SNS COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING

CE8602 STRUCTURAL ANALYSIS - II

N.Shanmugasundaram

Assistant Professor

Department of Civil Engineering

SNS College of Engineering

Coimbatore27 January 2020 CE8602-SA II/unit 3 by,Shanmugasundaram.N 1/41

SNS COLLEGE OF ENGINEERING

OBJECTIVES :

• To learn the method of drawing influence lines and its uses in various applications like beams and plane trusses.

• To analyse the arches, suspension bridges and space trusses.

• Also to learn Plastic analysis of beams and rigid frames.

OUTCOMES:

• Students will be able to draw influence lines for statically determinate structures and calculate critical stress resultants.

• Understand Muller Breslau principle and draw the influence lines for statically indeterminate beams.

• Analyse of three hinged, two hinged and fixed arches.

• Analyse the suspension bridges with stiffening girders

• Understand the concept of Plastic analysis and the method of analyzing beams and rigid frames.

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SNS COLLEGE OF ENGINEERING

SYLLABUS

UNITI-INFLUENCE LINES FOR DETERMINATE BEAMS 9

• Influence lines for reactions in statically determinate beams – Influence lines for shear force and

bending moment – Calculation of critical stress resultants due to concentrated and distributed moving

loads – absolute maximum bending moment - influence lines for member forces in pin jointed plane

frames.

UNITII-INFLUENCE LINES FOR INDETERMINATE BEAMS 9

• Muller Breslau’s principle– Influence line for Shearing force, Bending Moment and support reaction

components of propped cantilever, continuous beams (Redundancy restricted to one), and fixed beams.

UNIT III-ARCHES 9

• Arches - Types of arches – Analysis of three hinged, two hinged and fixed arches - Parabolic and

circular arches – Settlement and temperature effects.

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SNS COLLEGE OF ENGINEERING

UNIT IV-CABLES AND SUSPENSION BRIDGES 9

• Equilibrium of cable – length of cable - anchorage of suspension cables – stiffening girders - cables

with three hinged stiffening girders – Influence lines for three hinged stiffening girders.

UNIT V PLASTIC ANALYSIS 9

• Plastic theory - Statically indeterminate structures – Plastic moment of resistance – Plastic modulus –

Shape factor – Load factor – Plastic hinge and mechanism – collapse load - Static and kinematic

methods – Upper and lower bound theorems - Plastic analysis of indeterminate beams and frames.

TEXTBOOKS:

• Bhavikatti,S.S, Structural Analysis,Vol.1 & 2, Vikas Publishing House Pvt.Ltd., NewDelhi-4, 2014.

• Punmia.B.C, Ashok Kumar Jain and Arun Kumar Jain, Theory of structures, Laxmi,

Publications,2004.

• Vazrani.V.N And Ratwani,M.M, Analysis of Structures, Vol.II, Khanna Publishers,2015.

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References

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• Negi.L.S and Jangid R.S., Structural Analysis, Tata McGraw-Hill Publishers, 2004.

• Gambhir.M.L., Fundamentals of Structural Mechanics and Analysis, PHIL earning Pvt.Ltd.,2011.

• Prakash Rao D.S., Structural Analysis, Universities Press,1996.

• Alan Williams “Structural Analysis in theory and practice” Butterworth-Heinemann is an imprintof Elsevier, Burlington, MA 01803, USA

Kenneth M. Leet and Chia-Ming Uang “Fundamentals of Structural Analysis” Tata McGraw HillCompanies Private Limited.

• Reddy C S , “Basic Structural Analysis” , Mc Graw Hill Education (India) Pvt Ltd.

• Jindal R L “Indeterminate Structures”, S. Chand & Company, New Delhi

• Devdas Menon, “Structural Analysis”, Narosa Book Distributers PvtLtd, 2010.

• Vazirani V.N. & Ratwani M.M. “Analysis of Structures”, Khanna Publishers, Delhi, India.

• Punmia B.C. "Theory of Structures" (SMTS) Vol 1&II, Laxmi Publishing Pvt Ltd, New Delhi 2004.

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CONTENTS

• Overview

• Introduction about Rolling loads and ILD

• Positioning of loads for different cases

• Problems for practice

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INTRODUCTION

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Engineering Mechanics

Mechanics of Deformable

Bodies

Mechanics of Solids

Mechanics of Fluids

Mechanics of Rigid Bodies

Statics Dynamics

Studies of internal effects and Deformations that are caused by

applied loads

Studies of external effects on Rigid Bodies

1. Ideal fluid2. Viscous fluid3. Incompressible Fluid

Mechanics of Deformable

Bodies

Studies of internal effects and Deformations that are caused by

applied loads

Mechanics of Solids

Mechanics of

Materials

Strength of Materials

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Structural Analysis

Application

Theory of Elasticity and

Plasticity8/41

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Structure

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Structure

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• The arrangements of and relation between theparts or elements of something complex

• Some of the most common structures we seearound us are• buildings & bridges

• External forces: Loads acting on your structure.

• Internal forces: Forces that develop within every structure that keepthe different parts of the structure together

• Almost anything has an internal parts or elements that can be treatedas a "structure".

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Structure

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Structure

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Infrastructure DamsCommercial Buildings

Building on land to build the landWonders

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Introduction

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Introduction

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Static Loads Rolling Loads

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Examples of rolling loads

• Axle loads of moving trucks or vehicles

• Wheel loads of a railway train

• Wheel loads of a gantry assembly

• Walking a man

• Moving of a two wheeler

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Definition

• An influence line for a member is a graph representingthe variation in support reaction, shear, moment in themember due to any type of loads which are moving onthe structure.

• Note:

The variation in support reaction, variation in moment and the variation

in shear

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Applications of influence lines

Determination of maximum stresses in any structuresubjected to the action of live loads

• A live load moving across a bridge

• Movable loads in an office/industrial building

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Aerodynamic loads on the wings of an aeroplane Hydrostatic support caused by thedisplacement of waves on the hull of the ship

Applications of influence lines

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Properties of influence lines

Influence lines can be used for two very importantpurposes:

• To determine what position of live loads will lead to amaximum value of the particular function for which aninfluence line has been constructed.

• To compute the value of that function with the loads soplaced or, in fact, for any loading condition.

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Properties of influence lines

Influence lines can be used for two very importantpurposes:

• To determine what position of live loads will lead to amaximum value of the particular function for which aninfluence line has been constructed.

• To compute the value of that function with the loadsplaced or, in fact, for any loading condition.

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Different types of rolling loads

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Types of Rolling Loads

• Single point rolling loads

• Two point rolling loads at a fixed distance apart.

• Uniformly distributed rolling loads shorter than span

• Uniformly distributed rolling loads longer than span.

• Series of concentrated rolling loads.

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Sign Convention

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Single Point Load

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Support Reaction

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UDL Shorter than the span

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Multiple point loads

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(a) Stringers and cross beams

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(b) Influence lines for a Warren truss

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(c) Influence lines for a Pratt truss

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(d) Influence lines for a bowstring truss

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Three-hinged arch

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