Increase Decrease Remain the Same (Circle one) (2 pts)

Size: px
Start display at page:

Download "Increase Decrease Remain the Same (Circle one) (2 pts)"

Transcription

1 ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne the tenson n ropes AB and AC. NAME: T AB = T AC = (2 ponts) (3 ponts) PROBLEM 1B. (5 ponts) FIND: Plate AB s supported b a pn support at A and a rocker support at B and s n statc equlbrum. For the loadng shown (neglect the weght of the plate), determne the magntude of the reacton force at B. If the 100 n-lb couple were shfted to pont A, would F B ncrease, decrease or reman the same. F B = (3 pts) Increase Decrease Reman the Same (Crcle one) (2 pts)

2 NAME: ME 270 Sample Fnal Eam PROBLEM 1C. (5 ponts) 3.8 ft FIND: Truss ABCDEFG s loaded wth a sngle 600 lb force at jont C and s n statc equlbrum. Determne the magntude of the force n member BC and whether t s n tenson or compresson. Lst all zero-force members. F BC = T or C (Crcle one) (3 pts) Zero-Force Members = (2 pts) PROBLEM 1D. (5 ponts) FIND: The A-Frame shown s supported b a rocker support at A and a pn support at E and s n statc equlbrum. On the schematcs below, complete a free-bod dagram of each member of the A-Frame. C C B D A E B D

3 NAME: PROBLEM 1E. (5 ponts) FIND: For the 50 lb chest shown, determne the force P needed to tp the chest, assumng the dmenson d = 3 ft. If the 30 angle were ncreased, would t ncrease or decrease the probablt of tppng the chest? μ s = 0.7 P = (3 pts) Increase Decrease (Crcle One) (2 pts)

4 ME 270 Sample Fnal Eam NAME: z PROBLEM 2. (25 ponts) GIVEN: The vertcal mast supports the 4-kN force and s constraned b two cables BC and BD and b a ball-and-socket connecton at A. FIND: T BC T BD a) Draw a free bod dagram of the mast on the artwork provded below. (4 pts) b) Epress tenson vectors T BC and T BD n terms of ther unknown magntudes and ther known unt vectors. (4 pts) c) Determne the tenson magntudes T BC and T BD. (8 pts) d) Determne the magntudes of the reactons at the ball-and-socket A. (9 pts) z

5 PROBLEM 3 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 3A. (5 ponts) FIND: Determne the nternal forces on cross-secton C. of the beam shown (.e., the aal and shear-force and the bendng-moment). NAME: C = F n = C = V = M c = (1 pt) (2 pts) (2 pts) PROBLEM 3B. (5 ponts) FIND: Determne the average shear stress n the 20 mm-dameter pn at A and the 30 mmdameter pn at B that supports beam AB. (τ Avg ) A = (3 pts) (τ Avg ) B = (2 pts)

6 NAME: PROBLEM 3C. (5 ponts) FIND: Beam AB rests on the two short posts (AC and BD). Post AC has a dameter of 20 mm and s made of steel. Determne the stress and stran n post AC f t s made of steel and has a dameter of 20 mm. Assume Esteel = 200 GPA. τ= (3 pts) ϵ= (2 pts) PROBLEM 3D. (5 ponts) FIND: Tube AB has an nner dameter or 80 mm and an outer dameter of 100 mm. Gven the torque appled n the dagram, determne the shear stress actng on the nner and outer walls of the tube. τouter = (3 pts) τnner = (2 pts)

7 NAME: PROBLEM 4 (25 ponts) GIVEN: Beam AB s loaded as shown. Assume the beam has a rectangular cross-secton of 50 mm wde and 100 mm hgh. FIND: a) Determne the reacton forces at supports A and B. (4 pts) b) Sketch the shear-force and bendng-moment dagrams. (6 pts) c) Determne the shear stress dstrbuton just to the rght of the B reacton. (5 pts) d) Determne the normal stress dstrbuton just to the rght of the B reacton. (5 pts)

8 NAME: V (kn) X (m) V (kn) X (m)

9 ME 270 Fnal Eam Equatons Sprng 2013 Normal Stress and Stran σ F A σ M I ε σ E L L ε ε ε ε ρ FS σ σ Shear Stress and Stran τ V A τρ Tρ J τ Gγ G E 21 γ δ L π 2 θ For a rectangular crosssecton, τ 6V h Ah 4 τ 3V 2A Second Area Moment I da I 1 12 bh Rectangle I π 4 r I I Ad Crcle Polar Area Moment J π 2 r r Tube Shear Force and Bendng Moment V V0 pd M M0 Vd Buoanc F =ρgv B Flud Statcs p=ρgh ( ) F = p Lw eq avg Belt Frcton T T L S = e µβ Dstrbuted Loads F eq F eq = L 0 = L ( ) w d 0 Centrods = = da c da ( ) w d A = c A = In 3D, = da c da A c A V c V Centers of Mass ɶ = ɶ = ρda cm ρda ɶ = ρa cm ρa ɶ = ρda cm ρda ρa cm ρa

10 Termnolog V Shear Force (ch 13) M Bendng Moment (ch 13) F Aal load (ch 13, 14) σ σ σ N Y U Normal Stress (ch 14) Yeld Strength Ultmate Strength ε Stran (aal or transverse) (ch 14) E Young's Modulus, or Modulus of Elastct (ch 14) υ Posson's Rato (ch 14) FS Factor of Safet (ch 14) τ Shear Stress (ch 15) γ Shear Stran (ch 15) G Shear Modulus (ch 15)

11 Sample Fnal Eam Answers 1A. T AB = 1500 N T AC = 2500 N 1B. F B = 15.3 lbs Reman the same 1C. F BC = 632 lbs Zero-Force Members: BF, DE, CD, EF, CE 1D. FBD 1E. P = 26.8 lbs Increase 2. T BC = 4.47 kn T BD = 4.90 kn A = j +8k kn 3A. C X = -300 lbs C = lb M c = lb-n ( ) = 34.0 MPa ( ) = 17.7 MPa 3B. AVG A AVG B 3C. = 191 MPa 4 = mm/mm 3D. outer = 0.345MPa nner = 0.276MPa 4. 2 = 960,000 ( ) = 1,920,000

12

I have not received unauthorized aid in the completion of this exam.

I have not received unauthorized aid in the completion of this exam. ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem

More information

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Fall 2012 Fnal Exam Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Fall 2013 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Group # Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space

More information

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng

More information

Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur

Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur Instructonal Objectves: At the end o ths lesson, the

More information

IDE 110 Mechanics of Materials Spring 2006 Final Examination FOR GRADING ONLY

IDE 110 Mechanics of Materials Spring 2006 Final Examination FOR GRADING ONLY Spring 2006 Final Examination STUDENT S NAME (please print) STUDENT S SIGNATURE STUDENT NUMBER IDE 110 CLASS SECTION INSTRUCTOR S NAME Do not turn this page until instructed to start. Write your name on

More information

and F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points)

and F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) ME 270 3 rd Sample inal Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) IND: In your own words, please state Newton s Laws: 1 st Law = 2 nd Law = 3 rd Law = PROBLEM

More information

ME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints

ME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 2 Dr.. zz Bazoune Chapter

More information

UNIVERSITY OF BOLTON RAK ACADEMIC CENTRE BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 2017/2018 FINITE ELEMENT AND DIFFERENCE SOLUTIONS

UNIVERSITY OF BOLTON RAK ACADEMIC CENTRE BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 2017/2018 FINITE ELEMENT AND DIFFERENCE SOLUTIONS OCD0 UNIVERSITY OF BOLTON RAK ACADEMIC CENTRE BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 07/08 FINITE ELEMENT AND DIFFERENCE SOLUTIONS MODULE NO. AME6006 Date: Wednesda 0 Ma 08 Tme: 0:00

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Please indicate your group number (If applicable) Circle Your Instructor s Name and Section: MWF 8:30-9:20 AM Prof. Kai Ming Li MWF 2:30-3:20 PM Prof. Fabio Semperlotti MWF 9:30-10:20 AM Prof. Jim Jones

More information

Chapter 12 Equilibrium & Elasticity

Chapter 12 Equilibrium & Elasticity Chapter 12 Equlbrum & Elastcty If there s a net force, an object wll experence a lnear acceleraton. (perod, end of story!) If there s a net torque, an object wll experence an angular acceleraton. (perod,

More information

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros

More information

DUE: WEDS FEB 21ST 2018

DUE: WEDS FEB 21ST 2018 HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant

More information

LAB 4: Modulus of elasticity

LAB 4: Modulus of elasticity LAB 4: Modulus of elastcty 1. Preparaton: modulus of elastcty (chapter15, p.79) Hook s law graphcal determnaton of modulus of elastcty (p.8) determnaton of modulus of elastcty n tenson and flexural stress

More information

Mechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total

Mechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total Mechanics of Materials MENG 70 Fall 00 Eam Time allowed: 90min Name. Computer No. Q.(a) Q. (b) Q. Q. Q.4 Total Problem No. (a) [5Points] An air vessel is 500 mm average diameter and 0 mm thickness, the

More information

V i Δ 1. Influence diagrams for beams can be constructed by applying a unit deformation at the beam location of Δ

V i Δ 1. Influence diagrams for beams can be constructed by applying a unit deformation at the beam location of Δ CE 33, Sprng 0 nfluence Lnes for eams and Frames / 7 An nfluence dagram for a truss represents the aal force of a partcular member due to a load at locaton. nfluence dagrams can be constructed for beams

More information

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,

More information

Strain Energy in Linear Elastic Solids

Strain Energy in Linear Elastic Solids Duke Unverst Department of Cv and Envronmenta Engneerng CEE 41L. Matr Structura Anass Fa, Henr P. Gavn Stran Energ n Lnear Eastc Sods Consder a force, F, apped gradua to a structure. Let D be the resutng

More information

Solution ME 323 EXAM #2 FALL SEMESTER :00 PM 9:30 PM Nov. 2, 2010

Solution ME 323 EXAM #2 FALL SEMESTER :00 PM 9:30 PM Nov. 2, 2010 Solution ME 33 EXAM # FALL SEMESTER 1 8: PM 9:3 PM Nov., 1 Instructions 1. Begin each problem in the space provided on the eamination sheets. If additional space is required, use the paper provided. Work

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please review the followg statement: I certify that I have not given unauthorized aid nor have I received aid the completion of this eam. Signature: INSTRUCTIONS Beg each problem the space provided on

More information

Problem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323

Problem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323 Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine

More information

Chaper 2: Stress in beams

Chaper 2: Stress in beams Chaper : Stress n eams FLEURE Beams suject to enng wll fle COPRESSON TENSON On the lower surface the eam s stretche lengthwse. Ths sujects t to tensle stress. N.A. N.A. s the neutral as On the upper surface

More information

ENGI 1313 Mechanics I

ENGI 1313 Mechanics I ENGI 11 Mechancs I Lecture 40: Center of Gravty, Center of Mass and Geometrc Centrod Shan Kenny, Ph.D., P.Eng. ssstant Professor Faculty of Engneerng and ppled Scence Memoral Unversty of Nefoundland spkenny@engr.mun.ca

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. If I detect cheating I will write a note on my exam and raise

More information

Solution: The strain in the bar is: ANS: E =6.37 GPa Poison s ration for the material is:

Solution: The strain in the bar is: ANS: E =6.37 GPa Poison s ration for the material is: Problem 10.4 A prismatic bar with length L 6m and a circular cross section with diameter D 0.0 m is subjected to 0-kN compressive forces at its ends. The length and diameter of the deformed bar are measured

More information

Tutorial #1 - CivE. 205 Name: I.D:

Tutorial #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 information

MTE 119 STATICS FINAL HELP SESSION REVIEW PROBLEMS PAGE 1 9 NAME & ID DATE. Example Problem P.1

MTE 119 STATICS FINAL HELP SESSION REVIEW PROBLEMS PAGE 1 9 NAME & ID DATE. Example Problem P.1 MTE STATICS Example Problem P. Beer & Johnston, 004 by Mc Graw-Hill Companies, Inc. The structure shown consists of a beam of rectangular cross section (4in width, 8in height. (a Draw the shear and bending

More information

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: Instructor s Name and Section: (Circle Your Section)

More information

INDETERMINATE STRUCTURES METHOD OF CONSISTENT DEFORMATIONS (FORCE METHOD)

INDETERMINATE STRUCTURES METHOD OF CONSISTENT DEFORMATIONS (FORCE METHOD) INETNTE STUTUES ETHO OF ONSISTENT EFOTIONS (FOE ETHO) If all the support reactons and nternal forces (, Q, and N) can not be determned by usng equlbrum equatons only, the structure wll be referred as STTIY

More information

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

More information

One Dimensional Axial Deformations

One Dimensional Axial Deformations One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The -as s taken as the

More information

ME 323 Examination #2 April 11, 2018

ME 323 Examination #2 April 11, 2018 ME 2 Eamination #2 April, 2 PROBLEM NO. 25 points ma. A thin-walled pressure vessel is fabricated b welding together two, open-ended stainless-steel vessels along a 6 weld line. The welded vessel has an

More information

1. Please complete the following short problems.

1. Please complete the following short problems. Name 1. Please complete the following short problems. For parts 1A and 1B, we will consider three M88 recovery vehicles pulling an M1 tank back onto the road as shown below. F2 F1 50 M88 #1 50 M88 #2 y

More information

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. NAME: ME 270 Fall 2012 Examination No. 3 - Makeup Please review the following statement: Group No.: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

More information

Solution: The moment of inertia for the cross-section is: ANS: ANS: Problem 15.6 The material of the beam in Problem

Solution: The moment of inertia for the cross-section is: ANS: ANS: Problem 15.6 The material of the beam in Problem Problem 15.4 The beam consists of material with modulus of elasticity E 14x10 6 psi and is subjected to couples M 150, 000 in lb at its ends. (a) What is the resulting radius of curvature of the neutral

More information

Indeterminate pin-jointed frames (trusses)

Indeterminate pin-jointed frames (trusses) Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all

More information

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary

More information

ME 323 FINAL EXAM FALL SEMESTER :00 PM 9:00 PM Dec. 16, 2010

ME 323 FINAL EXAM FALL SEMESTER :00 PM 9:00 PM Dec. 16, 2010 ME 33 FINA EXAM FA SEMESTER 1 7: PM 9: PM Dec. 16, 1 Instructions 1. Begin each problem in the space provided on the eamination sheets. If additional space is required, use the paper provided. Work on

More information

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp. Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -

More information

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 2 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:

More information

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology,

More information

Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004

Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004 Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a

More information

MODELLING OF ELASTO-STATICS OF POWER LINES BY NEW COMPOSITE BEAM FINITE ELEMENT Bratislava

MODELLING OF ELASTO-STATICS OF POWER LINES BY NEW COMPOSITE BEAM FINITE ELEMENT Bratislava ODING OF ASTO-STATICS OF POW INS BY NW COPOSIT BA FINIT NT urín Justín 1 rabovský Jura 1 Gogola oman 1 utš Vladmír 1 Paulech Jura 1 1 Insttute of Automotve echatroncs FI STU n Bratslava Ilkovčova 3 812

More information

INTRODUCTION TO STRAIN

INTRODUCTION TO STRAIN SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,

More information

Eng Sample Test 4

Eng Sample Test 4 1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having

More information

Application to Plane (rigid) frame structure

Application to Plane (rigid) frame structure Advanced Computatonal echancs 18 Chapter 4 Applcaton to Plane rgd frame structure 1. Dscusson on degrees of freedom In case of truss structures, t was enough that the element force equaton provdes onl

More information

FUZZY FINITE ELEMENT METHOD

FUZZY FINITE ELEMENT METHOD FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments

More information

The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by

The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by Unit 12 Centroids Page 12-1 The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by (12-5) For the area shown

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

More information

. You need to do this for each force. Let s suppose that there are N forces, with components ( N) ( N) ( N) = i j k

. You need to do this for each force. Let s suppose that there are N forces, with components ( N) ( N) ( N) = i j k EN3: Introducton to Engneerng and Statcs Dvson of Engneerng Brown Unversty 3. Resultant of systems of forces Machnes and structures are usually subected to lots of forces. When we analyze force systems

More information

University of Pretoria Department of Mechanical & Aeronautical Engineering MOW 227, 2 nd Semester 2014

University of Pretoria Department of Mechanical & Aeronautical Engineering MOW 227, 2 nd Semester 2014 Universit of Pretoria Department of Mechanical & Aeronautical Engineering MOW 7, nd Semester 04 Semester Test Date: August, 04 Total: 00 Internal eaminer: Duration: hours Mr. Riaan Meeser Instructions:

More information

ME325 EXAM I (Sample)

ME325 EXAM I (Sample) ME35 EXAM I (Sample) NAME: NOTE: COSED BOOK, COSED NOTES. ONY A SINGE 8.5x" ORMUA SHEET IS AOWED. ADDITIONA INORMATION IS AVAIABE ON THE AST PAGE O THIS EXAM. DO YOUR WORK ON THE EXAM ONY (NO SCRATCH PAPER

More information

Equilibrium of Rigid Bodies

Equilibrium of Rigid Bodies Equilibrium of Rigid Bodies 1 2 Contents Introduction Free-Bod Diagram Reactions at Supports and Connections for a wo-dimensional Structure Equilibrium of a Rigid Bod in wo Dimensions Staticall Indeterminate

More information

Cover sheet and Problem 1

Cover sheet and Problem 1 over sheet and Problem nstructions M 33 FNL M FLL SMSTR 0 Time allowed: hours. There are 4 problems, each problem is of equal value. The first problem consists of three smaller sub-problems. egin each

More information

[5] Stress and Strain

[5] Stress and Strain [5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law

More information

Influence diagrams for beams can be constructed by applying a unit deformation at the beam location of. P x. Note: slopes of segments are equal

Influence diagrams for beams can be constructed by applying a unit deformation at the beam location of. P x. Note: slopes of segments are equal rdge esgn Revew of nfluence Lnes / 7 Sprng 0 nfluence dagrams can be constructed for beams for three types of forces : a) a partcular reacton b) the shear at a partcular locaton n the beam c) the bendng

More information

σ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit)

σ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit) PROBLEM #1.1 (4 + 4 points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length

More information

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [2910601] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I.

More information

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure.

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure. CE 331, Fall 2010 Influence Les for Trusses 1 / 7 An fluence le shows how the force a partcular member changes as a concentrated load s moved along the structure. For eample, say we are desgng the seven

More information

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding. Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays

More information

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

More information

FINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION

FINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION VOL. 6, NO. 3, MARCH 0 ISSN 89-6608 006-0 Asan Research Publshng Network (ARPN). All rghts reserved. FINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION Adel A. Al-Azzaw and Al S. Shaker

More information

Question 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H

Question 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H Question 1 (Problem 2.3 of rora s Introduction to Optimum Design): Design a beer mug, shown in fig, to hold as much beer as possible. The height and radius of the mug should be not more than 20 cm. The

More information

Equilibrium of a Rigid Body. Engineering Mechanics: Statics

Equilibrium of a Rigid Body. Engineering Mechanics: Statics Equilibrium of a Rigid Body Engineering Mechanics: Statics Chapter Objectives Revising equations of equilibrium of a rigid body in 2D and 3D for the general case. To introduce the concept of the free-body

More information

Torsion of Shafts Learning objectives

Torsion of Shafts Learning objectives Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

More information

Outline. Organization. Stresses in Beams

Outline. Organization. Stresses in Beams Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of

More information

SCREWS, FASTENERS AND NON PERMANENT JOINTS 2 MOW Department of Mechanical and Aeronautical Engineering

SCREWS, FASTENERS AND NON PERMANENT JOINTS 2 MOW Department of Mechanical and Aeronautical Engineering SCREWS, ASTENERS AND NON PERMANENT JOINTS 2 MOW 227 2014 Yeldng take place n the frst thread wth cold work strengthenng Never re-use nuts n structural connectons because ther thread gets daaged Washers

More information

Please initial the statement below to show that you have read it

Please initial the statement below to show that you have read it EN0: Structural nalyss Exam I Wednesday, March 2, 2005 Dvson of Engneerng rown Unversty NME: General Instructons No collaboraton of any nd s permtted on ths examnaton. You may consult your own wrtten lecture

More information

Axial Turbine Analysis

Axial Turbine Analysis Axal Turbne Analyss From Euler turbomachnery (conservaton) equatons need to Nole understand change n tangental velocty to relate to forces on blades and power m W m rc e rc uc uc e Analye flow n a plane

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the

More information

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5 BTECH MECHANICAL PRINCIPLES AND APPLICATIONS Level 3 Unit 5 FORCES AS VECTORS Vectors have a magnitude (amount) and a direction. Forces are vectors FORCES AS VECTORS (2 FORCES) Forces F1 and F2 are in

More information

P.E. Civil Exam Review:

P.E. Civil Exam Review: P.E. Civil Exam Review: Structural Analysis J.P. Mohsen Email: jpm@louisville.edu Structures Determinate Indeterminate STATICALLY DETERMINATE STATICALLY INDETERMINATE Stability and Determinacy of Trusses

More information

σ τ τ τ σ τ τ τ σ Review Chapter Four States of Stress Part Three Review Review

σ τ τ τ σ τ τ τ σ Review Chapter Four States of Stress Part Three Review Review Chapter Four States of Stress Part Three When makng your choce n lfe, do not neglect to lve. Samuel Johnson Revew When we use matrx notaton to show the stresses on an element The rows represent the axs

More information

6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads.

6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads. 6.6 FRAMES AND MACHINES APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a

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

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

2. Trusses and bars in axial load Contents

2. Trusses and bars in axial load Contents 2. Trusses and bars in axial load Contents 2. Trusses and bars in axial load... 1 2.1 Introduction... 2 2.2 Physics re-cap: spring mechanics... 3 2.3 Statics: Equilibrium of internal and external forces

More information

SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 2 EXAMINATIONS 2011/2012 DYNAMICS ME247 DR. N.D.D. MICHÉ

SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 2 EXAMINATIONS 2011/2012 DYNAMICS ME247 DR. N.D.D. MICHÉ s SCHOOL OF COMPUTING, ENGINEERING ND MTHEMTICS SEMESTER EXMINTIONS 011/01 DYNMICS ME47 DR. N.D.D. MICHÉ Tme allowed: THREE hours nswer: ny FOUR from SIX questons Each queston carres 5 marks Ths s a CLOSED-BOOK

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

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15 NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

More information

Name (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM

Name (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Name (Print) (Last) (First) Instructions: ME 323 - Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Circle your lecturer s name and your class meeting time. Gonzalez Krousgrill

More information

5. What is the moment of inertia about the x - x axis of the rectangular beam shown?

5. What is the moment of inertia about the x - x axis of the rectangular beam shown? 1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Group Number: Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem

More information

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Examination No. 2 Please review the following statement: Group Number: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin

More information

2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft

2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft Code No: 07A62102 R07 Set No. 2 III B.Tech II Semester Regular/Supplementary Examinations,May 2010 Aerospace Vehicle Structures -II Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE

More information

M. Vable Mechanics of Materials: Chapter 5. Torsion of Shafts

M. Vable Mechanics of Materials: Chapter 5. Torsion of Shafts Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

More information

Spring 2002 Lecture #13

Spring 2002 Lecture #13 44-50 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallel-as Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the md-term

More information