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RPI - ENGR - 2530
Exam II Tuesday (April 6) 2:00-3:50pm Covers Chapters 4-6 (L9-L15) Location: SAGE 3303 1 page crib sheet- double sided (no worked-out problems) 4 problemsCh7: Stress transformation state of stress: 6 components x , y , z xy , yz , zxnormal stresses s
RPI - ENGR - 2530
Strength of MaterialsSection 03 SAGE 4101Class Info Instructor: Prof. L. Zhang (MANE) Office: JEC 5020 Email: zhangL12@rpi.edu TA: Ms. Jiwang Mao (MSE, maoj4@rpi.edu, MRC 274B)Class info cont. Office hours: Prof. Zhang: Tu 4-5pm, F 1-2pm Ms. Jiwang M
RPI - ENGR - 2530
Syllabus Homework due at the beginning of the class on the day its due Announcements, syllabus, Homework solutions, Lecture notes are posted on LMS Study example problems in the textbook ABSOLUTELY NO LAPTOPS, CELLPHONES, MP3 PLAYERS IN CLASS AND EXAMSL
RPI - ENGR - 2530
Review: Chapter 1 - Concepts of stress (normal and shear stresses) - Components of stress - Design considerations (factor of safety)Chapter 2Axial loading (loads applied in the axial direction)PPStress & Strain: Axial Loading Under loading stresses
RPI - ENGR - 2530
Quick reviewChapter 2: Axial loading Normal Stress Normal Strain Deformation due to axial loadingStatic Indeterminate ProblemsStatically indeterminate: internal forces and reactions cannot be determined from statics alone. More supports than required t
RPI - ENGR - 2530
Chapter 2Quick Review: - normal stress/strain due to axial loading - deformation due to axial loading - solving statically indeterminate problems using - compatibility equation - superposition - thermal strainToday: - Poissons ratio, multi-dimensional e
RPI - ENGR - 2530
Quick ReviewLast class:- Poissons ratio, multi-dimensional effects due to axial loading, multi-axial loading - Bulk modulus, dilatation - Shear strain, Shear modulus Today: -Composite Materials -Stress concentration -Plastic deformation -Residual stres
RPI - ENGR - 2530
Chapter 2 - Axial loading - normal stress - normal strain - deformation Chapter 3 - Torsion - shear stress - shear strain - angle of twist- failure under torsionTorsional Loads on Circular ShaftsExample: Transmission shaft Wind turbine generatorhttp:/
RPI - ENGR - 2530
Quick Review: Torsion = L: radial dist. c: radius L: length : shear strain : angle of twist = max cTc T max = and = J J = L maxc = L maxTc = J max max Tc = = G JGTL = JGAnalogous to:FL = AEAngle of Twist in Elastic RangeTL = JG=> Adding
RPI - ENGR - 2530
Exam I Next Friday (3/5) Covers chapters 1-3 1 crib sheet double sided 4 problems (100 points)OverviewDifferent types of loadings: Chapter 2 - Axial loading Chapter 3 - Torsion Chapter 4 - BendingChapter 4 BendingPure BendingPrismatic members subject
RPI - ENGR - 2530
Exam I Friday (3/5) Covers chapters 1-3 1 crib sheet double sided no worked-out problems 4 problems (100 points) Bring a calculator (no cell phone calculator allowed)Bending: radial distance from neutral axis to C y: radial distance from neutral axis
RPI - ENGR - 2530
Chapter 4: BendingStress due to bending:x = -My IM: moment (couple) y: distance from the neutral surface I: moment of inertia of the cross sectionCurvature: Absolute maximum strain:1 1 m = cc m = 1 m = Ec 1 Mc 1 = I Ec 1M = EIDeformations in a
RPI - ENGR - 2530
Chapter 5Analysis and Design of Beams for Bending Shear and Bending Moment Diagrams Relations among Load, Shear, and Bending Moment Design of Prismatic Beams for BendingSo far: (in chapter 4)bendingBeam - structural member that supports loads at vari
RPI - ENGR - 2530
Why do we need shear and bending moment diagrams?ShearandBendingMomentDiagramsTo determine maximum normal and shearing stresses and their respective locations design safe beamsMomentdiagram M x xSheardiagram VBendingMomentDiagrams: Concentratedloads:
RPI - ENGR - 2530
Last Class: Beams shear and moment diagrams (Chapter 5)Moment + Shear ForceNormal stress (Chapter 4)Shear stress (Chapter 6)Chapter 6: Shearing stress in beamsTransverse Section (plane) Transverse (vertical) loading applied to a beam (V) normal (due
RPI - ENGR - 2530
Longitudinal Shear on a Beam Element of Arbitrary Shape Last class: vertical components xy on a transverse section of a beam. This class: horizontal components xz of the stresses.Horizontal planeTransverse Section (plane)Horizontal force Vertical shea
RPI - ENGR - 2530
Mohrs Circle for Plane Stress Estimate stress graphically using Mohrs circle For a known state of plane stress - plot center ( ave) - plot point X ( x , - xy) - plot point Y ( y, xy ) - connect X and Y through C ave =x + y2 x y 2 R= + xy 22 The pri
RPI - ENGR - 2530
Chapter 8 stress in a structural member or machine element due to a combination of loads how to find the corresponding principal stresses and maximum shearing stressPrincipal Stresses: in Beams in Transmission Shaft under Combined LoadingsPrincipal Str
RPI - ENGR - 2530
Chapter8con.nued stress in a structural member or machine element due to a combination of loads how to find the corresponding principal stresses and maximum shearing stressPrincipalStresses: inBeams(lastclass) inTransmissionSha< underCombinedLoadingsDe
RPI - ENGR - 2530
Chapter 9 Deflection of BeamsWhat is the elastic curve? (describe the deformed beam shape using equations) What are the slope and deflection at point B or C?Deformation of a Beam Under Transverse Loading Bending under general transverse loadings.1 M (
RPI - ENGR - 2530
Ch9 Deflection of Beams Last class Find reaction forces/moments Develop M(x) for section AB derive differential equation for elastic curve using .dy EI 2 = M (x ) dx2 Integrate differential equation twice and apply boundary conditionsCh9: Deflection
RPI - ENGR - 2530
Chapter 10ColumnsStability of Structures In the design of columns: - allowable stress is not exceeded=P all A- deformation falls within specifications=PL spec AE column is unstable under loading: suddenly becomes sharply curved or buckles.Unstab
RPI - ENGR - 2530
Exam III Tuesday (May 4) 2:00-3:50pm Covers Chapters 7-9 (L16-L21) Location: SAGE 3303 1 page crib sheet- double sided (no workedout problems) 4 problemsStrain EnergyWith increasing load: The elementary work done by the load P as the rod elongates by
RPI - ENGR - 2530
ENGR-2530 Strength of Materials Lecture 1 1/17/06 Introduction Concept of StressOutlineConcept of Stress Review of Statics Stress Analysis Axial Loading: Normal Stress Centric & Eccentric Loading Shearing Stress Bearing Stress in Connections Stress Anal
RPI - ENGR - 2530
TRA,110 ,or:D .f'-'t)fr":/ ' J.b K# <cW\,1,<5'"'A-Re-1'5-RA + R<!.z. .10 +.3'>4!1' ~:z. .:1b' (; \.<N ,G.~MA~0R(.)C 3 ~N ,2 ~:1-' 2. )<C .:1' I+- .i' 6" ox !2-) -+.iO >- i' '5'tRcz4.4 . 0 2.~D"~d)g)q~,C):73'8'tKN-YYI- h- A. l
RPI - ENGR - 2530
'Va't"'t lOp p1AYlk'A(.t-1-)(WJ)'D(AJ1.-cfw_rO"M"'icfw_Ie>'" M 2-, I/;:3'.60:2-5 9 2.'0.NJdd tP.x,tt Yl4.k'Pto.\A.k, L.I 2-c-&o-tbO2-S'.q 2-. 1(. "-, '.q2.5-:1'8-Itt~ I't-e-F~l S~f"rW'LCZ-~V~:EO[. z.IF~[C2q?$6. :3~
RPI - ENGR - 2530
SCHEDULE - STRENGTH OF MATERIALS ENGR-2530 SPRING 2006, SECTION 3 CLASS MEETS: Tu, F: 2:00 3:50INSTRUCTOR: Mourad Zeghal PHONE: x 2836 E-MAIL: zeghal@rpi.eduHomework should be turned in at the beginning of class on the due date. No late homework is acce
RPI - ENGR - 2530
SCHEDULE - STRENGTH OF MATERIALS ENGR-2530 SPRING 2006, SECTION 3 CLASS MEETS: Tu, F: 2:00 3:50INSTRUCTOR: Mourad Zeghal PHONE: x 2836 E-MAIL: zeghal@rpi.eduHomework should be turned in at the beginning of class on the due date. No late homework is acce
RPI - ENGR - 2530
f~~()(1J(--I. 1- t-\61 l .t r rue~' .t01; Ia-z:> ,r~= ~30"'tYI..-"X.~~ >I 3 ere ~ Io-c) )4.16"0 + 4 (J"() I ~>J 'P(g(j()+50)"-)I ~O-O'" II:rO +- ~O-O~ I 0-0Aex'"[~(!.Y\.tY>ic1tjoJ- 'FCJ~ \ pI~J-?l- CA'X1~Jz -~zf el!.C!-el\.I~1jo
RPI - ENGR - 2530
Name: _ Section: _Strength of MaterialsTest #1Problem 1 2 3 4Value 25 25 25 25 Total:Score1. Write your name and section number on all pages. 2. State all your assumptions and present your work in an organized and legible fashion. Neatness Counts, p
RPI - ENGR - 2530
Name: _ RIN: _Strength of Materials (ENGR 2530)Section 3Test #2Problem 1 2 3 4Value 25 25 25 25 Total:Score1. Write your name and RIN on all pages. 2. State all your assumptions and present your work in an organized and legible fashion. Neatness Co
Albany Technical College - FIN - 303
Final FIN370 Summer 2010 Key1. A sunk cost is: A. a form of erosion. B. a cost that has already been incurred and cannot be recouped. C. the value of an asset currently owned by a firm. D. a cost for which there is no alternative option. E. another name
ASU - EEE - 591
EEE 591/445 Fall10 MICROWAVESWeb URL: ASU blackboard: EEE 591, 75742; EEE 445, 70252 Class Meetings: MW 3:30 4:45 PM SCOB 101 (Tempe and Internet Section) Instructor: George Pan, Ph.D. Telephone: (480) 965-1732 Office: GWC-318 E-mail: george.pan@asu.edu
ASU - EEE - 445
EEE 445 Homework #1 Solutions 1.1 Assume that an infinite sheet of electric surface current density J s J 0 x A/m is placed on the z = 0 plane between free-space for z < 0, and a dielectric with r 0 forz > 0, as shown below. Find the resulting E and H f
ASU - EEE - 445
EEE 445 Homework #2 Solutions 2.2 A transmission line has the following per unit length parameters: L = 0.2 H/m, C = 300 pF/m, R = 5 /m, and G = 0.01 S/m. Calculate the propagation constant and characteristic impedance of this line at 500 MHz. Recalculate
ASU - EEE - 445
EEE 445 Homework #3 Solutions2.19 Use the Smith chart to find the following quantities for the transmission line circuit below: (a) The SWR on the line. (b) The reflection coefficient at the load. (c) The load admittance. (d) The input impedance of the l
ASU - EEE - 445
EEE 445 Homework #4 Solutions 3.4 Compute the TE10 mode attenuation, in dB/m, for K-band waveguide operating at f = 20 GHz . The waveguide is made from brass, and is filled with a dielectric material having r = 2.2 and tan = 0.002 . Solution:a = 1.07 cm
ASU - EEE - 445
3.19 Design a stripline transmission line for a 70 characteristic impedance. The ground plane separation is 0.316 cm, and the dielectric constant of the filling material is 2.20. What is the guide wavelength on this transmission line if the frequency is 3
ASU - EEE - 591
EEE 591 Homework #6 Solutions 4.4 Show that the input impedance, Z, of a parallel RLC circuit satisfies the condition that Z Z * . Solution: For a parallel RLC circuit, we haveZ 1 1 1 j C R j L2jLR 2 L2 R jLR 2 1 2 LC 2 R 1 2 LC jL R 2 1 2 LC 2 L2Z
ASU - EEE - 445
EEE 445 Homework #7 Solutions 4.16 A four-port network has the scattering matrix shown below. (a) Is this network lossless? (b) Is this network reciprocal? (c) What is the return loss into port 1 when all other ports are terminated with matched loads? (d)
ASU - EEE - 445
EEE 445 Homework #8 Solutions 5.1 Design lossless L-section matching networks for the following normalized load impedances: (a) z L 1.5 j 2.0 (c) z L 0.2 j 0.9 (b) z L 0.5 j 0.3 (d) z L 2.0 j 0.3Solution: Using the Matlab function listed below, we obtain
ASU - EEE - 445
EEE 445/591 Homework #10 Solutions 6.1 Consider the loaded parallel resonant RLC circuit shown below. Compute the resonant frequency, unloaded Q, and loaded Q.Solution: Resonant frequency: f0 1 2 LC 355 MHzUnloaded Q: Q 0 RC 17.9 Loaded Q:Qe 0 R L C 40
ASU - EEE - 445
EEE 591/445 Homework 11 6.22. Solution 1. Analytical, using near resonance approximation0 1 3.14185 1010 rad/sec LC Q 2 (5 109 )(1000)(0.804 1012 ) 25.2584 1 R 2Q jC0 1 j x /0 Let 0 (1 x)Z in 0e Z in R Z 0 x 0.086281 1 (2Qx) 2 1 2QRx m Z in 0 0C0 (1
ASU - EEE - 591
EEE 591 Homework #12 Solutions 7.9 Design a Wilkinson power divider with a power division ratio of P3 P2 1 3 , and a source impedance of 50.Solution:K2 P3 1 P2 3 K 1 3 0.5774Z 03 Z 0 Z 021 K 2 131.6 K3 K 2 Z 03 43.9 1 R Z 0 K 115.5 K R 2 Z 0 K 28.9
ASU - EEE - 445
Lecture 1 Objectives Motivate the study of microwave circuit design. Mention some of the aspects of microwave circuit design. Review some of the skills that students should have developed in previous classes (or from work experience).EEE591/4451What i