VERTICAL STRESS INCREASES IN SOIL TYPES OF LOADING. Point Loads (P) Line Loads (q/unit length) Examples: -Posts

Size: px
Start display at page:

Download "VERTICAL STRESS INCREASES IN SOIL TYPES OF LOADING. Point Loads (P) Line Loads (q/unit length) Examples: -Posts"

Transcription

1 VERTICAL STRESS INCREASES IN SOIL Point Loads (P) TYPES OF LOADING Line Loads (q/unit length) Revised 0/014 Figure Das FGE (005). Examples: -Posts Figure 6.1. Das FGE (005). Examples: - Railroad track Slide 1 of 4

2 VERTICAL STRESS INCREASES IN SOIL Strip Loads (q) TYPES OF LOADING Area Loads (q) Examples: - Exterior Wall Foundations Examples: - Column Footings Revised 0/014 Slide of 4

3 VERTICAL STRESS INCREASES IN SOIL ANALYSIS METHODS: BOUSSINESQ (1993) Based on homogeneous, weightless, elastic, isotropic infinitely large half-space free of initial stress and deformation. The modulus of elasticity is assumed constant and the principle of linear superposition is assumed valid (EM , 1990). Not accurate for layered soil stratigraphy with substantial thickness (NAVFAC DM7.01, 1986). Rigid Surface Layer Over Weaker Underlying Layer: If the surface layer is the more rigid, it acts as a distributing mat and the vertical stresses in the underlying soil layer are less than Boussinesq values. Weaker Surface Layer Over Stronger Underlying Layers: If the surface layer is less rigid than the underlying layer, then vertical stresses in both layers exceed the Boussinesq values. Revised 0/014 Slide 3 of 4

4 Revised 0/ SOIL MECHANICS VERTICAL STRESS INCREASES IN SOIL ANALYSIS METHODS: WESTERGAARD Based on the assumption that the soil on which load is applied is reinforced by closely spaced horizontal layers which prevent horizontal displacement. The effect of the Westergaard assumption is to reduce the stresses substantially below those obtained by the Boussinesq equations. VERTICAL STRESS INCREASES IN SOIL ANALYSIS METHODS: V:1H METHOD An approximate stress distribution assumes that the total applied load on the surface of the soil is distributed over an area of the same shape as the loaded area on the surface, but with dimensions that increase by an amount equal to the depth below the surface. Vertical stresses calculated V:1H method agree reasonably well with the Boussinesq method for depths between B and 4B below the foundation. Slide 4 of 4

5 VERTICAL STRESS INCREASE ( Z ) IN SOIL POINT LOADING (BOUSSINESQ 1883) z 3 3P z L 5 3P ( r z 3 z ) 5/ z P z 3 r / z 1 1 5/ P z I 1 Where: z = Change in Vertical Stress P = Point Load Stresses in an Elastic Medium Caused by Point Loading Figure Das FGE (005). *Based on homogeneous, elastic, isotropic infinitely large half-space Revised 0/014 I r / z 1 5/ Slide 5 of 4

6 VERTICAL STRESS INCREASE ( Z ) IN SOIL POINT LOADING (BOUSSINESQ 1883) Table 6.1 Variation of I 1 (Das, FGE 006). Revised 0/014 Slide 6 of 4

7 VERTICAL STRESS INCREASE ( Z ) IN SOIL LINE LOADING (BOUSSINESQ 1883) ( x qz 3 z ) Revised 0/014 Line Load over the Surface of a Semi-infinite Soil Mass Figure 6.1. Das FGE (005). *Based on flexible line load of infinite length on a homogeneous, elastic, isotropic semi-infinite half-space Dimensionless Form ( q / z) or x z 1 Where: = Change in Vertical Stress q = Load per Unit Length z = Depth x = Distance from Line Load Slide 7 of 4

8 VERTICAL STRESS INCREASE ( Z ) IN SOIL LINE LOADING (BOUSSINESQ 1883) Table 6.3 Variation of /(q/z) with x/z (Das, FGE 006). Revised 0/014 Slide 8 of 4

9 VERTICAL STRESS INCREASE ( Z ) IN SOIL STRIP LOADING (BOUSSINESQ 1883) q sin cos( ) Where: = Change in Vertical Stress q = Load per Unit Area z = Depth x = Distance from Line Load Flexible Strip Load over the Surface of a Semi-infinite Soil Mass Revised 0/014 Figure Das FGE (005). Angles measured in counterclockwise direction are taken as positive Slide 9 of 4

10 VERTICAL STRESS INCREASE ( Z ) IN SOIL STRIP LOADING (BOUSSINESQ 1883) Table 6.4 Variation of /q with z/b and x/b (Das, FGE 006). Revised 0/014 Slide 10 of 4

11 VERTICAL STRESS INCREASE ( Z ) IN SOIL CIRCULAR LOADING (BOUSSINESQ 1883) q1 1 (R / z) 1 3/ Where: = Change in Vertical Stress q = Load per Unit Area z = Depth R = Radius Revised 0/014 Vertical Stress Below Center of Uniformly Loaded Flexible Circular Area Figure Das FGE (005). Slide 11 of 4

12 VERTICAL STRESS INCREASE ( Z ) IN SOIL CIRCULAR LOADING (BOUSSINESQ 1883) Table 6.5 Variation of /q with z/r (Das, FGE 006). Revised 0/014 Slide 1 of 4

13 Slide 13 of 4 Revised 0/ SOIL MECHANICS 1 1 tan n m n m n m mn n m n m n m n m n m mn I B y L x qi z y x dxdy qz d 0 0 5/ 3 ) ( ) ( 3 Vertical Stress Below Corner of Uniformly Loaded Flexible Rectangular Area Figure Das FGE (005). Where: = Change in Vertical Stress q = Load per Unit Area z = Depth z L n z B m ; VERTICAL STRESS INCREASE ( Z ) IN SOIL RECTANGULAR LOADING (BOUSSINESQ 1883)

14 VERTICAL STRESS INCREASE ( Z ) IN SOIL RECTANGULAR LOADING (BOUSSINESQ 1883) Variation of I with m and n. Figure Das FGE (005) SOIL MECHANICS Revised 0/014 Slide 14 of 4

15 VERTICAL STRESS INCREASE ( Z ) IN SOIL RECTANGULAR LOADING (WESTERGAARD) SOIL MECHANICS Figure 1. NAVFAC DM7.01. Revised 0/014 Slide 15 of 4

16 VERTICAL STRESS INCREASE ( Z ) IN SOIL RECTANGULAR LOADED AREA Within a Rectangular Loaded Area: qi (1) I () I (3) I (4) Under Center of Footing: c qi c I c f (m 1, n 1 ) Figure Das FGE (005). m 1 L B ;n 1 z B Revised 0/014 Slide 16 of 4

17 VERTICAL STRESS INCREASE ( Z ) IN SOIL CENTER OF RECTANGULAR LOADED AREA Table 6.6 Variation of I c with m 1 and n 1 (Das, FGE 006). Revised 0/014 Slide 17 of 4

18 BOUSSINESQ SOLUTIONS SUMMARY (EM TABLE C-1) Revised 0/014 Slide 18 of 4

19 BOUSSINESQ SOLUTIONS SUMMARY (EM TABLE C-1) Revised 0/014 Slide 19 of 4

20 BOUSSINESQ SOLUTIONS SUMMARY (EM TABLE C-1) Revised 0/014 Slide 0 of 4

21 BOUSSINESQ GRAPHICAL SOLUTION (EM FIGURE 1-) STRIP FOOTING SQUARE FOOTING Revised 0/014 Slide 1 of 4

22 WESTERGAARD GRAPHICAL SOLUTION (NAVFAC DM7.01 FIGURE 11) Revised 0/014 Slide of 4

23 WESTERGAARD GRAPHICAL SOLUTION (NAVFAC DM7.01 FIGURE 11) Revised 0/014 Slide 3 of 4

24 VERTICAL STRESS INCREASES IN SOIL ANALYSIS METHODS: V:1H METHOD z Q ( B z)( L z) Where: z = Change in Total Vertical Stress Q = Applied Foundation Load B = Foundation Width L = Foundation Length Figure C-1. USACE EM Revised 0/014 Slide 4 of 4

STRESSES IN SOIL MASS

STRESSES IN SOIL MASS CHAPTER 4 Prepared by: Dr. Farouk Majeed Muhauwiss Civil Engineering Department College of Engineering Tikrit University STRESSES IN SOIL MASS 4.1 DEFIFINTIONS VERTTICAL STRESS Occurs due to internal or

More information

Lecture 2: Stresses in Pavements

Lecture 2: Stresses in Pavements Lecture 2: Stresses in Pavements Stresses in Layered Systems At any point, 9 stresses exist. They are 3 normal stresses (s z, s r, s t ) and 6 shearing stresses ( t rz = t zr, t rt = t tr, and t tz = t

More information

The theories to estimate lateral earth pressure due to a strip surcharge loading will

The theories to estimate lateral earth pressure due to a strip surcharge loading will Chapter LITERATURE REVIEW The theories to estimate lateral earth pressure due to a strip surcharge loading will be introduced in this chapter. Commonly geotechnical engineers apply the equations suggested

More information

Figure 2-1: Stresses under axisymmetric circular loading

Figure 2-1: Stresses under axisymmetric circular loading . Stresses in Pavements.1. Stresses in Fleible Pavements.1.1. Stresses in Homogeneous Mass Boussinesq formulated models for the stresses inside an elastic half-space due to a concentrated load applied

More information

Subsurface Stresses (Stresses in soils)

Subsurface Stresses (Stresses in soils) Subsurface Stresses (Stresses in soils) ENB371: Geotechnical Engineering Chaminda Gallage Contents Introduction: Subsurface stresses caused by surface loading Subsurface stresses caused by the soil mass

More information

Chapter Two: Mechanical Properties of materials

Chapter Two: Mechanical Properties of materials Chapter Two: Mechanical Properties of materials Time : 16 Hours An important consideration in the choice of a material is the way it behave when subjected to force. The mechanical properties of a material

More information

The following is an exhaustive list of assumptions made by Boussinesq in the derivation of his theory:

The following is an exhaustive list of assumptions made by Boussinesq in the derivation of his theory: 8 Vertical Stresses below Applied Loads 8.1 ntroduction Estimation of vertical stresses at any point in a soil-mass due to external vertical loadings are of great significance in the prediction of settlements

More information

Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay

Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Module - 5 Machine Foundations Lecture - 31 EHS Theory, Vibrational Control Let us start our

More information

BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION

BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION Ahmed Elgamal and Jinchi Lu October 07 Introduction In this study: I) The response

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

INFLUENCE VALUES FOR ESTIMATING STRESSES IN ELASTIC FOUNDATIONS RALPH E. FADUM Professor of Soil Mechanics Purdue University

INFLUENCE VALUES FOR ESTIMATING STRESSES IN ELASTIC FOUNDATIONS RALPH E. FADUM Professor of Soil Mechanics Purdue University 77 INFLUENCE VALUES FOR ESTIMATING STRESSES IN ELASTIC FOUNDATIONS RALPH E. FADUM Professor of Soil Mechanics Purdue University SUMMARY. This paper deals with the problem of estimating the vertical normal

More information

Examples to verify and illustrate ELPLA

Examples to verify and illustrate ELPLA Determining contact pressures, settlements, moments and shear forces of slab foundations by the method of finite elements Version 2010 Program authors: M. El Gendy A. El Gendy GEOTEC: GEOTEC Software Inc.

More information

Stresses and Strains in flexible Pavements

Stresses and Strains in flexible Pavements Stresses and Strains in flexible Pavements Multi Layered Elastic System Assumptions in Multi Layered Elastic Systems The material properties of each layer are homogeneous property at point A i is the same

More information

Soil that t support foundation subjected to net stresses increases. Net stresses increases depend on

Soil that t support foundation subjected to net stresses increases. Net stresses increases depend on Stresses in a Soil Mass updated pril 15, 008 Haro Dwito rmono, M.Eng, Ph.D Soil that t support foundation subjected to net stresses increases Net stresses increases depend on oad per unit area to which

More information

Fig. 1. Circular fiber and interphase between the fiber and the matrix.

Fig. 1. Circular fiber and interphase between the fiber and the matrix. Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In

More information

Module 9 : Foundation on rocks

Module 9 : Foundation on rocks LECTURE 32 9.3 BEARING CAPCITY contd... 9.3.2 Safe bearing pressure There are different methods are available to determine the safe bearing pressure on rocks. However, the applicability of different methods

More information

COMPRESSION AND BENDING STIFFNESS OF FIBER-REINFORCED ELASTOMERIC BEARINGS. Abstract. Introduction

COMPRESSION AND BENDING STIFFNESS OF FIBER-REINFORCED ELASTOMERIC BEARINGS. Abstract. Introduction COMPRESSION AND BENDING STIFFNESS OF FIBER-REINFORCED ELASTOMERIC BEARINGS Hsiang-Chuan Tsai, National Taiwan University of Science and Technology, Taipei, Taiwan James M. Kelly, University of California,

More information

Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 28 Stresses in Beams- III

Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 28 Stresses in Beams- III Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 28 Stresses in Beams- III Welcome to the 3 rd lesson of the 6 th module which is on Stresses in Beams part

More information

Chapter (5) Allowable Bearing Capacity and Settlement

Chapter (5) Allowable Bearing Capacity and Settlement Chapter (5) Allowable Bearing Capacity and Settlement Introduction As we discussed previously in Chapter 3, foundations should be designed for both shear failure and allowable settlement. So the allowable

More information

Foundation Engineering

Foundation Engineering Foundation Engineering Draft Version April 01 S. van Baars PREFACE This book is just a help for the students fort the old course Grundbau. Luxembourg, April 01 Stefan Van Baars CONTENT I SHALLOW FOUNDATIONS...

More information

(Refer Slide Time 02:20)

(Refer Slide Time 02:20) Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 33 Stress Distribution in Soils Lecture No. 6 Students once again we meet. Today s

More information

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress

More information

CHAPTER 4: BENDING OF BEAMS

CHAPTER 4: BENDING OF BEAMS (74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are

More information

SOIL MECHANICS Assignment #5: Stresses in a Soil Mass.

SOIL MECHANICS Assignment #5: Stresses in a Soil Mass. Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Edward L. Hajduk, D.Eng, PE Lecturer PA105D Tel: (978) 934 2621 Fax: (978) 934 3052 e mail: Edward_Hajduk@uml.edu

More information

Chapter 3. Load and Stress Analysis. Lecture Slides

Chapter 3. Load and Stress Analysis. Lecture Slides Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.

More information

Chapter (4) Ultimate Bearing Capacity of Shallow Foundations (Special Cases)

Chapter (4) Ultimate Bearing Capacity of Shallow Foundations (Special Cases) Chapter (4) Ultimate earing Capacity of Shallow Foundations (Special Cases) Ultimate.C. of Shallow Foundations (Special Cases) Introduction The ultimate bearing capacity theories discussed in Chapter 3

More information

CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES

CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric

More information

Objectives. In this section you will learn the following. Development of Bearing Capacity Theory. Terzaghi's Bearing Capacity Theory

Objectives. In this section you will learn the following. Development of Bearing Capacity Theory. Terzaghi's Bearing Capacity Theory Objectives In this section you will learn the following Development of Bearing Capacity Theory Terzaghi's Bearing Capacity Theory Assumptions in Terzaghi s Bearing Capacity Theory. Meyerhof's Bearing Capacity

More information

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

More information

Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT

Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT Topics Module 4 (Lecture 16) SHALLOW FOUNDATIONS: ALLOWABLE BEARING CAPACITY AND SETTLEMENT 1.1 STRIP FOUNDATION ON GRANULAR SOIL REINFORCED BY METALLIC STRIPS Mode of Failure Location of Failure Surface

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

Mechanical Design in Optical Engineering

Mechanical Design in Optical Engineering Torsion Torsion: Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member s longitudinal axis. In other words, the member is loaded

More information

[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21

[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21 [7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is

More information

STRESSES AROUND UNDERGROUND OPENINGS CONTENTS

STRESSES AROUND UNDERGROUND OPENINGS CONTENTS STRESSES AROUND UNDERGROUND OPENINGS CONTENTS 6.1 Introduction 6. Stresses Around Underground Opening 6.3 Circular Hole in an Elasto-Plastic Infinite Medium Under Hdrostatic Loading 6.4 Plastic Behaviour

More information

LATERAL EARTH PRESSURE AND RETAINING STRUCTURES

LATERAL EARTH PRESSURE AND RETAINING STRUCTURES Topic Outline LATERAL EARTH PRESSURE AND RETAINING STRUCTURES Types of retaining structures Lateral earth pressure Earth pressure at rest Rankine s Theory Coulomb s Theory Cullman s graphic solution Braced

More information

file:///d /suhasini/suha/office/html2pdf/ _editable/slides/module%202/lecture%206/6.1/1.html[3/9/2012 4:09:25 PM]

file:///d /suhasini/suha/office/html2pdf/ _editable/slides/module%202/lecture%206/6.1/1.html[3/9/2012 4:09:25 PM] Objectives_template Objectives In this section you will learn the following Introduction Different Theories of Earth Pressure Lateral Earth Pressure For At Rest Condition Movement of the Wall Different

More information

GG303 Lab 12 11/7/18 1

GG303 Lab 12 11/7/18 1 GG303 Lab 12 11/7/18 1 DEFORMATION AROUND A HOLE This lab has two main objectives. The first is to develop insight into the displacement, stress, and strain fields around a hole in a sheet under an approximately

More information

Members Subjected to Torsional Loads

Members Subjected to Torsional Loads Members Subjected to Torsional Loads Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F.d applied in a plane perpendicular

More information

Objectives: After completion of this module, you should be able to:

Objectives: After completion of this module, you should be able to: Chapter 12 Objectives: After completion of this module, you should be able to: Demonstrate your understanding of elasticity, elastic limit, stress, strain, and ultimate strength. Write and apply formulas

More information

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure.

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. UNIT V 1. Define Active Earth pressure. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. 2. Define Passive Earth pressure. The passive earth pressure occurs

More information

INTI COLLEGE MALAYSIA

INTI COLLEGE MALAYSIA EGC373 (F) / Page 1 of 5 INTI COLLEGE MALAYSIA UK DEGREE TRANSFER PROGRAMME INTI ADELAIDE TRANSFER PROGRAMME EGC 373: FOUNDATION ENGINEERING FINAL EXAMINATION : AUGUST 00 SESSION This paper consists of

More information

Hyperbolic Soil Bearing Capacity

Hyperbolic Soil Bearing Capacity 1 Introduction Hyperbolic Soil Bearing Capacity This example involves analyzing the bearing capacity of a round footing. The example is useful for illustrating several SIGMA/W features and procedures,

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion Introduction Stress and strain in components subjected to torque T Circular Cross-section shape Material Shaft design Non-circular

More information

Geotechnical Properties of Soil

Geotechnical Properties of Soil Geotechnical Properties of Soil 1 Soil Texture Particle size, shape and size distribution Coarse-textured (Gravel, Sand) Fine-textured (Silt, Clay) Visibility by the naked eye (0.05 mm is the approximate

More information

Analytical Strip Method for Thin Isotropic Cylindrical Shells

Analytical Strip Method for Thin Isotropic Cylindrical Shells IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 4 Ver. III (Jul. Aug. 2017), PP 24-38 www.iosrjournals.org Analytical Strip Method for

More information

FLEXIBILITY METHOD FOR INDETERMINATE FRAMES

FLEXIBILITY METHOD FOR INDETERMINATE FRAMES UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These

More information

Symmetric Bending of Beams

Symmetric Bending of Beams Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications

More information

HKIE-GD Workshop on Foundation Engineering 7 May Shallow Foundations. Dr Limin Zhang Hong Kong University of Science and Technology

HKIE-GD Workshop on Foundation Engineering 7 May Shallow Foundations. Dr Limin Zhang Hong Kong University of Science and Technology HKIE-GD Workshop on Foundation Engineering 7 May 2011 Shallow Foundations Dr Limin Zhang Hong Kong University of Science and Technology 1 Outline Summary of design requirements Load eccentricity Bearing

More information

Chapter 4-b Axially Loaded Members

Chapter 4-b Axially Loaded Members CIVL 222 STRENGTH OF MATERIALS Chapter 4-b Axially Loaded Members AXIAL LOADED MEMBERS Today s Objectives: Students will be able to: a) Determine the elastic deformation of axially loaded member b) Apply

More information

Analysis of forming- Slipline Field Method

Analysis of forming- Slipline Field Method Analysis of forming- Slipline Field Method R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 7 Table of Contents 1.

More information

Reference material Reference books: Y.C. Fung, "Foundations of Solid Mechanics", Prentice Hall R. Hill, "The mathematical theory of plasticity",

Reference material Reference books: Y.C. Fung, Foundations of Solid Mechanics, Prentice Hall R. Hill, The mathematical theory of plasticity, Reference material Reference books: Y.C. Fung, "Foundations of Solid Mechanics", Prentice Hall R. Hill, "The mathematical theory of plasticity", Oxford University Press, Oxford. J. Lubliner, "Plasticity

More information

Statics deal with the condition of equilibrium of bodies acted upon by forces.

Statics deal with the condition of equilibrium of bodies acted upon by forces. Mechanics It is defined as that branch of science, which describes and predicts the conditions of rest or motion of bodies under the action of forces. Engineering mechanics applies the principle of mechanics

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

More information

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is

More information

PILE SOIL INTERACTION MOMENT AREA METHOD

PILE SOIL INTERACTION MOMENT AREA METHOD Pile IGC Soil 2009, Interaction Moment Guntur, INDIA Area Method PILE SOIL INTERACTION MOMENT AREA METHOD D.M. Dewaikar Professor, Department of Civil Engineering, IIT Bombay, Mumbai 400 076, India. E-mail:

More information

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)

More information

STATICALLY INDETERMINATE STRUCTURES

STATICALLY INDETERMINATE STRUCTURES STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal

More information

both an analytical approach and the pole method, determine: (a) the direction of the

both an analytical approach and the pole method, determine: (a) the direction of the Quantitative Problems Problem 4-3 Figure 4-45 shows the state of stress at a point within a soil deposit. Using both an analytical approach and the pole method, determine: (a) the direction of the principal

More information

Chapter 6: Cross-Sectional Properties of Structural Members

Chapter 6: Cross-Sectional Properties of Structural Members Chapter 6: Cross-Sectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross

More information

GB/T / ISO 527-1:1993

GB/T / ISO 527-1:1993 Translated English of Chinese Standard: GB/T1040.1-2006 www.chinesestandard.net Sales@ChineseStandard.net GB NATIONAL STANDARD OF THE PEOPLE S REPUBLIC OF CHINA ICS 83.080.01 G 31 GB/T 1040.1-2006 / ISO

More information

Distributed: Wednesday, March 17, 2004

Distributed: Wednesday, March 17, 2004 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 019.00 MECHANICS AND MATERIALS II QUIZ I SOLUTIONS Distributed: Wednesday, March 17, 004 This quiz consists

More information

1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.

1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation

More information

Rigid pavement design

Rigid pavement design Rigid pavement design Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Overview 1 1.1 Modulus of sub-grade reaction.......................... 2 1.2 Relative stiffness

More information

Mechanics PhD Preliminary Spring 2017

Mechanics PhD Preliminary Spring 2017 Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n

More information

Problem 7.1 Determine the soil pressure distribution under the footing. Elevation. Plan. M 180 e 1.5 ft P 120. (a) B= L= 8 ft L e 1.5 ft 1.

Problem 7.1 Determine the soil pressure distribution under the footing. Elevation. Plan. M 180 e 1.5 ft P 120. (a) B= L= 8 ft L e 1.5 ft 1. Problem 7.1 Determine the soil pressure distribution under the footing. Elevation Plan M 180 e 1.5 ft P 10 (a) B= L= 8 ft L e 1.5 ft 1.33 ft 6 1 q q P 6 (P e) 180 6 (180) 4.9 kip/ft B L B L 8(8) 8 3 P

More information

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam.

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam. ALPHA COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING MECHANICS OF SOLIDS (21000) ASSIGNMENT 1 SIMPLE STRESSES AND STRAINS SN QUESTION YEAR MARK 1 State and prove the relationship

More information

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics

More information

Finite Element Analysis of Compression of Thin, High Modulus, Cylindrical Shells with Low-Modulus Core

Finite Element Analysis of Compression of Thin, High Modulus, Cylindrical Shells with Low-Modulus Core Finite Element Analysis of Compression of Thin, High Modulus, Cylindrical Shells with Low-Modulus Core Robert S. Joseph Design Engineering Analysis Corporation, McMurray, PA ABSTRACT Long, cylindrical

More information

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092

More information

EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES

EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES Abstract Jian Zhang 1 and Yuchuan Tang 2 The paper evaluates the radiation

More information

Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.

More information

Mechanical Behaviors of Cylindrical Retaining Structures in Ultra-deep Excavation

Mechanical Behaviors of Cylindrical Retaining Structures in Ultra-deep Excavation Mechanical Behaviors of Cylindrical Retaining Structures in Ultra-deep Excavation Pengfei Xu Tongji University August 4, 2015 Outline Introduction Two circular excavations for anchorage foundations 3D

More information

MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION

MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine

More information

(Received 5 May 1980; accepted for print 21 September 1980)

(Received 5 May 1980; accepted for print 21 September 1980) MECHANICS RESEARCH COMMUNICATIONS Vol. 7(6),351-358,1980. Printed in the USA. 0093-6413/80/060351-08502.00/0 Copyright (c) Pergamon Press Ltd ON THE DISPLACEMENT INDUCED IN A RIGID CIRCULAR PUNCH ON AN

More information

COMPARATIVE STUDIES ON SEISMIC INCOHERENT SSI ANALYSIS METHODOLOGIES

COMPARATIVE STUDIES ON SEISMIC INCOHERENT SSI ANALYSIS METHODOLOGIES Transactions, SMiRT-22 COMPARATIVE STUDIES ON SEISMIC INCOHERENT SSI ANALYSIS METHODOLOGIES Dan M. Ghiocel 1 1 Ghiocel Predictive Technologies, Inc., Rochester, New Yor, USA (dan.ghiocel@ghiocel-tech.com)

More information

9 MECHANICAL PROPERTIES OF SOLIDS

9 MECHANICAL PROPERTIES OF SOLIDS 9 MECHANICAL PROPERTIES OF SOLIDS Deforming force Deforming force is the force which changes the shape or size of a body. Restoring force Restoring force is the internal force developed inside the body

More information

CHAPTER 6: Shearing Stresses in Beams

CHAPTER 6: Shearing Stresses in Beams (130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.

More information

VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA

VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA FAKULTA METALURGIE A MATERIÁLOVÉHO INŽENÝRSTVÍ APPLIED MECHANICS Study Support Leo Václavek Ostrava 2015 Title:Applied Mechanics Code: Author: doc. Ing.

More information

7.4 The Elementary Beam Theory

7.4 The Elementary Beam Theory 7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be

More information

Rocking behaviour of a rigid foundation with an arbitrary embedment

Rocking behaviour of a rigid foundation with an arbitrary embedment Rocking behaviour of a rigid foundation with an arbitrary embedment H. Moghaddasi Islamic Azad University, Qazvin, Iran. M. Kalantari University of Tehran, Tehran, Iran N. Chouw The University of Auckland,

More information

Optimization of Thin-Walled Beams Subjected to Bending in Respect of Local Stability and Strenght

Optimization of Thin-Walled Beams Subjected to Bending in Respect of Local Stability and Strenght Mechanics and Mechanical Engineering Vol. 11, No 1 (2007) 37 48 c Technical University of Lodz Optimization of Thin-Walled Beams Subjected to Bending in Respect of Local Stability and Strenght Tadeusz

More information

Foundation Analysis LATERAL EARTH PRESSURE

Foundation Analysis LATERAL EARTH PRESSURE Foundation Analysis LATERAL EARTH PRESSURE INTRODUCTION Vertical or near-vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, sheet-pile bulkheads, braced cuts, and other

More information

Class XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions

Class XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions Downloaded from Class XI Physics Ch. 9: Mechanical Properties of solids NCERT Solutions Page 242 Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount

More information

Chapter 6 Bearing Capacity

Chapter 6 Bearing Capacity Chapter 6 Bearing Capacity 6-1. Scope This chapter provides guidance for the determination of the ultimate and allowable bearing stress values for foundations on rock. The chapter is subdivided into four

More information

Introduction to structural dynamics

Introduction to structural dynamics Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static

More information

AREAS, RADIUS OF GYRATION

AREAS, RADIUS OF GYRATION Chapter 10 MOMENTS of INERTIA for AREAS, RADIUS OF GYRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the MoI for an area by integration.

More information

Settlements and stresses of multi-layered grounds and improved grounds by equivalent elastic method

Settlements and stresses of multi-layered grounds and improved grounds by equivalent elastic method INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. (in press) Published online in Wiley InterScience (www.interscience.wiley.com)..636 Settlements

More information

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude

More information

CHAPTER 5. Beam Theory

CHAPTER 5. Beam Theory CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions

More information

FIXED BEAMS IN BENDING

FIXED BEAMS IN BENDING FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported

More information

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly .3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original

More information

EN Eurocode 7. Section 3 Geotechnical Data Section 6 Spread Foundations. Trevor L.L. Orr Trinity College Dublin Ireland.

EN Eurocode 7. Section 3 Geotechnical Data Section 6 Spread Foundations. Trevor L.L. Orr Trinity College Dublin Ireland. EN 1997 1: Sections 3 and 6 Your logo Brussels, 18-20 February 2008 Dissemination of information workshop 1 EN 1997-1 Eurocode 7 Section 3 Geotechnical Data Section 6 Spread Foundations Trevor L.L. Orr

More information

Neutral Axis Depth for a Reinforced Concrete Section. Under Eccentric Axial Load

Neutral Axis Depth for a Reinforced Concrete Section. Under Eccentric Axial Load Neutral Axis Depth for a Reinforced Concrete Section Doug Jenkins; Interactive Design Services Pty Ltd Under Eccentric Axial Load To determine the stresses in a reinforced concrete section we must first

More information

Slope Stability. loader

Slope Stability. loader Slope Stability Slope Stability loader Lower San Fernando Dam Failure, 1971 Outlines Introduction Definition of key terms Some types of slope failure Some causes of slope failure Shear Strength of Soils

More information

Rigid Pavement Mechanics. Curling Stresses

Rigid Pavement Mechanics. Curling Stresses Rigid Pavement Mechanics Curling Stresses Major Distress Conditions Cracking Bottom-up transverse cracks Top-down transverse cracks Longitudinal cracks Corner breaks Punchouts (CRCP) 2 Major Distress Conditions

More information

Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC Structures: Nonhomogeneous Soil Condition

Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC Structures: Nonhomogeneous Soil Condition ABSTRACT: Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC Structures: Nonhomogeneous Soil Condition G. Dok ve O. Kırtel Res. Assist., Department of Civil Engineering, Sakarya University,

More information

Chapter (3) Ultimate Bearing Capacity of Shallow Foundations

Chapter (3) Ultimate Bearing Capacity of Shallow Foundations Chapter (3) Ultimate Bearing Capacity of Shallow Foundations Introduction To perform satisfactorily, shallow foundations must have two main characteristics: 1. They have to be safe against overall shear

More information

Get Discount Coupons for your Coaching institute and FREE Study Material at Force System

Get Discount Coupons for your Coaching institute and FREE Study Material at   Force System Get Discount Coupons for your Coaching institute and FEE Study Material at www.pickmycoaching.com Mechanics Force System When a member of forces simultaneously acting on the body, it is known as force

More information

Tikrit University. College of Engineering Civil engineering Department CONSOILDATION. Soil Mechanics. 3 rd Class Lecture notes Up Copyrights 2016

Tikrit University. College of Engineering Civil engineering Department CONSOILDATION. Soil Mechanics. 3 rd Class Lecture notes Up Copyrights 2016 Tikrit University CONSOILDATION College of Engineering Civil engineering Department Soil Mechanics 3 rd Class Lecture notes Up Copyrights 2016 Stresses at a point in a soil mass are divided into two main

More information