Theory of Elasticity Homework 13 M96520009 高聖凱 M96520007 林羿州.

Slides:

Advertisements

Similar presentations

Torsion of a Circular Cylinder A Course Project By George Kodikulam Mukesh Nagapuri Bharath Kumar Vudhamari Pradeep Kumar Bitla SriLakshmi Ganoothula Continuum.

Advertisements

Chapter 9 Extension, Torsion and Flexure of Elastic Cylinders

Beams and Frames.

TORSION Introduction, Round bar torsion, Non- uniform torsion

Torsion: Shear Stress & Twist ( )

DESIGNING OF SHAFTS.

STRUCTURAL MECHANICS: CE203

Strength of Materials I EGCE201 กำลังวัสดุ 1

Torsion Introduction -- Analyzing the stresses and strains in machine parts which are subjected to torque T Circular -- Cross-section Non-circular.

BFC (Mechanics of Materials) Chapter 6: Torsion

Chapter 3 Torsion Torsion Engr. Othman A. Tayeh. DEFORMATIONS IN A CIRCULAR SHAFT Φ the angle of twist.

Chapter 3 Torsion Introduction -- Analyzing the stresses and strains in machine parts which are subjected to torque T Circular -- Cross-section Non-circular.

Complex Static Stresses and Torsion

Torsion cracked bar problem using BIEM S. K. Kao HR2-307/2008/01/21.

CTC / MTC 222 Strength of Materials

MECH303 Advanced Stresses Analysis Lecture 5 FEM of 1-D Problems: Applications.

Copyright 2005 by Nelson, a division of Thomson Canada Limited FIGURES FOR CHAPTER 3 TORSION Click the mouse or use the arrow keys to move to the next.

ENGR 220 Section

CE 579: STRUCTRAL STABILITY AND DESIGN

Principal Stresses and Strain and Theories of Failure

© Teaching Resource in Design of Steel Structures – IIT Madras, SERC Madras, Anna Univ., INSDAG 1 BENDING AND TORSION.

ME 520 Fundamentals of Finite Element Analysis

School of Civil EngineeringSpring 2007 CE 595: Finite Elements in Elasticity Instructors: Amit Varma, Ph.D. Timothy M. Whalen, Ph.D.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Mechanics of Materials – MAE 243 (Section 002) Spring 2008

Lecture #13 Concluding lecture. PLACE OF STRUCTURAL ANALYSIS IN THE ASSURANCE OF AIRCRAFT STRENGTH 2 Mechanics of Materials Structural Analysis Strength.

Saint-Venant Torsion Problem Finite Element Analysis of the Saint-Venant Torsion Problem Using ABAQUS.

Mechanics of Thin Structure Lecture 15 Wrapping Up the Course Shunji Kanie.

Energy Methods The Stationary Principle AERSP 301 Energy Methods The Stationary Principle Jose Palacios July 2008.

1 20-Oct-15 Last course Lecture plan and policies What is FEM? Brief history of the FEM Example of applications Discretization Example of FEM softwares.

Section 2.4 Dividing Polynomials; Remainder and Factor Theorems.

Pure Bending of Straight Symmetrical Beams

TABLES AND VALUES Section 1.5. Open Sentence Equation.

UNIT-05. Torsion And Buckling of columns Lecture Number-2 Mr. M. A. Mohite Mechanical Engineering S.I.T., Lonavala.

Last course Bar structure Equations from the theory of elasticity

Large deflection of a supercavitating hydrofoil

Section 5-4(e) Solving quadratic equations by factoring and graphing.

Torsional Resistance of Standard Steel Shapes

Main Steps of Beam Bending Analysis Step 1 – Find Reactions at External Supports –Free Body Diagram (FBD) of Entire Beam –Equations of Force and Moment.

Warmup  1.) 4x 2 = 202.) 3x = 29  3.)4.)  5.)6.)

11 10-Jan-16 Last course Interpretations and properties of the stiffness matrix (cont’d) The DSM for plane and space trusses.

Lecture # 21 This chapter serves as a review of the stress analysis that has been developed in the previous chapters regarding axial load, torsion, bending.

Computational Mechanics JASS 2006 Survey of Wave Types and Characteristics Longitudinal Waves (For reminding only)  Pure longitudinal waves  Quasi-longitudinal.

Differential Equations Linear Equations with Variable Coefficients.

EULER, CARNOT, TORSION by Evie Antholis A Cluster 3 Production.

Do Now Solve using elimination: 3x + 2y = – 19 – 3x – 5y = 25.

EGM 5653 Advanced Mechanics of Materials

Principal Stresses and Strain and Theories of Failure

Theory of Elasticity Chapter 10 Three-Dimensional Problems.

Use Inverse Matrices to Solve Linear Systems

Chapter 7 Transverse Shear

1D OF FINITE ELEMENT METHOD Session 4 – 6

Solving Systems Of Equations Algebraically

Find the equation of the tangent line for y = x2 + 6 at x = 3

Questions – Elasticity and Plasticity

Review for Final Exam Basic knowledge of vector & index notation, matrix-tensor theory, coordinate transformation, principal value problems, vector calculus.

Beams and Frames.

CE 579: STRUCTRAL STABILITY AND DESIGN

Revision for Mechanics of Materials

Introduction to Finite Element Analysis for Skeletal Structures

FEM Steps (Displacement Method)

DESIGNING OF SHAFTS.

Equation Review Given in class 10/4/13.

Systems of Equations Solve by Graphing.

Equation Review.

Solving Systems of Equations by Elimination Part 2

Problem of the Day Janice is solving the quadratic equation as shown:

5.1 -Systems of Linear Equations

The Chain Rule Section 3.4.

Topics Since Exam 2 Shear and Moment Diagrams Torsion Bending

Presentation transcript:

Theory of Elasticity Homework 13 M 高聖凱 M 林羿州

Determination of the torsional rigidity for the torsion bar with the following cross sections h Equation of boundary

Prandtl function

Thus, the shear stresses on the cross-section are Comparative coefficient

Cauchy-Riemann equations Comparative coefficient

Complex function

where J is the torsional rigidity

Warping function -Mathematica Our solution

Warping function Herbert

Warping function Our solution Herbert

Warping function Surfer