CE 715: Advanced Strength of Materials

Transcription

1 CE 715: Advanced Strength of Materials Lecture 1 CE 715 Course Information Instructor: Tasnim Hassan Office: Mann Hall 419 Office Hours: TTh 2:00-4:00 pm Phone: thassan@eos.ncsu.edu 1

2 Course Information (contd.) There may be occasions when I cannot keep my office hours due to meetings, graduate exams, etc. I will keep you informed about these missed office hours. You are welcome to drop by any time my office door is open. Objectives of the Course Bridge the gap between elementary strength of materials and the more advanced courses in structural analysis and structural mechanics Provide the student with a background in the classical theory of elasticity (mathematical stress analysis) Understand approximate theories of structural analysis (engineering stress analysis; strength of materials) 2

3 Objectives (Contd.) Establish the relationship between the simplified and more general theories Demonstrate systematic solution of a number of representative problems indicating basic principles of structural analysis Enrich student s skill for physical interpretation of analysis results Topics to be covered Introduction, review of undergrad strength of materials (1.5 lectures) Fundamentals of stress, strain and deformation (4.5 lectures) Isotropic, anistropic and orthotropic constitutive equations, linear elastic theory (1.5 lectures) St. Venant s Classical Theory of Torsion: non-circular bars, thin-walled open sections, thin-walled single-cell tubes, multi-cell thin-walled tubes (4.5 lectures) 3

4 Topics (contd.) Unsymmetric bending and transverse shear, shear flow and shear center in thin-walled sections (4 lectures) Curved beams (1.5 lectures) Pressurized cylinder, plates with circular holes (2 lectures) Beams on elastic foundations (2 lectures) Topics (contd.) Nonlinear beams, transverse shear on beams (2 lectures) Introduction to plasticity theory: yield criteria, flow rules; rigid-perfectly plastic bodies and failure criteria (3 lectures) Introduction to fracture mechanics (3 lectures) 4

5 Grade Distrinution and Exam Schedule Homework 20% (assigned weekly, due in one week) Mid-Sem Exam 30% (Tue., Oct. 7 th, 4:30-7:30 pm ) Final Exam 30% (Tue., Dec. 16 th, 1:00-4:00 pm) Final-Take Home 20% ( ed Dec. 8 th, due Dec. 12 th by 4:00 pm) Distance education students will take the exams at about the same time as the campus students. Please contact me ASAP if any changes in the exam schedule is needed. Others Homework - will normally be assigned weekly and due EXACTLY in one week. Late submission will not be accepted without a valid reason. 5

6 Others Prerequisite An undergraduate course on Mechanics of Solids or Strength of Materials Textbook Advanced Mechanics of Materials by A.P. Boresi and R.J. Schmidt 6 th Edition, John Wiley & Sons, Inc. Reference Books in Library Ugural, A.C. and Fenster, S.K., Advanced Strength and Applied Elasticity, Prentice Hall. J.T. Oden and E.A. Ripperger, Mechanics of Elastic Structures, Hemisphere Publishing Corp. 6

7 Important Dates and others Oct. 17 th -Last day to withdraw or drop the course without a grade and last day to change from credit to audit at level Mark your calendar for the Exam dates Please see course info handout on: Lecture Schedule Online Class Evaluation Academic Integrity Students with Disability Introduction Strength of Materials deals with engineering analysis and design of components of structural and machine systems Examples: analysis and design of buildings, bridges, dams, communication system, energy (gas, oil and nuclear power industry) system. (Others: machines, medical equipment, electronics, aerospace and space shuttle, automobile, etc.) 7

8 Introduction (contd.) Generally, a structural system is built after the design process is completed. One major purpose of the design process is to analyze or evaluate various design alternatives before a final design is selected. The analysis is essential for refining the design and meeting required conditions such as adequate strength, minimum weight, and minimum cost of production. Design process of a system Function of the system Geometry or shape of the system Loading Material Finally, analysis is performed to design the system that is strong and stiff enough to serve the purpose of the structure safely and economically 8

9 Failure and Limits of Design To design a structural system, the designer must have a clear understanding of the modes of failure and establish suitable failure criteria that predict the failure modes This step needs the knowledge on the response of structures to loads, and this in turn needs a comprehensive analysis of the system to evaluate stresses, strains and displacements Modes of Failure Failure by Excessive Deflection Elastic deflection Plastic deflection (yielding) Elastic and plastic instability Deflection due to creep Failure by Fatigue and Fracture Sudden fracture of brittle material Fracture of cracked or flawed components Fracture initiation and progressive fatigue 9

10 Steps in stress analysis Consider deformation produced by loadsconduct experiments or make assumption based on intuition or experience Determine strain-deformation relationship Determine stress distribution using stress-strain relation of the material Relate stresses to loads or stress resultants Relate loads to displacements Few words about the importance of derivation of a formula in studying the strength of materials (from R.D. Cook and W.C. Young, Advanced Mechanics of Materials, 2nd Edition, Chapter 1) "It makes the formula plausible. A more important reason is that a derivation makes clear the assumptions and restrictions needed in order to obtain the formula. Thus, by knowing the derivation, one can recognize situations in which a formula should not be applied." 10

11 Axial Load on Straight Prismatic Bar 1: Assumption: uniform deformation 2: ε = 3: σ = (material independent) P (constitutive equation) L δ P Axial bar problem 4: P= (equilibrium equation, material independent) σ = Eδ/L δ L 5: P= E A PL δ = EA L δ = P EA 11

12 Torsional Deformation A x Undeformed Deformed B φ T B* T y r L Circular cross-section bar Shearing Strain γ dx γ =shearing strain 12

13 Torsion (contd.) 1: Deformation Rigid rotation of cross-section 2: γdx = rdθ γ r dθ γ = r dθ dx γ = r φ L dx Shearing Strain γ max = r ( ) ρ r γ= ρ( )? 13

14 Torsion 3: τ = τ da 4: dt = ( τ da)ρ ρ Torsion 4: T = dt = A A τρ da T = φ L τρ da = G A A ρ 2 da I P = A ρ 2 da Polar Moment of Inertia 14

15 Torsion T φ = G I L p φ L = T GI p 5: Rotation φ = TL GI p 15