Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
|
|
- Arron Sherman
- 5 years ago
- Views:
Transcription
1 51
2 Module 4: Lecture 2 on Stress-strain relationship and Shear strength of soils
3 Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-coulomb failure criteria and its limitations, correlation with p-q space; Stress-strain behavior; Isotropic compression and pressure dependency, confined compression, large stress compression, Definition of failure, Interlocking concept and its interpretations, Drainage conditions; Triaxial behaviour, stress state and analysis of UC, UU, CU, CD, and other special tests, Stress paths in triaxial and octahedralplane; Elastic modulus from triaxial tests.
4 Mohr s stress circle Mohr's circle is a geometric representation of the twodimensional stress state and is very useful to perform quick and efficient estimations. It is also popularly used in geotechnical fields such as soil strength, stress path, earth pressure and bearing capacity. It is often used to interpret the test data, to analyze complex geotechnical problems, and to predict soil behaviours. The pole point on Mohr's circle is a point so special that it can help to readily find stresses on any specified plane by using diagram instead of complicated computation.
5 Mohr s stress circle: Pole points A Pole is a unique point located on the circumference of Mohr s circle. The point of intersection of Mohr s stress circle and line drawn through the pole parallel to a given plane, gives the stresses on that plane. Two pole points can be established, a) Relating to the direction of action of stresses, and b) Relating to the direction of planes on which stresses are acting. Usually the pole point relating to the direction of the planes are in use.
6 Mohr s stress circle: Pole points for stresses- Procedure Step : Project the line from the point (σ z, τ zx ) in the line of action of σ z (Vertical) OR Project the line from the point (σ x, τ xz ) in the line of action of σ x (Horizontal) till it intersects the circumference of the circle. The intersection point gives the POLE point P s for stresses. τ (σ z, τ zx ) τ xz σ x τ zx τ (σ z, τ zx ) σ z σ σ (σ x, τ xz ) P (σ s Pole points x, τ xz ) for stresses P s
7 Mohr s stress circle: Pole points for planes- Procedure Step : Project the line from the point (σ z, τ zx ) OR (σ x, τ xz ) in the direction of plane on which these stresses are acting till it intersect circumference of the circle. The intersection point gives the POLE point P p for planes. Pole point for planes τ P p (σ z, τ zx ) σ x τ xz τ P p (σ z, τ zx ) τ zx σ σ z σ (σ x, τ xz ) P s Pole point (σ x, τ xz ) for stresses P s
8 Mohr s stress circle: Pole points for planes The pole of a Mohr s circle is defined thus: If a line is drawn from the pole to a point on the circle where the stresses are τ i, σ i then, in the (x, z) plane the line is parallel to the plane on which τ I and σ i act.
9 Mohr s stress circle: Use of pole point τ σ x τ xz σ z σ c τca τ zx P p E(σ z, τ zx ) Objective: To find out stresses σ c, σ a, τ ac, and τ ca on the plane which is inclined at θ to the plane on which σ z acts. Step 1: Locate the pole point for planes extending point E horizontally. i.e. in the direction of plane on which σ z acts. σ a σ c τca σ τ ac τ ac (σ x, τ xz ) σ c τ ca σ a
10 Mohr s stress circle: Use of pole point τ σ x τ xz σ z σ c τca τ zx Stresses on σ a plane P p E(σ z, τ zx ) Step 2: Draw a line parallel to the plane on which σ c acts. Step 3: Extend a line from point D through centre of the circle till it intersects the circle. Parallel planes (σ a, τ ac ) (σ x, τ xz ) D(σ c, τ ca ) σ Stresses on σ c plane σ c τca σ a τ ac τ ac σ c τ ca σ a
11 Use of pole point P to locate stresses (σc, τca) at angle θ to the reference stress direction The stress point on the Mohr circle is found by simply projecting a line from Pp parallel to the plane on which (σ c, τ ca ) acts until it intersects the circle at point D.
12 Fundamental relationships by Mohr s stress circle The maximum shearing stress, often called the principal shearing stress, has a magnitude of (σ 1 -σ 3 )/2, which equals the radius of the Mohr circle. The principal shearing stress occurs on planes inclined at 45. Principal shearing stresses
13 Fundamental relationships by Mohr s stress circle Shearing stress on planes at right angles to each other are numerically equal but are of opposite sign. These stresses are called conjugate shearing stresses. Conjugate shearing stresses
14 Fundamental relationships by Mohr s stress circle The resultant stress on any plane has a magnitude expressed by and has an obliquity which is equal to Obliquity and resultant stress
15 Fundamental relationships by Mohr s stress circle The maximum of all the possible obliquity angles on the various planes is called the maximum angle of obliquity α m. The coordinates of the point of tangency are the stresses on the plane of maximum obliquity and is less than the plane of principal shear (i.e. maximum shear stress). Since a limiting obliquity is the criterion of slip and where as on the plane of principal shear failure is liable to happen. Maximum Obliquity
16 Mohr s stress circle: Pole point- example Draw the Mohr stress circle at failure on a cylindrical specimen of stiff clay with a shear strength of 100 kpa, if the radial stress is maintained constant at 80 kpa. By using pole point method find the inclination θ to the radial direction of the planes on which the shear stress is one-half the maximum shear stress, and determine the normalstresses acting on these planes.
17 Mohr s stress circle: Pole point- Solution 100 (All units are in kpa) τ max = radius of circle σ 1 = σ 3 +2τ max = 280 τ max =100 σ 3 =80 σ 1 = Step 1: Plot Mohr s circle based on above information, i.e. radius and two points on circle.
18 Mohr s stress circle: Pole point- Solution 100 (All units are in kpa) 50 τ max = Step 2: Draw a line at τ = 50 kpa which is half to τ max
19 Mohr s stress circle: Pole point- Solution 100 (All units are in kpa) 50 τ max =100 P p Step 3: As the principal stresses are acting on edges the σ 3 point will act as a pole.
20 Mohr s stress circle: Pole point- Solution (All units are in kpa) 100 Inclination of the plane on which τ = τ max /2 is, θ = 15 or P p τ max =100 σ n15 = 267 kpa, σ n75 = 93 kpa -100 Step 3: Draw line from pole to the intersection of 50 kpa line and Mohr s circle.
21 Example problem: Mohr s circle of total stress In the figure below, the normal loads applied to the faces of a soil cube are F 1 = 0.45 kn and F 2 = 0.30 kn and the shear loads are F 3 = F 4 = 0.1 kn. The sides of the soil cube are each 40 mm. Construct the Mohr s circle of total stress and find the magnitudes of the principal total stresses and the direction of the principal planes in the soil. F 1 F 3 F 4 F 2 z x F 2 F 4 F 1 F 3
22 Solution: Mohr s circle of total stress σ z = 0.45/(40x40x10-6 ) = kn/m 2 σ x = 0.30/(40x40x10-6 ) = kn/m 2 τ xz = τ zx = 0.10/(40x40x10-6 ) = 62.5 kn/m 2 (Minor difference in magnitudes can be ignored)
23 Example problem Pole P
24 1) Solution: 2) Establish pole point P or origin of planes. A line through the pole inclined at an angle α = 35 from the horizontal plane would be parallel to the plane on the element. 3) The intersection is at point C and we find that σ α = 39 kpa and τ α = 18.6 kpa.
25 Example problem Note: Resulting σ α = 39 kpa and τ α = 18.6 kpa are same because nothing has changed except orientation in space of the element.
26 Example problem The stress shown on the element in the figure below: Required: a) Evaluate σ α, τ α when α = 30 b) Evaluate σ 1 and σ 3 when α = 30 a
27 Solution 1) Plot the state of stress on the horizontal plane (6, 2) at point a. Note that the shear stress makes a clockwise moment about a and therefore is positive. 2) Plot point B (-4,-2). The shear stress on the vertical plane is negative since it makes a counterclockwise moment. 3) Points A and B are two points on a circle; Construct the Mohr Circle with center at (1,0). 4) Find the pole, by drawing horizontal line through A or vertical line through B. 5) Find the state of stress on the plane inclined at angle α = 30, draw the line PC. C (1.8, 5.3 ) MPa. 6) Lines drawn from P to σ 1 and σ 3 establish the orientation of major and minor principal planes.
28 Solution
29 Mohr circles of total and effective stresses τ Effective stress circle Total stress circle σ θ, τ θ σ θ, τ θ θ θ σ σ 3 σ 1 σ 3 σ 1 σ 1 = σ 1 - u σ 3 = σ 3 - u u
30 Mohr circles of total and effective stresses The effective stress circle has the same diameter as the total stress circle and is separated from it by the pore water pressure. The stresses τ θ and σ θ are the effective stresses acting on plane inclined at an angle θ By examining the circles we note that τ θ = τ θ σ θ = σ θ - u Thus, for a given state of total stress, changes in pore pressure have no effect on the effective shear stresses, they alter only the effective normal stresses.
31 Mohr circles of total and effective stresses Use the pole construction on the effective stress Mohr s circle to calculate the effective stresses on any plane is exactly same way as we used the pole construction to calculate total stresses. The position of the pole in the Mohr s circle of effective stress is the same as in the Mohr s circle of total stress and the locations of the principal planes of total and effective stresses in the soil are identical.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
50 Module 4: Lecture 1 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-Coulomb failure
More informationboth 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 informationProf. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
56 Module 4: Lecture 7 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-Coulomb failure
More information1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION 1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION
Module 6 Lecture 40 Evaluation of Soil Settlement - 6 Topics 1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION 1.5.1 Definition of Stress Path 1.5. Stress and Strain Path for Consolidated Undrained Undrained
More information9. Stress Transformation
9.7 ABSOLUTE MAXIMUM SHEAR STRESS A pt in a body subjected to a general 3-D state of stress will have a normal stress and shear-stress components acting on each of its faces. We can develop stress-transformation
More informationCHAPTER 4 Stress Transformation
CHAPTER 4 Stress Transformation ANALYSIS OF STRESS For this topic, the stresses to be considered are not on the perpendicular and parallel planes only but also on other inclined planes. A P a a b b P z
More informationSoil strength. the strength depends on the applied stress. water pressures are required
Soil Strength Soil strength u Soils are essentially frictional materials the strength depends on the applied stress u Strength is controlled by effective stresses water pressures are required u Soil strength
More informationChapter 5 Shear Strength of Soil
Page 5 Chapter 5 Shear Strength of Soil. The internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it is called (a) strength (b) shear strength
More informationCh 4a Stress, Strain and Shearing
Ch. 4a - Stress, Strain, Shearing Page 1 Ch 4a Stress, Strain and Shearing Reading Assignment Ch. 4a Lecture Notes Sections 4.1-4.3 (Salgado) Other Materials Handout 4 Homework Assignment 3 Problems 4-13,
More informationMohr s Circle of Stress
Department of Civil Engineering Mohr s Circle of Stress by David Nash Department of Civil Engineering University of Bristol David.Nash@bristol.ac.uk 1 Principal planes and principal stresses Within any
More information7. STRESS ANALYSIS AND STRESS PATHS
7-1 7. STRESS ANALYSIS AND STRESS PATHS 7.1 THE MOHR CIRCLE The discussions in Chapters and 5 were largely concerned with vertical stresses. A more detailed examination of soil behaviour requires a knowledge
More informationSHEAR STRENGTH OF SOIL
SHEAR STRENGTH OF SOIL Necessity of studying Shear Strength of soils : Soil failure usually occurs in the form of shearing along internal surface within the soil. Shear Strength: Thus, structural strength
More informationSHEAR STRENGTH OF SOIL UNCONFINED COMPRESSION TEST
SHEAR STRENGTH OF SOIL DEFINITION The shear strength of the soil mass is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it. INTRODUCTION
More informationWelcome back. So, in the last lecture we were seeing or we were discussing about the CU test. (Refer Slide Time: 00:22)
Geology and Soil Mechanics Prof. P. Ghosh Department of Civil Engineering Indian Institute of Technology Kanpur Lecture - 43 Shear Strength of Soils Keywords: Triaxial shear test, unconsolidated undrained
More information(Refer Slide Time: 02:18)
Geology and Soil Mechanics Prof. P. Ghosh Department of Civil Engineering Indian Institute of Technology Kanpur Lecture 40 Shear Strength of Soil - C Keywords: Shear strength of soil, direct shear test,
More information1.8 Unconfined Compression Test
1-49 1.8 Unconfined Compression Test - It gives a quick and simple measurement of the undrained strength of cohesive, undisturbed soil specimens. 1) Testing method i) Trimming a sample. Length-diameter
More informationFollowing are the results of four drained direct shear tests on an overconsolidated clay: Diameter of specimen 50 mm Height of specimen 25 mm
444 Chapter : Shear Strength of Soil Example. Following are the results of four drained direct shear tests on an overconsolidated clay: Diameter of specimen 50 mm Height of specimen 5 mm Normal Shear force
More informationSHEAR STRENGTH OF SOIL
Soil Failure Criteria SHEAR STRENGTH OF SOIL Knowledge about the shear strength of soil important for the analysis of: Bearing capacity of foundations, Slope stability, Lateral pressure on retaining structures,
More informationSHEAR STRENGTH OF SOIL. Chapter 10: Sections Chapter 12: All sections except
SHEAR STRENGTH OF SOIL Chapter 10: Sections 10. 10.3 Chapter 1: All sections ecept 1.13 1.14 1.15 1.17 1.18 TOPICS Introduction Components of Shear Strength of Soils Normal and Shear Stresses on a Plane
More informationWith high enough plate forces in opposite directions Bolts. How do these fail? Each pin has sheared into two pieces.
SHEAR STRENGTH In general, the shear strength of any material is the load per unit area or pressure that it can withstand before undergoing shearing failure. Shearing When you Pins hear can Shear be used
More informationD1. A normally consolidated clay has the following void ratio e versus effective stress σ relationship obtained in an oedometer test.
(d) COMPRESSIBILITY AND CONSOLIDATION D1. A normally consolidated clay has the following void ratio e versus effective stress σ relationship obtained in an oedometer test. (a) Plot the e - σ curve. (b)
More information8.1. What is meant by the shear strength of soils? Solution 8.1 Shear strength of a soil is its internal resistance to shearing stresses.
8.1. What is meant by the shear strength of soils? Solution 8.1 Shear strength of a soil is its internal resistance to shearing stresses. 8.2. Some soils show a peak shear strength. Why and what type(s)
More informationStress and Strains in Soil and Rock. Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University
Stress and Strains in Soil and Rock Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University Stress and Strain ε 1 1 2 ε 2 ε Dimension 1 2 0 ε ε ε 0 1 2 ε 1 1 2 ε 2 ε Plane Strain = 0 1 2
More information(Refer Slide Time: 04:21 min)
Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 44 Shear Strength of Soils Lecture No.2 Dear students today we shall go through yet
More informationGeology 229 Engineering Geology. Lecture 5. Engineering Properties of Rocks (West, Ch. 6)
Geology 229 Engineering Geology Lecture 5 Engineering Properties of Rocks (West, Ch. 6) Common mechanic properties: Density; Elastic properties: - elastic modulii Outline of this Lecture 1. Uniaxial rock
More informationTriaxial Shear Test. o The most reliable method now available for determination of shear strength parameters.
TOPICS Introduction Components of Shear Strength of Soils Normal and Shear Stresses on a Plane Mohr-Coulomb Failure Criterion Laboratory Shear Strength Testing Direct Shear Test Triaxial Compression Test
More informationChapter (12) Instructor : Dr. Jehad Hamad
Chapter (12) Instructor : Dr. Jehad Hamad 2017-2016 Chapter Outlines Shear strength in soils Direct shear test Unconfined Compression Test Tri-axial Test Shear Strength The strength of a material is the
More informationStress transformation and Mohr s circle for stresses
Stress transformation and Mohr s circle for stresses 1.1 General State of stress Consider a certain body, subjected to external force. The force F is acting on the surface over an area da of the surface.
More informationStress, Strain, Mohr s Circle
Stress, Strain, Mohr s Circle The fundamental quantities in solid mechanics are stresses and strains. In accordance with the continuum mechanics assumption, the molecular structure of materials is neglected
More informationCHAPER THREE ANALYSIS OF PLANE STRESS AND STRAIN
CHAPER THREE ANALYSIS OF PLANE STRESS AND STRAIN Introduction This chapter is concerned with finding normal and shear stresses acting on inclined sections cut through a member, because these stresses may
More informationSOIL SHEAR STRENGTH. Prepared by: Dr. Hetty Muhammad Azril Fauziah Kassim Norafida
SOIL SHEAR STRENGTH Prepared by: Dr. Hetty Muhammad Azril Fauziah Kassim Norafida What is shear strength Shear strength of a soil is the maximum internal resistance to applied shearing forces Why it is
More informationARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13
ARC241 Structural Analysis I Lecture 10: MM1.3 MM1.13 MM1.4) Analysis and Design MM1.5) Axial Loading; Normal Stress MM1.6) Shearing Stress MM1.7) Bearing Stress in Connections MM1.9) Method of Problem
More informationThe hitch in all of this is figuring out the two principal angles and which principal stress goes with which principal angle.
Mohr s Circle The stress basic transformation equations that we developed allowed us to determine the stresses acting on an element regardless of its orientation as long as we know the basic stresses σx,
More informationChapter 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 informationTheory of Shear Strength
SKAA 1713 SOIL MECHANICS Theory of Shear Strength Prepared by, Dr. Hetty 1 SOIL STRENGTH DEFINITION Shear strength of a soil is the maximum internal resistance to applied shearing forces The maximum or
More informationSOIL MECHANICS Assignment #7: Shear Strength Solution.
14.330 SOIL MECHANICS Assignment #7: Shear Strength Solution. PROBLEM #1: GIVEN: Direct Shear test results from a SP soil shown in Figure A (from 14.330_2012_Assignment_#8_P1.csv on the course website).
More informationShear Strength of Soils
Shear Strength of Soils STRESSES IN A SOIL ELEMENT t s v Analyze Effective Stresses (s ) Load carried by Soil t Where: s H t t s H s = t f = s v = s H = t = s v Stresses in a Soil Element after Figure
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationShear Strength of Soils
Shear Strength of Soils Soil strength Most of problems in soil engineering (foundations, slopes, etc.) soil withstands shear stresses. Shear strength of a soil is defined as the capacity to resist shear
More informationD : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.
GTE 2016 Q. 1 Q. 9 carry one mark each. D : SOLID MECHNICS Q.1 single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system
More information2017 Soil Mechanics II and Exercises Final Exam. 2017/7/26 (Wed) 10:00-12:00 Kyotsu 4 Lecture room
2017 Soil Mechanics II and Exercises Final Exam 2017/7/26 (Wed) 10:00-12:00 Kyotsu 4 Lecture room Attention: The exam consists of five questions for which you are provided with five answer sheets. Write
More informationA circular tunnel in a Mohr-Coulomb medium with an overlying fault
MAP3D VERIFICATION EXAMPLE 9 A circular tunnel in a Mohr-Coulomb medium with an overlying fault 1 Description This example involves calculating the stresses and displacements on a fault overlying a 5 m
More informationModule 5: Theories of Failure
Module 5: Theories of Failure Objectives: The objectives/outcomes of this lecture on Theories of Failure is to enable students for 1. Recognize loading on Structural Members/Machine elements and allowable
More informationTheory of Shear Strength
MAJ 1013 ADVANCED SOIL MECHANICS Theory of Shear Strength Prepared by, Dr. Hetty 1 Strength of different materials Steel Concrete Soil Tensile strength Compressive strength Shear strength Complex behavior
More informationPrincipal Stresses, Yielding Criteria, wall structures
Principal Stresses, Yielding Criteria, St i thi Stresses in thin wall structures Introduction The most general state of stress at a point may be represented by 6 components, x, y, z τ xy, τ yz, τ zx normal
More informationCHAPTER 2 Failure/Fracture Criterion
(11) CHAPTER 2 Failure/Fracture Criterion (12) Failure (Yield) Criteria for Ductile Materials under Plane Stress Designer engineer: 1- Analysis of loading (for simple geometry using what you learn here
More informationLaboratory Testing Total & Effective Stress Analysis
SKAA 1713 SOIL MECHANICS Laboratory Testing Total & Effective Stress Analysis Prepared by: Dr. Hetty Mohr Coulomb failure criterion with Mohr circle of stress 2 ' 2 ' ' ' 3 ' 1 ' 3 ' 1 Cot Sin c ' ' 2
More informationModule 4 Lecture 20 Pore water pressure and shear strength - 4 Topics
Module 4 Lecture 20 Pore water pressure and shear strength - 4 Topics 1.2.6 Curvature of the Failure Envelope Effect of angularity of soil particles Effect of rate of loading during the test 1.2.7 Shear
More informationThe Mohr Stress Diagram. Edvard Munch as a young geologist!
The Mohr Stress Diagram Edvard Munch as a young geologist! Material in the chapter is covered in Chapter 7 in Fossen s text The Mohr Stress Diagram A means by which two stresses acting on a plane of known
More informationVerification Manual GT
Verification Manual GT Written by: The SoilVision Systems Ltd. Team Last Updated: Tuesday, February 20, 2018 SoilVision Systems Ltd. Saskatoon, Saskatchewan, Canada Software License The software described
More informationCombined Stresses and Mohr s Circle. General Case of Combined Stresses. General Case of Combined Stresses con t. Two-dimensional stress condition
Combined Stresses and Mohr s Circle Material in this lecture was taken from chapter 4 of General Case of Combined Stresses Two-dimensional stress condition General Case of Combined Stresses con t The normal
More informationTutorial #1 - CivE. 205 Name: I.D:
Tutorial # - CivE. 0 Name: I.D: Eercise : For the Beam below: - Calculate the reactions at the supports and check the equilibrium of point a - Define the points at which there is change in load or beam
More informationYOUR HW MUST BE STAPLED YOU MUST USE A PENCIL (no pens)
Spring 2008 CIVE 462 HOMEWORK #1 1. Print out the syllabus. Read it. Write the grade percentages in the first page of your notes. 2. Go back to your 301 notes, internet, etc. and find the engineering definition
More informationBone Tissue Mechanics
Bone Tissue Mechanics João Folgado Paulo R. Fernandes Instituto Superior Técnico, 2016 PART 1 and 2 Introduction The objective of this course is to study basic concepts on hard tissue mechanics. Hard tissue
More informationShear Strength of Soil
8 Shear Strength of Soil 8 1 INTRODUCTION As a structural member, a piece of steel is capable of resisting compression, tension, and shear. Soil, however, like concrete and rock, is not capable of resisting
More informationMohr Circles, Stress Paths and Geotechnics. Second Edition
Mohr Circles, Stress Paths and Geotechnics Second Edition Mohr Circles, Stress Paths and Geotechnics Second Edition R H G Parry First published 2004 by Spon Press 11 New Fetter Lane, London EC4P 4EE Simultaneously
More informationGG303 Lecture 17 10/25/09 1 MOHR CIRCLE FOR TRACTIONS
GG303 Lecture 17 10/5/09 1 MOHR CIRCLE FOR TRACTIONS I Main Topics A Stresses vs. tractions B Mohr circle for tractions II Stresses vs. tractions A Similarities between stresses and tractions 1 Same dimensions
More informationStructural Analysis I Chapter 4 - Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More informationPhiladelphia University Faculty of Engineering
Final Exam, Second Semester: 2015/2016 Civil Engineering Department Course Title: SOIL MECHANICS Date: 9/6/2016 Course No: 0670331 Time: 2 hours Lecturer: Dr. Mohammed Mustafa Al-Iessa No. of pages: 9
More informationModule 5: Failure Criteria of Rock and Rock masses. Contents Hydrostatic compression Deviatoric compression
FAILURE CRITERIA OF ROCK AND ROCK MASSES Contents 5.1 Failure in rocks 5.1.1 Hydrostatic compression 5.1.2 Deviatoric compression 5.1.3 Effect of confining pressure 5.2 Failure modes in rocks 5.3 Complete
More informationLecture Notes 5
1.5 Lecture Notes 5 Quantities in Different Coordinate Systems How to express quantities in different coordinate systems? x 3 x 3 P Direction Cosines Axis φ 11 φ 3 φ 1 x x x x 3 11 1 13 x 1 3 x 3 31 3
More informationModule 6: Stresses around underground openings. 6.2 STRESSES AROUND UNDERGROUND OPENING contd.
LECTURE 0 6. STRESSES AROUND UNDERGROUND OPENING contd. CASE : When σ x = 0 For σ x = 0, the maximum tangential stress is three times the applied stress and occurs at the boundary on the X-axis that is
More informationLateral Earth Pressure
1 of 11 6/2/2012 4:28 AM Lateral Earth Pressure The magnitude of lateral earth pressure depends on: 1. Shear strength characteristics of soil 2. Lateral strain condition 3. Pore water pressure 4. State
More informationME 243. Lecture 10: Combined stresses
ME 243 Mechanics of Solids Lecture 10: Combined stresses Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil
More informationUNIT 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 informationSHEAR STRENGTH I YULVI ZAIKA
SHEAR STRENGTH I YULVI ZAIKA MATERI Keruntuhan mohr coulomb, stress paths, kuat geser tanah non kohesif dan kohesif, evaluasi kuat geser di lapangan, tegangan normal dan tegangan geser pada sebuah bidang
More informationTIME-DEPENDENT BEHAVIOR OF PILE UNDER LATERAL LOAD USING THE BOUNDING SURFACE MODEL
TIME-DEPENDENT BEHAVIOR OF PILE UNDER LATERAL LOAD USING THE BOUNDING SURFACE MODEL Qassun S. Mohammed Shafiqu and Maarib M. Ahmed Al-Sammaraey Department of Civil Engineering, Nahrain University, Iraq
More informationModule 2 Stresses in machine elements. Version 2 ME, IIT Kharagpur
Module Stresses in machine elements Lesson Compound stresses in machine parts Instructional Objectives t the end of this lesson, the student should be able to understand Elements of force system at a beam
More informationME 202 STRENGTH OF MATERIALS SPRING 2014 HOMEWORK 4 SOLUTIONS
ÇANKAYA UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 202 STRENGTH OF MATERIALS SPRING 2014 Due Date: 1 ST Lecture Hour of Week 12 (02 May 2014) Quiz Date: 3 rd Lecture Hour of Week 12 (08 May 2014)
More informationRecent Research on EPS Geofoam Seismic Buffers. Richard J. Bathurst and Saman Zarnani GeoEngineering Centre at Queen s-rmc Canada
Recent Research on EPS Geofoam Seismic Buffers Richard J. Bathurst and Saman Zarnani GeoEngineering Centre at Queen s-rmc Canada What is a wall (SEISMIC) buffer? A compressible inclusion placed between
More informationModule 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 informationME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.
ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2
More informationFailure from static loading
Failure from static loading Topics Quiz /1/07 Failures from static loading Reading Chapter 5 Homework HW 3 due /1 HW 4 due /8 What is Failure? Failure any change in a machine part which makes it unable
More informationChapter 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(Refer Slide Time 1:07 min)
Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 46 Shear Strength of Soils Lecture No.4 Students we had 3 lectures so far on this
More informationMaterial is perfectly elastic until it undergoes brittle fracture when applied stress reaches σ f
Material is perfectly elastic until it undergoes brittle fracture when applied stress reaches σ f Material undergoes plastic deformation when stress exceeds yield stress σ 0 Permanent strain results from
More informationEquilibrium of Deformable Body
Equilibrium of Deformable Body Review Static Equilibrium If a body is in static equilibrium under the action applied external forces, the Newton s Second Law provides us six scalar equations of equilibrium
More informationWEEK 10 Soil Behaviour at Medium Strains
WEEK 10 Soil Behaviour at Medium Strains 14. Onset of yielding 14-1. What is yielding: Remember? We have already studied what yielding means; if you don t remember, refer back to Week 2. It is defined
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Surface and body forces Tensors, Mohr circles. Theoretical strength of materials Defects Stress concentrations Griffith failure
More informationFOUNDATION ENGINEERING UNIT V
FOUNDATION ENGINEERING UNIT V RETAINING WALLS Plastic equilibrium in soils active and passive states Rankine s theory cohesion less and cohesive soil - Coloumb s wedge theory condition for critical failure
More informationELASTICITY (MDM 10203)
ELASTICITY () Lecture Module 3: Fundamental Stress and Strain University Tun Hussein Onn Malaysia Normal Stress inconstant stress distribution σ= dp da P = da A dimensional Area of σ and A σ A 3 dimensional
More informationEN 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 informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationShear strength. Common cases of shearing In practice, the state of stress in the ground will be complex. Common cases of shearing Strength
Shear strength Common cases of shearing Strength Near any geotechnical construction (e.g. slopes, excavations, tunnels and foundations) there will be both mean and normal stresses and shear stresses. The
More informationReview Lecture. AE1108-II: Aerospace Mechanics of Materials. Dr. Calvin Rans Dr. Sofia Teixeira De Freitas
Review Lecture AE1108-II: Aerospace Mechanics of Materials Dr. Calvin Rans Dr. Sofia Teixeira De Freitas Aerospace Structures & Materials Faculty of Aerospace Engineering Analysis of an Engineering System
More informationGeotechnical 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 informationFUNDAMENTALS SOIL MECHANICS. Isao Ishibashi Hemanta Hazarika. >C\ CRC Press J Taylor & Francis Group. Taylor & Francis Group, an Informa business
SOIL MECHANICS FUNDAMENTALS Isao Ishibashi Hemanta Hazarika >C\ CRC Press J Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an Informa business
More informationQ. 1 Q. 5 carry one mark each.
General ptitude G Set-8 Q. 1 Q. 5 carry one mark each. Q.1 The chairman requested the aggrieved shareholders to him. () bare with () bore with (C) bear with (D) bare Q.2 Identify the correct spelling out
More informationSOIL MODELS: SAFETY FACTORS AND SETTLEMENTS
PERIODICA POLYTECHNICA SER. CIV. ENG. VOL. 48, NO. 1 2, PP. 53 63 (2004) SOIL MODELS: SAFETY FACTORS AND SETTLEMENTS Gabriella VARGA and Zoltán CZAP Geotechnical Department Budapest University of Technology
More informationON THE FACE STABILITY OF TUNNELS IN WEAK ROCKS
33 rd 33 Annual rd Annual General General Conference conference of the Canadian of the Canadian Society for Society Civil Engineering for Civil Engineering 33 e Congrès général annuel de la Société canadienne
More informationFoundation 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 informationModule 7 (Lecture 25) RETAINING WALLS
Module 7 (Lecture 25) RETAINING WALLS Topics Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure
More informationStrength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture - 18 Torsion - I
Strength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture - 18 Torsion - I Welcome to the first lesson of Module 4 which is on Torsion
More informationSoil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 51 Earth Pressure Theories II
Soil Mechanics Prof. B.V.S. Viswanathan Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 51 Earth Pressure Theories II Welcome to lecture number two on earth pressure theories.
More informationExample-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium
Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic
More informationFinite Element Investigation of the Interaction between a Pile and a Soft Soil focussing on Negative Skin Friction
NGM 2016 Reykjavik Proceedings of the 17 th Nordic Geotechnical Meeting Challenges in Nordic Geotechnic 25 th 28 th of May Finite Element Investigation of the Interaction between a Pile and a Soft Soil
More informationCite this paper as follows:
Cite this paper as follows: Naughton P.J. and O Kelly B.C. 2001. An overview of the University College Dublin hollow cylinder apparatus. Proceedings of the 14th Young European Geotechnical Engineer s Conference,
More informationVerification of the Hyperbolic Soil Model by Triaxial Test Simulations
1 Introduction Verification of the Hyperbolic Soil Model by Triaxial Test Simulations This example simulates a series of triaxial tests that can be used to verify that the Hyperbolic constitutive model
More informationTectonics. Lecture 12 Earthquake Faulting GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Tectonics Lecture 12 Earthquake Faulting Plane strain 3 Strain occurs only in a plane. In the third direction strain is zero. 1 ε 2 = 0 3 2 Assumption of plane strain for faulting e.g., reverse fault:
More informationAPPLICATION OF THE EXPERIMENTAL TESTS OF THE SHEAR STRENGTH OF SOILS IN THE GEOTECHNICAL DESIGN. 1. Introduction
ROCZNIKI INŻYNIERII BUDOWLANEJ ZESZYT 14/014 Komisja Inżynierii Budowlanej Oddział Polskiej Akademii Nauk w Katowicach APPLICATION OF THE EXPERIMENTAL TESTS OF THE SHEAR STRENGTH OF SOILS IN THE GEOTECHNICAL
More information