301

94

141

543

203

617

297

[4] Strain

-24

-37

-18

-47

-67

-56

-84

-74

7

[5] Strain

42

85

43

87

150

152

191

188

1

[6] Strain

12

20

10

21

32

30

42

40

-1

[7] Strain

-11

-80

-53

-19

-30

-100

-41

-104

-44

[8] Strain

55

112

52

115

192

192

253

248

-4

[9] Strain

52

107

53

104

150

148

201

203

1

[10] Strain

-4

3

2

-3

-11

-3

-12

-9

7

[11] Strain

-52

-106

-50

-110

-177

-178

-232

-229

3

[12] Strain

1

-20

-13

0

0

-20

0

-19

-13

[13] Strain

10

4

-2

21

29

11

39

24

-13

[14] Strain

6

-28

0

-21

-19

-28

-14

-22

-4

[15] Strain

-23

-42

-19

-51

-77

-71

-107

-96

7

GAUGE NUMBER

Table 4.3: Micro-Strains for Ten Loading Combinations 70

50 -448 423 10 2 -3 -58 -5 0 10 4 -19 -17 -35 13



4.3 FREE VIBRATION ANALYSIS The free vibration analysis of the model is carried out to determine the natural frequency of vibration of the model in the particular direction. Although the dynamics of structure is a very vast topic, we have decided to incorporate only a small part of dynamics of structure. The scaled model was given some initial displacement and the structure was released from this position. The resulting motion of the model is recorded with the help of accelerometers. This forms the basis of free vibration analysis.

4.3.1 Test Setup The scaled model is given some initial displacement by pulling the model with the help of a non-extensible string run over a pulley with loads attached at the other end. The model is released from this position by cutting the string and the resulting motion is recorded with the help of accelerometers. In all three accelerometers have been used for this purpose. They are placed at three different levels and measure the vibrations in only one direction. The positions of the accelerometers are: 1. At the floor level- to measure vertical vibrations at the floor level. 2. At the tip of parabolic roof member -to measure horizontal vibrations at the floor level. 3. At the floor level- to measure horizontal vibrations at the floor level. Three different iterations are carried out. We have restricted ourselves to determine the natural frequency of the model along the width of the model as this might prove to be the critical case. The test data has been given in the following table:

71


Iteration no.


Angle of inclination of

Force in N

the string

Initial displacement in cm

Iteration 1

18.640

193.65

1.0

Iteration 2

24..560

373.56

2.5

Iteration 3

29.680

567.80

3.5

Table 4.4: Test Data for Free Vibration Analysis

Figure 4.26: Test Setup for Free Vibration Test

4.3.2 Observations The First Fourier Transform graphs which are the variation of the acceleration versus the frequency of the model for the three iterations are reproduced here:

72



Iteration 1




73



Iteration 2




74



Iteration 3




75



4.3.3 Conclusion 1. As the load was increased, the amplitude of the vibration of structure increased. 2. The natural frequency of the structure, which remained same for all the three iterations, was found out to be 4.375 Hz in the X-direction. Modal analysis of the structure was carried out on the structure using ANSYS-10 which yielded the natural frequency as 5.023 Hz in X-direction i.e. along the width.

4.3.4 Scope Free vibration analysis of the model forms the first step in the dynamic analysis of the model. To determine the natural frequency of the model forms the most preliminary prerequisite of performing any dynamic test on the model. After the free vibration analysis, response of the structure to forced vibrations has to be studied. However this is beyond the scope of this project. Forced vibration response of the structure consists of two parts: 1. Transient vibrations which take place at the damped natural frequency of the system. 2. Steady state vibrations which occur at the frequency of excitation which is sustained for the period of excitation. The critical case occurs when the exciting frequency and the natural frequency of the structure interfere constructively leading to a potential harmful state of resonance. This state has to be avoided since the resonating frequency causes the structure to vibrate vigorously which may lead to failure in the model. Hence, before we go for the forced vibration analysis it is imperative to carry out the free vibration analysis of the structure.

76


Chapter 5 - Results And Discussions

CHAPTER FIVE – RESULTS AND DISCUSSIONS 5.1 VALIDATION The results from STAAD Pro-2005, ANSYS 10 and the experimental results were compared to validate the software analysis. Stresses at 11 different locations were compared for the validation purpose. For the purpose of validation, live load (400 kg) and wind load (10 kg), are the two load cases which are compared. Sign convention for the same is: Positive – Tensile, Negative – Compressive.

5.1.1 Live Load (400 kg) GAUGE NUMBER

STRESSES FOR LIVE LOAD EXPERIMENTAL

ANSYS 10

STAAD Pro-2005

Primary Column

-1

-1.52

-0.38

Secondary Column- Right

-34

-9.9

-9.75

Secondary Column- Left

40.6

9.9

6.15

Curved Beam

-16.8

-14

-2.81


38.2

40

32.41

Secondary Beam

8.4

15

6.9


-8.2

-7.1

-6.91

Primary Beam

40.6

43

36.61

Purlin

-2.4

-13

-7.14

Roof Member

0

-1.3

-1.38

Inclined Strut

7.8

15.2

5.33

Table 5.1: Stresses in different Structural Members for Live Load= 400 kg

77



5.1.2 Wind Load (10 kg) GAUGE NUMBER

STRESSES FOR WIND LOAD (MPa) EXPERIMENTAL

ANSYS 10

STAAD Pro-2005

Primary Column

7

8

20.22

Secondary Column- Right

-63.2

-62

-76.15

Secondary Column- Left

59.4

60

66.71

Curved Beam

1.4

13

8.17


0.2

2.0

1.82

Secondary Beam

-0.2

-0.5

-1.02


-8.8

-12

-11.19

Primary Beam

-0.8

-1.2

-3.23

Purlin

1.4

7.8

3.37

Roof Member

2.6

16.05

8.33

Inclined Strut

2.6

16.01

24.9

Table 5.2: Stresses in different Structural Members for Wind Load=10 kg

78



5.2 Interpretation From the comparison it can be seen that the results obtained are within close agreement of each other. Few of the results obtained tend to vary from each other. About 80 % of the stresses at different positions match with each other. Thus, it can be concluded that the software models are validated within practical limits and hence can be used for parametric study.

5.3 Discrepancies The discrepancies seen in the comparison can be explained considering following factors: 1. The experimental test setup was different as compared to software model. The axes in case of structural model are concurrent while that in case of experimental model some of the members were placed one above the other. This lead to non-concurrency of the axes in case of the experimental model. 2. An additional steel mesh was used to facilitate application of wind load. Wind load is simulated instead of application of wind force directly using a wind tunnel. To apply the wind force uniformly over the inclined portion of the model, a steel mesh is used. This increased the overall stiffness of the model. In addition to this, the steel mesh also reduced the effective length of the member, which may lead to variation in results. 3. The loading applied might tend to be asymmetrical. This might be considered as human error and might lead to torsion moments developing in the model. This might further increase the stresses. 4. The members were loaded for a small period of time during testing, while in software models, the loading is considered permanent.

79


Chapter 6 - Parametric Study

CHAPTER SIX – PARAMETRIC STUDY For the shape of the structure under consideration, the only parameter changed is clear span and the reflected change in design of individual members is noted.

6.1 OBJECTIVE The objective of this parametric study is to examine common structure configurations in response to variation in span and to determine the required section modulus from the interaction charts drawn using the optimized sections obtained from STAAD Pro 2005.

6.2 SKY WALK STRUCTURE

Varies

Figure 6.1: Parametric study

80



The parametric study of this sky walk structure is done by varying the span i.e. column to column distance. For this purpose three different models of 9m, 15m and 21m are prepared and designed for optimum sections in STAAD Pro 2005. Then Interaction charts are plotted using the section modulus and span. The graph thus obtained from the above mentioned spans helps in establishing a trend line. This trend line is then used to predict the sections for spans ranging between 9m and 21m which are verified for 12m and 18m span. Such exhaustive charts are prepared for each and every member.

6.3 INTERACTION CHARTS The above study is worked out with the help of interaction charts depicting relation between the modified parameter and design. These interaction charts are prepared using the optimized sections obtained directly from STAAD Pro 2005. Interaction chart for Zx, Zy and Zz of every member has been plotted.

The following members are considered: 1. Curved Beam 2. Primary Beam 3. Primary Column 4. Straight Plate Girder 5. Secondary Column 6. Inclined Roof Member 7. Parabolic Member 8. Inclined Strut

81



Curved Beam 25 20 Zx (*10 m3)

15 10 5 0 0

5

10

15 Span (m)

20

25

Curved beam Zx v/s Span

Zy (*10-3 m3)

Figure 6.2: Curved Beam Zx

16 14 12 10 8 6 4 2 0 0

5

10

15 Span (m)

20

25

Curved beam Zy v/s Span

Figure 6.3: Curved Beam Zy

12

Zz ( *10-3 m3)

10 8 6 4 2 0 0

5

10

15 Span (m)

20

Curved beam Zz v/s Span

Figure 6.4: Curved Beam Zz 82

25



0.0057 0.0056 0.0055 0.0054 0.0053 0.0052 0.0051 0.005 0.0049 0

5

10 Span (m) 15

20

25

Primary beam Zx v/s Span

Figure 6.5: Primary Beam Zx

3

Zy(*10-3 m3)

2.5 2 1.5 1 0.5 0 0

5

10 15 Span (m)

20

25

Primary beam Zy v/s Span

Figure 6.6: Primary Beam Zy

Zz (*10-3 m3)

Zx (*10-3 m3)

Primary Beam

0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

5

10

15 Span (m)

20

Primary beam Zz v/s Span

Figure 6.7: Primary Beam Zz 83

25



Primary Column 12 10 Zx (*10-3 m3)

8 6 4 2 0 0

5

10 Span (m)

15

20

Primary column Zx v/s Span…

Figure 6.8: Primary Column Zx 30

Zy (*10-3 m3)

25 20 15 10 5 0 0

5

10 Span (m) 15

20

25

Primary column Zy v/s Span

Zz (*10-3 m3)

Figure 6.9: Primary Column Zy 9 8 7 6 5 4 3 2 1 0 0

5

10

15 Span (m)

20

Primary column Zz v/s Span

Figure 6.10: Primary Column Zz 84

25



Straight Plate Girder 0.007

Zx(*10-3 m3)

0.006 0.005 0.004 0.003 0.002 0.001 0 0

5

10 Span (m) 15

20

25

Straight plate girder Zx v/s Span

Figure 6.11: Straight Plate Girder Zx

0.53 0.52 Zy(*10-3 m3)

0.51 0.5 0.49 0.48 0.47 0.46 0

5

10

15 Span (m)

20

25

Straight plate girder Zy v/s Span

Zz(*10-3 m3)

Figure 6.12: Straight Plate Girder Zy 7 6 5 4 3 2 1 0 0

5

10

15 Span (m)

20

Straight plate girder Zz v/s Span

Figure 6.13: Straight Plate Girder Zz

85

25



Secondary Column 9

Zx (*10-3 m3)

8 7 6 5 4 3 2 1 0 0

5

10

15 Span (m)

20

25

Secondary column Zx v/s Span

Figure 6.14: Secondary Column Zx

Zy (*10-3 m3)

0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0

5

10 Span (m)15

20

25

Secondary column Zy v/s Span

Figure 6.15: Secondary Column Zy 0.07 0.06 Zz (*10-3 m3)

0.05 0.04 0.03 0.02 0.01 0 0

5

10

15 Span (m)

20

Secondary column Zz v/s Span

Figure 6.16: Secondary Column Zz

86

25



Zx (*10-3 m3)

Inclined Roof Member 9 8 7 6 5 4 3 2 1 0 0

5

10 Span (m) 15

20

25

Inclined roof Zx v/s Span

Zy (*10-3 m3)

Figure 6.17: Inclined Roof Member Zx 8 7 6 5 4 3 2 1 0 0

5

10

15 Span (m)

20

25

Inclined roof Zy v/s Span

Figure 6.18: Inclined Roof Member Zy 1.4

Zz (*10-3 m3)

1.2 1 0.8 0.6 0.4 0.2 0 0

5

10 15 Span (m)

20

Inclined roof Zz v/s Span

Figure 6.19: Inclined Roof Member Zz

87

25



Parabolic Member 12 10 Zx (*10-3 m3)

8 6 4 2 0 0

5

10

15 Span (m)

20

25

Parabolic member Zx v/s Span

Zy (*10-3 m3)

Figure 6.20: Parabolic Member Zx 9 8 7 6 5 4 3 2 1 0 0

5

10

15 Span (m)

20

25

Parabolic member Zy v/s Span

Figure 6.21: Parabolic Member Zy 7 6 5 Zz (*10-3 m3)

4 3 2 1 0 0

5

10 Span (m) 15

20

Parabolic member Zz v/s Span

Figure 6.22: Parabolic Member Zz

88

25



Inclined Strut 7 6 Zx (*10-3 m3)

5 4 3 2 1 0 0

5

10

15 Span (m)

20

25

Inclined strut Zx v/s Span

Zy (*10-3 m3)

Figure 6.23: Inclined Strut Zx 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

5

10

15 Span (m)

20

25

Inclined strut Zy v/s Span

Zz (*10-3 m3)

Figure 6.24: Inclined Strut Zy 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0

5

10

15

20

Span (m)

Figure 6.25: Inclined Strut Zz

89

25



6.4 SAMPLE VERIFICATION Primary Column Description

Span(m)

STAAD Pro

Interaction Charts

Zx(10^-3 m3)

12

8.4

8.88

18

10.8

10.54

Primary Beam Description

Span(m)

STAAD Pro

Interaction Charts

Zx(10^-3 m3)

12

4.95

5.16

18

5.24

5.38

Table 6.1:Comparison of Section Modulus and Moment of Inertia

6.5 SIGNIFICANCE OF INTERACTION CHARTS Formulation of interaction charts has proved highly beneficial. Their significance can be described as follows: 1. The required section modulus can be obtained for the given span directly from these charts, thus simplifying the design process. 2. As each and every structural member was optimized using STAAD Pro 2005, the interaction charts give the optimized sections for the given span. 3. It is a usable tool for practicing Structural Engineers.

6.6 LIMITATIONS The interaction charts which are formulated in this project are of restricted scope and possess following limitations: 1. Such Interaction charts are limited to particular geometry only. 2. Limited to variation in span whereas the width is kept constant. 3. No material variation is allowed. 90


Chapter 7 - Conclusions And Recommendations

CHAPTER SEVEN – CONCLUSIONS AND RECOMMENDATIONS 7.1 CONCLUSIONS AND RECOMMENDATIONS The results obtained from experimental testing and software analysis are in close agreement with each other within practical limits. This comparison has given way to validation of analytical model processed through ANSYS 10 software and STAAD Pro 2005 software which has fulfilled the basic purpose of the project. The validated software model is then used to devise interaction charts for the concerned skywalk geometry thereby providing practicing engineers an effective design tool. Optimized design of individual members is possible from the use of interaction charts and also is time saving. Through this project, the authors got the experience of designing a whole skeletal structure ourselves. This project involves use of design and analysis softwares which are highly beneficial in the practical field. Incorporation of finite element analysis helped to study important concepts of the upcoming method of analysis. The actual behavior of the structure under various kinds of loads was understood through experimental testing. It has greatly helped in understanding the true response of the steel structure thereby giving feel of a practical problem. However, there are a lot of practical limitations which arise during modeling any prototype. These limitations give way to variations in some of the results for the experimental testing. The understanding of such discrepancies and their effect on structural behavior gives a thorough knowledge about several structural basics and concepts. The prototype can be used by future batches and project groups to understand its behavior under various loads. Dynamic testing, i.e. shake table test can be arranged to study its behavior under earthquake forces. Health monitoring of the steel prototype is also possible. Ergonomic study of the structure may prove significant in determining the true purpose of the project. The final year project is restricted to superstructure and rigid foundation conditions have been assumed. Substructure behavior and specific details pertaining to geo technical and foundation engineering can also be considered in future studies. 91

References


REFERENCES 1. Design of steel structures- B.C.Punmia (Standard Publishers 2005) 2. Cook R.D, Malkus D.S, and Plesha M. E., Concepts and Applications of Finite Element Analysis, 3rd Ed., JohnWiley and Sons, 1989. 3. Huebner K.H., Thornton E.A., The Finite Element Method for Engineers, Second Edition, John Wiley and Sons,1982. 4. Joints in Steel Construction - Moment Connections, BCSA/SCI Pub. No. 207/95. 5. MYSTRO/LUSAS is produced by FEA Ltd, Kingston-upon-Thames, KT1 1HN. 6. Nethercott D.A., Steel beam to column connections - A review of test data, Construction Industry Research & Information Association, 1985. 7. D. V. Hutton(2004) , Basic concepts of finite element method, Fundamentals of Finite Element Analysis. 1,1-16. 8. K. Chopra(1997), Free Vibration, Dynamics of structures, 2,35-61.

92


Index

INDEX Analytical Method

23

ANSYS - Applying Loads

37

ANSYS - Applying Loads and Obtaining the Solution

36

ANSYS - BEAM4 Element Description

34

ANSYS - Building the Sky Walk Model

33

ANSYS - Creating the Model Geometry

36

ANSYS - Defining Element Real Constants

35

ANSYS - Defining Element Types

34

ANSYS - Defining Material Properties

35

ANSYS - Defining the Analysis Type and Analysis Options

36

ANSYS - Defining Units

33

ANSYS - Initiating the Solution

38

ANSYS - Introduction

33

ANSYS - Material Model Interface

35

ANSYS - Meshing

36

ANSYS - Purpose

33

ANSYS - Reviewing the Results

39

ANSYS - Specifying a Jobname and Analysis Title

33

ANSYS Model

33

Buckling Load Test

53

Conclusions and Recommendations

91

Current Scenario

04

Discrepancies

79

Dual Penetration Test

50

Experimental Model

41

Experimental Model - Introduction

41

Experimental Model - Limitations

44

Experimental Model - Scaling Procedure

42

FEM - History

20

FEM - Introduction

20

i


Index

Finite Element Method

20

Free Vibration Analysis

71

Free Vibration Analysis - Conclusion

76

Free Vibration Analysis - Observations

72

Free Vibration Analysis - Scope

76

Free Vibration Analysis - Test Setup

71

Interaction Charts

81

Interaction Charts - Curved beam

82

Interaction Charts - Inclined roof member

87

Interaction Charts - Inclined strut

89

Interaction Charts - Limitations

90

Interaction Charts - Parabolic member

88

Interaction Charts - Primary beam

83

Interaction Charts - Primary column

84

Interaction Charts - Sample Verification

90

Interaction Charts - Secondary column

86

Interaction Charts - Straight plate girder

85

Interaction Charts- Significance

90

Interpretation

79

Live Load

67

Live Load - Loading Combinations

67

Live Load + Wind Load - Loading Combinations

70

Manual Analysis & Design

23

Member Stiffness Relations

12

Model Testing

55

Need for Skywalk

02

Preliminary Testing

45

Sample Manual Design (Beam)

23

Shear Test

48

Skyway

01

STAAD Pro - Input File (Excerpts)

25

ii


Index

STAAD Pro - Output File (Excerpts)

31

STAAD Pro Model

25

Static Load Testing

55

Static Load Testing - Observations

70

Stiffness Method

12

Stiffness Method - Applications

19

Stiffness Method - Example

14

Stiffness Method - History

12

Strain Gauge - Bonding

62

Strain Gauge - Introduction

55

Strain Gauge - Location

65

Strain Gauge - Single element (G.F. 2.1 approx.)

59

Strength of Weld Test

49

Suitability of Skywalk

03

Tension Test

45

The Direct Stiffness Method

14

Torsion Test

47

Validation

77

Validation - Live Load (400 kg)

77

Validation - Wind Load (10 kg)

78

Wind Load Simulation

68

Wind Load Simulation - Test Assembly

68

iii

Skywalk Report

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