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

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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.

Final Year Project Report Abstract

Final Year Project Report Acknowledgement

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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.

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TABLE OF CONTENTS

ABSTRACT

ACKNOWLEDGEMENT

LIST OF FIGURES

LIST OF TABLES

LIST OF SYMBOLS

CHAPTER ONE – INTRODUCTION

1.1 Background

1.2 Objectives

1.3 Problem Definition

1.4 Scope

CHAPTER TWO – LITERATURE REVIEW

2.1 Background

2.2 Stiffness Method

2.3 Finite Element Method

CHAPTER THREE – MODELING METHODOLOGY

3.1 Analytical Model

3.2 STAAD Pro Model

3.3 ANSYS Model

3.4 Experimental Model

CHAPTER FOUR – TESTING METHODOLOGY

4.1 Preliminary Testing

4.2 Model Testing

4.3 Free Vibration Analysis

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Final Year Project Report Table of Contents

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CHAPTER FIVE – RESULTS AND DISCUSSIONS

5.1 Validation

5.2 Interpretation

5.3 Discrepancies

CHAPTER SIX – PARAMETRIC STUDY

6.1 Objective

6.2 Skywalk Structure – Parametric Study

6.3 Interaction Charts

6.4 Sample Verification

6.5 Significance of Interaction Charts

6.6 Limitations of Interaction Charts

CHAPTER SEVEN– CONCLUSIONS AND

RECOMMENDATIONS

7.1 Conclusions and Recommendations

REFERENCES

INDEX

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Final Year Project Report Table of Contents

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LIST OF FIGURES PAGE NO.

Figure 1.1: Skyway

Figure 1.2: Typical scene in any metropolitan city

Figure 1.3: Plan and Section

Figure 1.4: Perspective

Figure 2.1: Truss

Figure 2.2: Deconstruction

Figure 2.3: Displacement Vector

Figure 2.4: Stiffness Matrix

Figure 2.5: Stiffness Matrix with known Data

Figure 2.6: FEM-Concept

Figure 3.1: Beam 3D Element

Figure 3.2: Material Model Interface Initial Screen

Figure 3.3: Sample output window showing mass and other properties

Figure 3.4: Mode 1 (Deformed + Undeformed shape)

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

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

Figure 3.7: Skywalk Model in Working Stage

Figure 3.8: Completed Skywalk Model

Figure 4.1: Tension Test – Stress vs. Strain

Figure 4.2: Torsion Test – Torque vs. Angle

Figure 4.3: DPT – Purlin and Roof Joint

Figure 4.4: DPT – Primary and Secondary Beam Joint

Figure 4.5: Buckling Load Test Assembly

Figure 4.6: Typical Strain Gauge

Figure 4.7: Wheatstone Bridge Circuit

Figure 4.8: Working of a Strain Gauge

Figure 4.9: Strain Gauge

Figure 4.10: Strain Gauge Package and Strain Gauge Color Coding

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

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Final Year Project Report List of Figures

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Figure 4.12: Explanation of Strain Gauge Test Data

Figure 4.13: Surface Preparation –Dry Abrading

Figure 4.14: Surface Preparation –Wet Abrading

Figure 4.15: Application of Adhesive

Figure 4.16: Curing and Pressing

Figure 4.17: Raising the Gauge Leads

Figure 4.18: Bonding Connecting Terminals

Figure 4.19: Soldering the Gauge Leads

Figure 4.20: Soldering Extension Lead Wires

Figure 4.21: Location of Strain Gauges

Figure 4.22: Strain Reading Equipment

Figure 4.23: Test Setup for Static Load Test

Figure 4.24: Wind Load Simulation

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

Figure 4.26: Test Setup for Free Vibration Test

Figure 4.27: FFT Graph – Iteration 1 Accelerometer 1









Figure 6.1: Parametric Study

Figure 6.2: Curved Beam Zx

Figure 6.3: Curved Beam Zy

Figure 6.4: Curved Beam Zz

Figure 6.5: Primary Beam Zx

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Figure 6.6: Primary Beam Zy

Figure 6.7: Primary Beam Zz

Figure 6.8: Primary Column Zx

Figure 6.9: Primary Column Zy

Figure 6.10: Primary Column Zz

Figure 6.11: Straight Plate Girder Zx

Figure 6.12: Straight Plate Girder Zy

Figure 6.13: Straight Plate Girder Zz

Figure 6.14: Secondary Column Zx

Figure 6.15: Secondary Column Zy

Figure 6.16: Secondary Column Zz

Figure 6.17: Inclined Roof Member Zx

Figure 6.18: Inclined Roof Member Zy

Figure 6.19: Inclined Roof Member Zz

Figure 6.20: Parabolic Member Zx

Figure 6.21: Parabolic Member Zy

Figure 6.22: Parabolic Member Zz

Figure 6.23: Inclined Strut Zx

Figure 6.24: Inclined Strut Zy

Figure 6.25: Inclined Strut Zz

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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

Final Year Project Report List of Table

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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.

Final Year Project Report List of Symbols

Final Year Project Report Chapter 1 - Introduction

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CHAPTER ONE – INTRODUCTION

1.1 BACKGROUND

1.1.1 SKYWAY

In an urban setting, a skyway, catwalk, or skywalk is a type of pedestrian walk-

way 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.


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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


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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.


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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.


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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.


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Present Status:

Sr. No.

Station Scope of WorksImplementing

Agency1 Mumbai CST Construction of Subway (instead of

Skywalk due to surface space constraint) at Chhatrapati Shivaji Terminus Station. (20 meters wide x 500 meter long)

MSRDC

2 Sandhurst Road Skywalk connecting from (South side of) 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)

MSRDC

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

MSRDC

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

MSRDC

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 Skywalk connecting existing Railway’s 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)

MSRDC

Skywalk connecting existing Railway’s middle Foot Over Bridge (of East Side) to Nehru Nagar. (4.88 meters wide x 150 meters long)

6 Vidyavihar Skywalk connecting East & West side of the Station and with existing Railway’s Foot Over Bridge (Under construction).(4.88 meters wide x 150 meters long)

MMRDA

7 Kanjurmarg Skywalk connecting existing Railway’s Foot Over Bridge (at Mumbai end) to the West side of L.B.S. Marg.(4.88 meters wide x 200 meters long)

MMRDA


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8 Bhandup Skywalk connecting existing Railway’s Foot Over Bridge to L.B.S. Marg. (3.66 meters wide x 350 meters long)

MMRDA

9 Mulund Skywalk connecting East & West with existing Railway’s Foot Over Bridge (at Mumbai end). (4.88 meters wide x 100 meters long)

MMRDA

10 Thane Skywalk (towards Kalyan end) 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.

MMRDA

11 Koper Skywalk connecting existing Railway’s 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)

MMRDA

12 Kalyan Skywalk connecting existing Railway’s 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)

MMRDA

13 Reay Road Skywalk across D’Mello Road (at Kurla end) a landing at all Platforms.(3.66 meters wide x 100 meters long)

MSRDC

14 Sewri Skywalk connecting Railway’s Foot Over Bridge to Public Foot Over Bridge (of D’Mello Road). (3.66 meters wide x 100 meters long)

MSRDC

15 Vadala Road 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)

MSRDC

16 Borivali (W) Platform No.8 to R.O.B.- BMC MMRDA17 Borivali Platform No. 7 to PF No. 6 and East side MMRDA18 Virar (West) Platform No.1 from South West Booking

office to M.S.R.T.C. Bus Terminus.MMRDA

19 Virar (East) From existing F.O.B. to L.C. No.40. MMRDA

20 Bandra (East) BA Local station to BDTS station MMRDA

21 Bandra (East) BA Local station to Kalanagar MMRDA

22 Bandra (West) Construction of Sky walk MMRDA

23 Nallasopara Construction of Sky walk MSRDC


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24 Vasai Road Construction of Sky walk MSRDC

25 Ambernath Construction of Sky walk MSRDC

26 Goregaon Construction of Sky walk MSRDC

27 Vileparle Construction of Sky walk MSRDC

28 Kandivali Construction of Sky walk MSRDC

29 Lowerparel-Currey road walkway

Construction of Sky walk MSRDC

30 Masjid station area


31 CST to Churgegate


32 Naigaon Construction of Sky walk MSRDC

33 Grantroad Construction of Sky walk MSRDC

34 Dadar – Ranade Rd.

Construction of Sky walk MMRDA

35 Dadar – Towards Kabutarkhana


36 Dadar - East Construction of Sky walk MMRDA

37 Dadar - East-west connector


38 Chembur Construction of Sky walk MMRDA

39 Ghatkopar Construction of Sky walk MMRDA

40 Andheri (E) Construction of Sky walk MMRDA

41 Andheri (W) Construction of Sky walk MMRDA

42 AndheriTelegali


43 Malad -Laljipada,MLR


44 Dahisar (E) Construction of Sky walk MMRDA

45 Dahisar (W) Construction of Sky walk MMRDA

46 Mira Road Construction of Sky walk MMRDA

47 Bhayander Construction of Sky walk MMRDA

48 Santacruz (E) Construction of Sky walk MMRDA

49 Santacruz (W) Construction of Sky walk MMRDA

50 Ulhasnagar Construction of Sky walk MMRDA

Table 1.1: Proposed skywalks in and around Mumbai


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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.


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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


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Figure 1.4: Perspective

Final Year Project Report Chapter 2 - Literature Review

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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.


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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

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

If qm are member deformations rather than absolute displacements, then Qm are

independent member forces, and in such case (1) can be inverted to yield the so-

called 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:

The member deformations qm 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.

The member forces Qm 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 right-

hand-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

matrices km.

= 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.


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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 member-

end 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

Final Year Project Report

Once the elements are identified, the structure is disconnected at the nodes, the points

which connect the different elements together.

Each element is then analyzed

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

two dimensions, each node has two

displacement. The resulting equation contains a four by four stiffness matrix.

A frame element is able to withstand bending moments in addition t

tension. This results in three degrees of

displacement and in-plane rotation. The stiffness matrix in this case is six by six.


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which connect the different elements together.

Figure 2.2: Deconstruction

Each element is then analyzed individually to develop member stiffness equations. The


on the geometry and properties of the element.

A truss element can only transmit forces in compression or tension. This means that in

two dimensions, each node has two degrees of freedom (DOF): horizontal and vertical


A frame element is able to withstand bending moments in addition to compression and

results in three degrees of freedom: horizontal displacement, vertical

plane rotation. The stiffness matrix in this case is six by six.

Literature Review


individually to develop member stiffness equations. The


on. This means that in

(DOF): horizontal and vertical


o compression and

freedom: horizontal displacement, vertical

plane rotation. The stiffness matrix in this case is six by six.


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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.


17

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.


18

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


19

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.


20

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


21

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


22

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.

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.

1 P(x, y)

Final Year Project Report Chapter 3 - Modeling Methodology

23

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


24

Step 1:

Z required = Moment/ bc

=341.285*106/165

=2769.69*103 Select section ISMB 600 @122.6 Kg/m

Zxx = 3060.4 Zyy = 252.5 h = 600 mm 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


25

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 -


26

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


27

*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

*___________________________________________________________________*


28

LOAD 3 LOADTYPE Dead TITLE DL

*DEAD WEIGHT OF SLAB= 0.1X25=2.5 KN/SQ.M. (Assuming 100mm THK. Slab)

*FLOOR FINISH LOAD = =1.5 KN/SQ.M.

*SERVICE LOAD = =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


29

*** 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


30

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 X-

DIRECTION

3 1.0 7 1.0 5 1.0

LOAD COMB 32 DL+WL ON PARRABOLLIC ROOF+1.2COLLISION LOAD IN X-

DIRECTION

3 1.0 8 1.0 5 1.0

LOAD COMB 36 DL+WL ON SLOPING ROOF+1.2COLLISION LOAD IN Z-

DIRECTION

3 1.0 7 1.0 6 1.0

LOAD COMB 37 DL+WL ON PARRABOLLIC ROOF+1.2COLLISION LOAD IN Z-

DIRECTION

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


31

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 TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/

FX MY MZ LOCATION

============================================================

1 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.038 130.45 C 0.00 -0.01 0.102 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.038 130.45 C 0.00 -0.01 0.003 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.043 190.45 C -0.01 0.01 0.074 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.066 160.03 C 0.00 -0.02 0.005 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.083 160.14 C 0.00 0.03 0.096 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.111 160.10 C 0.00 0.04 0.027 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.1(A) 0.046 140.41 C -0.02 0.00 0.098 PRI SMAT (INDIAN SECTIONS)


32

PASS IS-7.1.1(A) 0.050 140.41 C -0.02 0.00 0.009 PRI SMAT (INDIAN SECTIONS)PASS IS-7.1.2 0.305 170.01 T -0.02 0.01 0.00STAAD SPACE -- PAGE NO. 14

ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED)

MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/

FX MY MZ LOCATION

=============================================================

Member

Maximum Combined

Stress (MPa)Loading Combination

Compressive Tensile Compressive Tensile

Primary Column 19.68 20.23DL + WL on

Sloping Roof

WL on Sloping

Roof

Secondary Column 76.14 75.94WL on Sloping

Roof

DL + WL on

Sloping Roof

Curved Beam Member 8.38 8.17 DL + LL - EQXWL on Sloping

Roof

Load Transfer Member 35.78 18.19 DL + LL + EQZWL on Sloping

Roof

Secondary Beam 10.22 19.7WL on Sloping

Roof

DL + LL -

EQX

Primary Beam 17.06 3.12 DL + LL - EQXWL on Sloping

Roof

Purlin 4.41 31.63 DL + LL + EQZ EQZ

Parabolic Roof Member 11.2 20.42 DL + LL - EQZDL + WL on

Sloping Roof

Inclined Strut 13.05 24.83 DL + LL + EQZWL on Sloping

Roof

Table 3.2: Maximum Stresses in STAAD Pro Analysis


33

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 electro-

magnetic 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.)


34

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


35

3.3.5 Defining Element Real Constants

Element real constants are properties that depend on the element type, such as cross-

sectional 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


36

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.


37

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.


38

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


39

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

follows-

Modal 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.


40

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

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


41

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

MemberMaximum Combined Stress

(MPa)

Loading

Combination

Primary Column -15.2 DL + LL

Secondary Column -69 DL + LL

Curved Beam Member -14 DL + LL

Load Transfer Member -22.5 DL + LL

Secondary Beam 15 DL + LL

Primary Beam 43 DL + LL

Purlin -13 DL + LL

Parabolic Roof Member -12 DL + WL

Inclined Strut 16 DL + WL


42

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.


43

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

Table 3.4: Comparison of Members in Actual Structure and Model

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

MEMBER

DESIGNATIONACTUAL 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 PIPE 0.9 mφ, 12mm Thk. ROD 34mmφ

Inclined struts PIPE 0.15 mφ, 6mm Thk. ROD 10mmφ

MEMBER

DESIGNATION

MODULUS OF

SECTION (ACTUAL

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


44

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.

Final Year Project Report Chapter 4 - Testing Methodology

45

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 Mild steel and medium tensile steel bars.

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

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.


46

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


47

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


48

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.


49

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.


50

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)


51

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.


52

Figure 4.3: DPT – Purlin and Roof Joint

Figure 4.4: DPT – Primary and Secondary Beam Joint


53

4.1.6 Buckling Load Test

Buckling load test is carried out to determine buckling load and failure load of the Y-

shaped 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.


54

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


55

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.


56

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.


57

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:


58

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:


Main Test

MaterialsMetal,Mortar

Operating

Temperature-

Compensation

range+10 to +80°C

Bonding adhesive

Single element (G.F. 2.1 approx.)

0.11mm2PVC Lead wire pre

Total resistance per meter: 0.32Ω

TML PFL-30-11

TypeGaugelength(mm)

Gaugewidth(mm)

PFL-30-11

30 2.3


59

Metal,MortarMaterials

BackingPolyester

-20 to +80°CMaterials

ElementCu-Ni alloy foil

+10 to +80°C Strain limit(20000×10

CN,RP-2Fatigue life at

room temp.

1×10

(±1500×10

Table 4.1: Strain Gauge Specifications

Single element (G.F. 2.1 approx.)

PVC Lead wire pre-attached

Total resistance per meter: 0.32Ω

Figure 4.9: Strain Gauge

Table 4.2: Specifications of PFL-30-11

Gaugewidth(mm)

Backinglength(mm)

Backingwidth(mm)

Resistance(Ω)

Lead wire pre-

attached

40 7 120

Paralleled 1m

Paralleled 3m

Paralleled 5m

3-wire 3m3-wire 5m

Testing Methodology

Polyester

Ni alloy foil

2%

(20000×10-6)

1×106

(±1500×10-6)

Lead wire

attached

Type name

of lead wire

Paralleled

Paralleled

Paralleled

wire 3mwire 5m

-1L-3L-5L

-3LT-5LT


60

Figure 4.10: Strain Gauge Package and Strain Gauge Color Coding


61

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

Figure 4.12: Explanation of Strain Gauge Test Data


62

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.


63

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


64

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


65

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




Figure 4.21: Locations of Strain Gauges



66

Figure 4.21: Locations of Strain Gauges


Testing Methodology


67

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


68

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.


69

Figure 4.24: Wind Load Simulation

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


70

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]

GAUGE

NUMBER

LL=

100

kg

LL= 200

kg +

WL=15kg

LL= 100

kg +

WL=10kg

LL=

200

kg

LL=

300

kg

LL= 300

kg +

WL=15kg

LL=

400

kg

LL= 400

kg +

WL=15kg

WL=

10

kg

WL=

15 kg

[1] Strain -2 46 30 -4 -4 46 -5 48 35 50

[2] Strain -23 -483 -302 -79 -118 -522 -170 -587 -316-448

[3] Strain 32 492 301 94 141 543 203 617 297423

[4] Strain -24 -37 -18 -47 -67 -56 -84 -74 7 10

[5] Strain 42 85 43 87 150 152 191 188 12

[6] Strain 12 20 10 21 32 30 42 40 -1-3

[7] Strain -11 -80 -53 -19 -30 -100 -41 -104 -44 -58

[8] Strain 55 112 52 115 192 192 253 248 -4-5

[9] Strain 52 107 53 104 150 148 201 203 10

[10] Strain -4 3 2 -3 -11 -3 -12 -9 7 10

[11] Strain -52 -106 -50 -110 -177 -178 -232 -229 34

[12] Strain 1 -20 -13 0 0 -20 0 -19 -13-19

[13] Strain 10 4 -2 21 29 11 39 24 -13 -17

[14] Strain 6 -28 0 -21 -19 -28 -14 -22 -4 -35

[15] Strain -23 -42 -19 -51 -77 -71 -107 -96 713

Table 4.3: Micro-Strains for Ten Loading Combinations


71

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:


72

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:

Iteration no.Angle of inclination of

the stringForce in N

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


73

Iteration 1





74

Iteration 2





75

Iteration 3





76

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 pre-

requisite 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.

Final Year Project Report Chapter 5 - Results And Discussions

77

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

Load Transfer Member 38.2 40 32.41

Secondary Beam 8.4 15 6.9

Parabolic Roof Member -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


78

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

Load Transfer Member 0.2 2.0 1.82

Secondary Beam -0.2 -0.5 -1.02

Parabolic Roof Member -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


79

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.

Final Year Project Report Chapter 6 - Parametric Study

80

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

Figure 6.1: Parametric study

Varies


81

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


82

Curved Beam

Figure 6.2: Curved Beam Zx

Figure 6.3: Curved Beam Zy

Figure 6.4: Curved Beam Zz

0

5

10

15

20

25

0 5 10 15 20 25

Zx (*

10 m

3)

Span (m)Curved beam Zx v/s Span

02468

10121416

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Curved beam Zy v/s Span

0

2

4

6

8

10

12

0 5 10 15 20 25

Zz (

*10-3

m3)

Span (m)Curved beam Zz v/s Span


83

Primary Beam

Figure 6.5: Primary Beam Zx

Figure 6.6: Primary Beam Zy

Figure 6.7: Primary Beam Zz

0.00490.005

0.00510.00520.00530.00540.00550.00560.0057

0 5 10 15 20 25

Zx (*

10-3

m3)

Span (m)Primary beam Zx v/s Span

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Zy(*

10-3

m3)

Span (m)Primary beam Zy v/s Span

00.020.040.060.08

0.10.120.140.160.18

0.2

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)Primary beam Zz v/s Span


84

Primary Column

Figure 6.8: Primary Column Zx

Figure 6.9: Primary Column Zy

Figure 6.10: Primary Column Zz

0

2

4

6

8

10

12

0 5 10 15 20

Zx (*

10-3

m3)

Span (m)Primary column Zx v/s Span…

0

5

10

15

20

25

30

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Primary column Zy v/s Span

0123456789

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)Primary column Zz v/s Span


85

Straight Plate Girder

Figure 6.11: Straight Plate Girder Zx

Figure 6.12: Straight Plate Girder Zy

Figure 6.13: Straight Plate Girder Zz

00.0010.0020.0030.0040.0050.0060.007

0 5 10 15 20 25

Zx(*

10-3

m3)

Span (m)Straight plate girder Zx v/s Span

0.46

0.47

0.48

0.49

0.5

0.51

0.52

0.53

0 5 10 15 20 25

Zy(*

10-3

m3)

Span (m)Straight plate girder Zy v/s Span

01234567

0 5 10 15 20 25

Zz(*

10-3

m3)

Span (m)Straight plate girder Zz v/s Span


86

Secondary Column

Figure 6.14: Secondary Column Zx

Figure 6.15: Secondary Column Zy

Figure 6.16: Secondary Column Zz

0123456789

0 5 10 15 20 25

Zx (*

10-3

m3)

Span (m)Secondary column Zx v/s Span

00.005

0.010.015

0.020.025

0.030.035

0.040.045

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Secondary column Zy v/s Span

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)Secondary column Zz v/s Span


87

Inclined Roof Member

Figure 6.17: Inclined Roof Member Zx

Figure 6.18: Inclined Roof Member Zy

Figure 6.19: Inclined Roof Member Zz

0123456789

0 5 10 15 20 25

Zx (*

10-3

m3)

Span (m)Inclined roof Zx v/s Span

012345678

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Inclined roof Zy v/s Span

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)Inclined roof Zz v/s Span


88

Parabolic Member

Figure 6.20: Parabolic Member Zx

Figure 6.21: Parabolic Member Zy

Figure 6.22: Parabolic Member Zz

0

2

4

6

8

10

12

0 5 10 15 20 25

Zx (*

10-3

m3)

Span (m)Parabolic member Zx v/s Span

0123456789

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Parabolic member Zy v/s Span

0

1

2

3

4

5

6

7

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)Parabolic member Zz v/s Span


89

Inclined Strut

Figure 6.23: Inclined Strut Zx

Figure 6.24: Inclined Strut Zy

Figure 6.25: Inclined Strut Zz

0

1

2

3

4

5

6

7

0 5 10 15 20 25

Zx (*

10-3

m3)

Span (m)Inclined strut Zx v/s Span

00.5

11.5

22.5

33.5

44.5

5

0 5 10 15 20 25

Zy (*

10-3

m3)

Span (m)Inclined strut Zy v/s Span

-0.20

0.20.40.60.8

11.21.4

0 5 10 15 20 25

Zz (*

10-3

m3)

Span (m)


90

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.

Final Year Project Report Chapter 7 - Conclusions And Recommendations

91

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.

Final Year Project Report References

92

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.

Final Year Project Report Index

i

INDEX

Analytical Method

ANSYS - Applying Loads

ANSYS - Applying Loads and Obtaining the Solution

ANSYS - BEAM4 Element Description

ANSYS - Building the Sky Walk Model

ANSYS - Creating the Model Geometry

ANSYS - Defining Element Real Constants

ANSYS - Defining Element Types

ANSYS - Defining Material Properties

ANSYS - Defining the Analysis Type and Analysis Options

ANSYS - Defining Units

ANSYS - Initiating the Solution

ANSYS - Introduction

ANSYS - Material Model Interface

ANSYS - Meshing

ANSYS - Purpose

ANSYS - Reviewing the Results

ANSYS - Specifying a Jobname and Analysis Title

ANSYS Model

Buckling Load Test

Conclusions and Recommendations

Current Scenario

Discrepancies

Dual Penetration Test

Experimental Model

Experimental Model - Introduction

Experimental Model - Limitations

Experimental Model - Scaling Procedure

FEM - History

FEM - Introduction

23

37

36

34

33

36

35

34

35

36

33

38

33

35

36

33

39

33

33

53

91

04

79

50

41

41

44

42

20

20


ii

Finite Element Method

Free Vibration Analysis

Free Vibration Analysis - Conclusion

Free Vibration Analysis - Observations

Free Vibration Analysis - Scope

Free Vibration Analysis - Test Setup

Interaction Charts

Interaction Charts - Curved beam

Interaction Charts - Inclined roof member

Interaction Charts - Inclined strut

Interaction Charts - Limitations

Interaction Charts - Parabolic member

Interaction Charts - Primary beam

Interaction Charts - Primary column

Interaction Charts - Sample Verification

Interaction Charts - Secondary column

Interaction Charts - Straight plate girder

Interaction Charts- Significance

Interpretation

Live Load

Live Load - Loading Combinations

Live Load + Wind Load - Loading Combinations

Manual Analysis & Design

Member Stiffness Relations

Model Testing

Need for Skywalk

Preliminary Testing

Sample Manual Design (Beam)

Shear Test

Skyway

STAAD Pro - Input File (Excerpts)

20

71

76

72

76

71

81

82

87

89

90

88

83

84

90

86

85

90

79

67

67

70

23

12

55

02

45

23

48

01

25


iii

STAAD Pro - Output File (Excerpts)

STAAD Pro Model

Static Load Testing

Static Load Testing - Observations

Stiffness Method

Stiffness Method - Applications

Stiffness Method - Example

Stiffness Method - History

Strain Gauge - Bonding

Strain Gauge - Introduction

Strain Gauge - Location

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

Strength of Weld Test

Suitability of Skywalk

Tension Test

The Direct Stiffness Method

Torsion Test

Validation

Validation - Live Load (400 kg)

Validation - Wind Load (10 kg)

Wind Load Simulation

Wind Load Simulation - Test Assembly

31

25

55

70

12

19

14

12

62

55

65

59

49

03

45

14

47

77

77

78

68

68

Documents

Skywalk Report