DESIGN OF BEAMS AND SHAFTS

Size: px
Start display at page:

Download "DESIGN OF BEAMS AND SHAFTS"

Transcription

1 DESIGN OF EAMS AND SHAFTS! asis for eam Design! Stress Variations Throughout a Prismatic eam! Design of pristmatic beams! Steel beams! Wooden beams! Design of Shaft! ombined bending! Torsion 1

2 asis for eam Design - The effects of an internal axial force are often neglected in design. - Application of shear and flexure formulas are limited to beams made of a homogeneous material that has linear-elastic behavior. - The cross-sectional area must have an axis of symmetry in the plane of the loading. - The design does provide an adequate means of obtaining both a safe and economical design. 2

3 Stress Variations Throughout a Prismatic eam P w A R A - 2 m 2 m R V M R A R A R A - P - M max x -R x V M τ 4 τ 3 τ 2 Shear stress distribution (τ) σ 5 σ 4 σ 5 σ 2 ending stress distribution (σ) 3

4 V M τ 4 τ 3 τ 2 τ max σ 5 σ 4 τ σ 2 σ 5 5 y x σ 5 σ 1 x (-σ 5, 0) σ 2 σ y (0, 0) 4 y x σ 4 x (-σ 4, τ 4 ) σ 1 τ max τ max τ σ 2 σ τ 4 τ max τ y (0, -τ 4 ) x (0, τ 3 ) 3 y x σ 1 σ 2 σ τ 3 y (0, -τ 3 ) 4

5 V M σ 5 τ 4 σ 4 τ 3 τ 2 2 σ1σ τ τ max x (σ 2, τ 2 ) 2 y x σ 2 σ 1 σ 2 σ τ 2 y (0, -τ 2 ) τ max τ τ max 1 y x σ 1 σ 1 y (0, 0) σ 2 σ x (σ 1, 0) τ max 5

6 Prismatic eam Design Section Modulus (S) σ Mc I M I / c M S S req' d M σ allow 6

7 Example 1 A beam is to be made of steel that has an allowable bending stress of σ allow 150 MPa and an allowable shear stress of τ allow 100 MPa. Select an appropriate W shape that will carry the loading shown. 200 kn 100 kn 2 m 2 m 2 m 7

8 200 kn 100 kn 50 kn 250 kn 2 m 2 m 2 m V(kN) 50 M(kN m) x(m) x (m) Allowable normal stress: σ allow 150 MPa σ S req d M S M σ allow (200x10 3 ) 1333x10 3 mm 3 150x10 6 Using the table in Appendix, the following beams are adequate: W 610x82 S 1870x10 3 mm 3 W 460x97 S 1910x10 3 mm 3 W 460x89 S 1770x10 3 mm 3 W 460x82 S 1610x10 3 mm 3 W 460x74 S 1460x10 3 mm 3 W 410x85 S 1510x10 3 mm 3 Use W 460x74 because the beam having the least weight. 8

9 200 kn 100 kn W 460x74 : A 9460 mm 2, d 457 mm, t w 9.02 mm, b f 190 mm, t f 14.5 mm, I 333x10 6 mm 4, 50 kn 250 kn 2 m 2 m 2 m V(kN) x(m) heck allowable shear stress: τ allow 100 MPa Q (221.25)(190x14.5) (214/2)(214x9.02) τ max x10-6 m 3 VQ It V(816.08x10-6 ) (333x10-6 )( ) 32.6 MPa <100 MPa, O.K V (271.7 )(150x10 3 ) 9

10 200 kn 100 kn heck shear and normal stress at 50 kn 250 kn 2 m 2 m 2 m 200 kn m σ max MPa τ max V(kN) 50 M(kN m) MPa MPa kn Β x(m) σ, MPa τ I 333x10 6 mm 4 x (m) - ending: σ σ - Shear: τ τ My V max Q It (150x10 3 )[(0.2213)(0.19x0.0145)] (333x10-6 )( ) I σ τ (-200x10 3 )(0.214) (333x10-6 ) MPa Q MPa 10

11 30.44 MPa y x MPa σ average σ x σ y MPa 2 2 R σ x - σ y ( ) (τ xy ) 2 2 (64.27) 2 (30.44) 2 ± MPa σ avg MPa (-64.27, 71.11) τ σ - R average (-135.4, 0) 2 (-128.5, ) x R O y (0, 30.44) 1 (6.84, 0) σ σ average R τ max MPa < 100 MPa, O.K. σ max MPa < 150 MPa, O.K. (-64.27, ) (σ x - σ y )/2 (-128.5)/

12 omments Q ya Q (221.25)(190x14.5) (214/2)(214x9.02) mm x10-6 m τ max VQ It V(816.08x10-6 ) (333x10-6 )( ) 271.7V τ avg V max A web V ( x0.0145)( ) V 4.7 % off τ avg V max A web V (0.457)( ) V 10.7 % off Note: dimension in mm I 333x10 6 mm 4, 12

13 Example 2 The laminated wooden beam shown supports a uniform distributed loading of 12 kn/m. If the beam is to have a height-to-width ratio of 1.5, determine its smallest width. The allowable bending stress is σ allow 9 MPa and the allowable shear stress is τ allow 0.6 MPa. Neglect the weight of the beam. 12 kn/m 1.5a A 1 m 3 m a 13

14 12 kn/m A 1 m 32 kn 3 m V (kn) M (kn m) 16 kn a x 0 x1.33 m x (m) a heck allowable shear stress τ allow 0.6 MPa VQ τ It V τ 1.5 A 20x10 0.6x (a 2 ) a m 183 mm - x (m) Use a 185 mm -6 14

15 12 kn/m A 1 m 32 kn 3 m V (kn) kn x 0 1.5a a 185 mm heck allowable normal stress σ allow 9 MPa x1.33 m x(m) σ max Mc I (10.67x10 3 )(278/2) (1/12)(185)(278 3 ) M (kn m) 4.48 MPa MPa < 9 MPa, O.K. - x (m) Use a 185 mm -6 15

16 Example 3 The wooden T-beam shown is made from two x 30 mm boards. If the allowable bending stress is σ allow 12 MPa and the allowable shear stress is τ allow 0.8 MPa, determine if the beam can safely support the loading shown without having the deflection more than L/240. The spacing of nails specified to hold the two boards together if each nail can resist 1.50 kn in shear are: between use 125 mm, and D use 250 mm. Take E 12 GPa, and the formula for deflection at the the mid-span: 4 3 5wL PL υ ( ) 768EI 48EI w0.5 kn/m P1.5 kn 30 mm 2 m 2 m D 30 mm 16

17 0.5 kn/m 1.5 kn 1.5 kn 2 m 2 m V (kn) 1.5 D 1 kn x (m) M (kn m) 2.0 x (m) 17

18 Section property y ' y 30 mm y ya A (100 )( ) (215 )( 200 2( ) 30 ) 30 mm mm y ' mm I Σ ( I Ad 2 ) ( I Ad 2 ) ( I Ad 2 ) web flang [(1/12)(30)(200 3 ) (30x200)( ) 2 ] [(1/12)(200)(30 3 ) (200x30)( ) 2 ] x10 6 mm x10-6 m 4 18

19 0.5 kn/m 1.5 kn - Stress distribution at point 1.5 kn 2 m 2 m D 1 kn V (kn) kn τ -, MPa (60.12x10-6 )(0.03) x(m) heck allowable shear stress: τ allow 0.8 MPa τ max V max Q It (1.5x10 3 )[( )(0.03x0.1575)] MPa MPa < 0.8 MPa, O.K. 30 I 60.12x10-6 m 4 19

20 0.5 kn/m 1.5 kn - Stress distribution at point 1.5 kn 2 m 2 m M(kN m) 2.0 D 1 kn x (m) 20 kn m kn τ, MPa 5.24 σ, MPa 200 heck allowable normal stress: σ allow 12 MPa σ max Mc I (2x103 )(0.1575) (60.12x10-6 ) kn m 5.24 MPa 5.24 MPa < 12 MPa, O.K. 30 I 60.12x10-6 m 4 20

21 w0.5 kn/m P1.5 kn υ L 4 5wL 768EI 1.5 k N L/22 m L/22 m 3 PL ( ) 48EI D kn I 60.12x10-6 m 4 heck maximum deflection: υ allow L/240 υ L 4 5wL 768EI 3 PL ) ( 48EI 4 5(.5)4 ) 9 768(12 10 )( m, ( ) < ) 3 (1.5)4 9 48(12 10 )( ( m, O. K. ) ) 21

22 0.5 kn/m 1.5 kn 1.5 kn 2 m 2 m V(kN) x(m) I x10-6 m 4 Nail spacing: s 125 mm, and s D 250 mm; (F s ) allow 1.5 kn - Segment D 1 kn F nail τa shear VQ ( It ) 200 (s x0.03) τ -, MPa τ F nail (1.5x10 3 )[(0.0575)(0.2x0.03)] (0.125x0.03) (60.12x10-6 )(0.03) kn < 1.5 kn, O.K. 22

23 0.5 kn/m 1.5 kn 1.5 kn 2 m 2 m - Segment D D 1 kn V (kn) 1 m x(m) I x10-6 m 4 Nail spacing: s 125 mm, and s D 250 mm; (F s ) allow 1.5 kn F nail τa shear VQ ( It ) 200 (s D x0.03) τ -, MPa τ F nail (1x10 3 )(0.0575)(0.2x0.03) (60.12x10-6 )(0.03) (0.25x0.03) kn < 1.5 kn, O.K. 23

24 Example 4 From the beam shown, determine the largest load P that can be applied to the beam. Requirements specified: σ allow 12 MPa τ allow 0.8 MPa Nail 150 mm φ 3 mm τ allow 200 MPa P 2 m 2 m D 72.5 mm 30 mm mm I 60.12x10-6 mm 4 24

25 V (N) M (N m) P P/2 2 m 2 m P/2 P/2 -P/2 P 30 mm 72.5 mm D P/ mm I x10-6 mm 4 x (m) -P/2 x (m) Q neck A neck y 30 ( )(72.5 ) m Maximum shear force on Nail: Nail 150 mm, φ 3 mm, τ allow 200 MPa F s (τ allow ) nail (A nail ) (200x10 6 )(πx ) 1414 N VQ 1414 ( )( t s) It P ( )(0.345) )(0.150) 6 ( ) P 3286 N 25

26 V (N) M (N m) P 2 m 2 m P/2 P/2 -P/2 P 30 mm 72.5 mm D mm I x10-6 mm 4 x (m) -P/2 x (m) Q max A max y ( )( ) m ending: σ allow 12 MPa Shear : τ allow 0.8 MPa σ Mc I P(0.1575) P 4580 N VQ τ It P 3 ( )( ) ( )(0.03) 0 6 P 3879 N 26

27 σ allow 12 MPa τ allow 0.8 MPa Nail 150 mm φ 3 mm τ allow 200 MPa P 2 m 2 m D Summary: Nail, shear 3.28 kn, use 3 kn eam, bending 4.58 kn eam, shear 3.88 kn 27

28 Example 5 From the beam shown, determine the largest load w that can be applied to the beam. onditions specified: Wood σ allow 12 MPa in tension σ allow 8 MPa in compression τ allow 0.8 MPa For each nail, (F nail ) allow mm spacing w 72.5 mm 30 mm 4 m 2 m D mm I 60.12x10-6 mm 4 28

29 w 1.5w 4 m 4.5w 2 m D 72.5 mm mm 30 mm M (N m) 1.125w I 60.12x10-6 mm 4 x (m) -2w eam : ending : σ allow 12 MPa in tension, σ allow 8 MPa in compression - ompression - Tension 6 (2w)(0.1575) 6 ( w)( ) w kn/m w kn/m 6 (1.125w)(0.725) (2w)(0.725) w kn/m w kn/m 29

30 w 1.5w 4 m 4.5w 2 m D 72.5 mm mm 30 mm V (N) 1.5w 2 w I 60.12x10-6 mm 4 x (m) M (N m) 1.125w -2.5w x (m) -2w eam: τ allow 0.8 MPa VQ τ It (2.5w)( ) ( )(0.03) w 1.55 kn/m Shear on nail : (F nail ) allow 1.5 kn spacing 100 mm VQ F s (τ allow ) nail (A s ) ( )( t s) It (2.5w)( ) 1.5 ( t)(0.1) 6 ( )( t) w 1.04 kn/m 30

31 σ allow 12 MPa in tension σ allow 8 MPa in compression τ allow 0.8 MPa (F nail ) allow 1.5 kn Nail spacing 100 mm w 4 m 2 m D Summary: eam bending, compression 1.53 kn/m tension 4.07 kn/m eam shear, 1.55 kn/m Nail shear 1.04 kn/m, use 1 kn/m 31

Chapter Objectives. Design a beam to resist both bendingand shear loads

Chapter Objectives. Design a beam to resist both bendingand shear loads Chapter Objectives Design a beam to resist both bendingand shear loads A Bridge Deck under Bending Action Castellated Beams Post-tensioned Concrete Beam Lateral Distortion of a Beam Due to Lateral Load

More information

Stress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 4 ME 76 Spring 017-018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a

More information

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

More information

UNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 6 Shearing Stress in Beams & Thin-Walled Members

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 6 Shearing Stress in Beams & Thin-Walled Members EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 6 Shearing Stress in Beams & Thin-Walled Members Beams Bending & Shearing EMA 3702 Mechanics & Materials Science Zhe Cheng (2018)

More information

Use Hooke s Law (as it applies in the uniaxial direction),

Use Hooke s Law (as it applies in the uniaxial direction), 0.6 STRSS-STRAIN RLATIONSHIP Use the principle of superposition Use Poisson s ratio, v lateral longitudinal Use Hooke s Law (as it applies in the uniaxial direction), x x v y z, y y vx z, z z vx y Copyright

More information

[8] Bending and Shear Loading of Beams

[8] Bending and Shear Loading of Beams [8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight

More information

CHAPTER 4. Stresses in Beams

CHAPTER 4. Stresses in Beams CHAPTER 4 Stresses in Beams Problem 1. A rolled steel joint (RSJ) of -section has top and bottom flanges 150 mm 5 mm and web of size 00 mm 1 mm. t is used as a simply supported beam over a span of 4 m

More information

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar 5.10 Examples 5.10.1 Analysis of effective section under compression To illustrate the evaluation of reduced section properties of a section under axial compression. Section: 00 x 80 x 5 x 4.0 mm Using

More information

7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses

7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses 7 TRANSVERSE SHEAR Before we develop a relationship that describes the shear-stress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within

More information

= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200

= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200 Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength

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

2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C

2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C CE-1259, Strength of Materials UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS Part -A 1. Define strain energy density. 2. State Maxwell s reciprocal theorem. 3. Define proof resilience. 4. State Castigliano

More information

QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS

QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,

More information

Mechanics of Solids I. Transverse Loading

Mechanics of Solids I. Transverse Loading Mechanics of Solids I Transverse Loading Introduction o Transverse loading applied to a beam results in normal and shearing stresses in transverse sections. o Distribution of normal and shearing stresses

More information

Mechanics of Structure

Mechanics of Structure S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI

More information

Symmetric Bending of Beams

Symmetric Bending of Beams Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications

More information

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State

More information

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd Chapter Objectives To generalize the procedure by formulating equations that can be plotted so that they describe the internal shear and moment throughout a member. To use the relations between distributed

More information

JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER:

JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name: Tutorial class day & time: SPRING

More information

Samantha Ramirez, MSE

Samantha Ramirez, MSE Samantha Ramirez, MSE Centroids The centroid of an area refers to the point that defines the geometric center for the area. In cases where the area has an axis of symmetry, the centroid will lie along

More information

STRESS. Bar. ! Stress. ! Average Normal Stress in an Axially Loaded. ! Average Shear Stress. ! Allowable Stress. ! Design of Simple Connections

STRESS. Bar. ! Stress. ! Average Normal Stress in an Axially Loaded. ! Average Shear Stress. ! Allowable Stress. ! Design of Simple Connections STRESS! Stress Evisdom! verage Normal Stress in an xially Loaded ar! verage Shear Stress! llowable Stress! Design of Simple onnections 1 Equilibrium of a Deformable ody ody Force w F R x w(s). D s y Support

More information

Made by SMH Date Aug Checked by NRB Date Dec Revised by MEB Date April 2006

Made by SMH Date Aug Checked by NRB Date Dec Revised by MEB Date April 2006 Job No. OSM 4 Sheet 1 of 8 Rev B Telephone: (0144) 45 Fax: (0144) 944 Made b SMH Date Aug 001 Checked b NRB Date Dec 001 Revised b MEB Date April 00 DESIGN EXAMPLE 9 - BEAM WITH UNRESTRAINED COMPRESSION

More information

Strength of Materials II (Mechanics of Materials) (SI Units) Dr. Ashraf Alfeehan

Strength of Materials II (Mechanics of Materials) (SI Units) Dr. Ashraf Alfeehan Strength of Materials II (Mechanics of Materials) (SI Units) Dr. Ashraf Alfeehan 2017-2018 Mechanics of Material II Text Books Mechanics of Materials, 10th edition (SI version), by: R. C. Hibbeler, 2017

More information

Beam Design and Deflections

Beam Design and Deflections Beam Design and Deflections tation: a = name for width dimension A = name for area Areq d-adj = area required at allowable stress when shear is adjusted to include self weight Aweb = area of the web of

More information

SSC-JE MAINS ONLINE TEST SERIES / CIVIL ENGINEERING SOM + TOS

SSC-JE MAINS ONLINE TEST SERIES / CIVIL ENGINEERING SOM + TOS SSC-JE MAINS ONLINE TEST SERIES / CIVIL ENGINEERING SOM + TOS Time Allowed:2 Hours Maximum Marks: 300 Attention: 1. Paper consists of Part A (Civil & Structural) Part B (Electrical) and Part C (Mechanical)

More information

NAME: Given Formulae: Law of Cosines: Law of Sines:

NAME: Given Formulae: Law of Cosines: Law of Sines: NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial : IG1_CE_G_Concrete Structures_100818 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: E-mail: info@madeeasy.in Ph: 011-451461 CLASS TEST 018-19 CIVIL ENGINEERING

More information

6. Bending CHAPTER OBJECTIVES

6. Bending CHAPTER OBJECTIVES CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where

More information

Mechanics of Materials CIVL 3322 / MECH 3322

Mechanics of Materials CIVL 3322 / MECH 3322 Mechanics of Materials CIVL 3322 / MECH 3322 2 3 4 5 6 7 8 9 10 A Quiz 11 A Quiz 12 A Quiz 13 A Quiz 14 A Quiz 15 A Quiz 16 In Statics, we spent most of our time looking at reactions at supports Two variations

More information

National Exams May 2015

National Exams May 2015 National Exams May 2015 04-BS-6: Mechanics of Materials 3 hours duration Notes: If doubt exists as to the interpretation of any question, the candidate is urged to submit with the answer paper a clear

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

FLOW CHART FOR DESIGN OF BEAMS

FLOW CHART FOR DESIGN OF BEAMS FLOW CHART FOR DESIGN OF BEAMS Write Known Data Estimate self-weight of the member. a. The self-weight may be taken as 10 percent of the applied dead UDL or dead point load distributed over all the length.

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

PES Institute of Technology

PES Institute of Technology PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject

More information

CHAPTER 6: Shearing Stresses in Beams

CHAPTER 6: Shearing Stresses in Beams (130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.

More information

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly .3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.

D : 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 information

Advanced Structural Analysis EGF Section Properties and Bending

Advanced Structural Analysis EGF Section Properties and Bending Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear

More information

2014 MECHANICS OF MATERIALS

2014 MECHANICS OF MATERIALS R10 SET - 1 II. Tech I Semester Regular Examinations, March 2014 MEHNIS OF MTERILS (ivil Engineering) Time: 3 hours Max. Marks: 75 nswer any FIVE Questions ll Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~

More information

Module 2 Stresses in machine elements. Version 2 ME, IIT Kharagpur

Module 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 information

Application nr. 3 (Ultimate Limit State) Resistance of member cross-section

Application nr. 3 (Ultimate Limit State) Resistance of member cross-section Application nr. 3 (Ultimate Limit State) Resistance of member cross-section 1)Resistance of member crosssection in tension Examples of members in tension: - Diagonal of a truss-girder - Bottom chord of

More information

needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns.

needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns. CHAPTER OBJECTIVES Discuss the behavior of columns. Discuss the buckling of columns. Determine the axial load needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods

More information

Question 1. Ignore bottom surface. Problem formulation: Design variables: X = (R, H)

Question 1. Ignore bottom surface. Problem formulation: Design variables: X = (R, H) Question 1 (Problem 2.3 of Arora 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

This procedure covers the determination of the moment of inertia about the neutral axis.

This procedure covers the determination of the moment of inertia about the neutral axis. 327 Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the T-beam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination

More information

MECE 3321: Mechanics of Solids Chapter 6

MECE 3321: Mechanics of Solids Chapter 6 MECE 3321: Mechanics of Solids Chapter 6 Samantha Ramirez Beams Beams are long straight members that carry loads perpendicular to their longitudinal axis Beams are classified by the way they are supported

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

Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are

Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are very small,

More information

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the

More information

UNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2

UNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 UNIT-I STRESS, STRAIN 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 Young s modulus E= 2 x10 5 N/mm 2 Area1=900mm 2 Area2=400mm 2 Area3=625mm

More information

mportant nstructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may

More information

CIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:

CIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR: MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine

More information

Sub. Code:

Sub. Code: Important Instructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may

More information

,. 'UTIS. . i. Univcnity of Technology, Sydney TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE.

,. 'UTIS. . i. Univcnity of Technology, Sydney TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. ,. 'UTIS. i,i I Univcnity of Technology, Sydney TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name:

More information

CHAPTER 4: BENDING OF BEAMS

CHAPTER 4: BENDING OF BEAMS (74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are

More information

Review 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 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 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

Design of Beams (Unit - 8)

Design of Beams (Unit - 8) Design of Beams (Unit - 8) Contents Introduction Beam types Lateral stability of beams Factors affecting lateral stability Behaviour of simple and built - up beams in bending (Without vertical stiffeners)

More information

Homework 6.1 P = 1000 N. δ δ δ. 4 cm 4 cm 4 cm. 10 cm

Homework 6.1 P = 1000 N. δ δ δ. 4 cm 4 cm 4 cm. 10 cm Homework 6.1 Three thick and wide boards are connected together by two parallel rows of uniformly distributed nails separated by longitude distance δ to form a beam that is subject to constant vertical

More information

Chapter 7: Internal Forces

Chapter 7: Internal Forces Chapter 7: Internal Forces Chapter Objectives To show how to use the method of sections for determining the internal loadings in a member. To generalize this procedure by formulating equations that can

More information

Name :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS

Name :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers

More information

Structural Steelwork Eurocodes Development of A Trans-national Approach

Structural Steelwork Eurocodes Development of A Trans-national Approach Structural Steelwork Eurocodes Development of A Trans-national Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads

More information

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)? IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at

More information

ME 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 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 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

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are

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

SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling.

SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. Find: Determine the value of the critical speed of rotation for the shaft. Schematic and

More information

FIXED BEAMS IN BENDING

FIXED BEAMS IN BENDING FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)

More information

CIV E 205 Mechanics of Solids II. Course Notes

CIV E 205 Mechanics of Solids II. Course Notes Department of Civil Engineering CIV E 205 Mechanics of Solids II Instructor: Tarek Hegazi Email: tarek@uwaterloo.ca Course Notes Mechanics of Materials Objectives: - Solve Problems in a structured systematic

More information

CIV100 Mechanics. Module 5: Internal Forces and Design. by: Jinyue Zhang. By the end of this Module you should be able to:

CIV100 Mechanics. Module 5: Internal Forces and Design. by: Jinyue Zhang. By the end of this Module you should be able to: CIV100 Mechanics Module 5: Internal Forces and Design by: Jinyue Zhang Module Objective By the end of this Module you should be able to: Find internal forces of any structural members Understand how Shear

More information

STRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains

STRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains STRENGTH OF MATERIALS-I Unit-1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between

More information

Beams. Beams are structural members that offer resistance to bending due to applied load

Beams. Beams are structural members that offer resistance to bending due to applied load Beams Beams are structural members that offer resistance to bending due to applied load 1 Beams Long prismatic members Non-prismatic sections also possible Each cross-section dimension Length of member

More information

PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK

PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM - 613 403 - THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310

More information

Determine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.

Determine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a. E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct

More information

71- Laxmi Nagar (South), Niwaru Road, Jhotwara, Jaipur ,India. Phone: Mob. : /

71- Laxmi Nagar (South), Niwaru Road, Jhotwara, Jaipur ,India. Phone: Mob. : / www.aarekh.com 71- Laxmi Nagar (South), Niwaru Road, Jhotwara, Jaipur 302 012,India. Phone: 0141-2348647 Mob. : +91-9799435640 / 9166936207 1. Limiting values of poisson s ratio are (a) -1 and 0.5 (b)

More information

2012 MECHANICS OF SOLIDS

2012 MECHANICS OF SOLIDS R10 SET - 1 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~

More information

3. BEAMS: STRAIN, STRESS, DEFLECTIONS

3. BEAMS: STRAIN, STRESS, DEFLECTIONS 3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets

More information

Entrance exam Master Course

Entrance exam Master Course - 1 - Guidelines for completion of test: On each page, fill in your name and your application code Each question has four answers while only one answer is correct. o Marked correct answer means 4 points

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

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

Job No. Sheet 1 of 7 Rev A. Made by ER/EM Date Feb Checked by HB Date March 2006

Job No. Sheet 1 of 7 Rev A. Made by ER/EM Date Feb Checked by HB Date March 2006 Job No. Sheet of 7 Rev A Design Example Design of a lipped channel in a Made by ER/EM Date Feb 006 Checked by HB Date March 006 DESIGN EXAMPLE DESIGN OF A LIPPED CHANNEL IN AN EXPOSED FLOOR Design a simply

More information

QUESTION BANK. SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I

QUESTION BANK. SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I QUESTION BANK DEPARTMENT: CIVIL SEMESTER: V SUBJECT CODE / Name: CE 6501 / STRUCTURAL ANALYSIS-I Unit 5 MOMENT DISTRIBUTION METHOD PART A (2 marks) 1. Differentiate between distribution factors and carry

More information

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3. ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on

More information

The University of Melbourne Engineering Mechanics

The University of Melbourne Engineering Mechanics The University of Melbourne 436-291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 9-22 from Hibbeler - Statics and Mechanics of Materials) A short

More information

8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method

8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method The basis for the method comes from the similarity of eqn.1 &. to eqn 8. & 8. To show this similarity, we can write these eqn as shown dv dx w d θ M dx d M w dx d v M dx Here the shear V compares with

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

3 Hours/100 Marks Seat No.

3 Hours/100 Marks Seat No. *17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

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

Downloaded from Downloaded from / 1

Downloaded from   Downloaded from   / 1 PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their

More information

R13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PART-A

R13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PART-A SET - 1 II B. Tech I Semester Regular Examinations, Jan - 2015 MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) Time: 3 hours Max. Marks: 70 Note: 1. Question Paper consists of two parts (Part-A and Part-B)

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

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

More information

Dr. Hazim Dwairi. Example: Continuous beam deflection

Dr. Hazim Dwairi. Example: Continuous beam deflection Example: Continuous beam deflection Analyze the short-term and ultimate long-term deflections of end-span of multi-span beam shown below. Ignore comp steel Beam spacing = 3000 mm b eff = 9000/4 = 2250

More information

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete

More information

Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics)

Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Week 7, 14 March Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Ki-Bok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear

More information

Stress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y.

Stress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y. 014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 9 7. Determine the normal stress and shear stress acting

More information

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002 REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental

More information