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  • 12 pages SCE5381 AY1617 Suggested Solutions to T8
    • SCE5381 AY1617 Suggested Solutions to T8
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 8 Question 1 3 2 5 10 3 3 8 5 10 11 1 14 3 7 10 10 4 14 A 0 0 C 3 13 10 10 0 14 3 4 7 10 4 14 E G 10 10 0 4 18 H 0 3 14 F 3 6 Minimum duration: 18 months Critical paths: A-C-F-H & A-C-G-H D B 0 3 14 14 0 18 18 Step 0: Read the question carefully
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    SCE5381 AY1617 Suggested Solutions to T8

  • 10 pages Tutorial 3 (1)
    • Tutorial 3 (1)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • STIFFNESS METHODS TUTORIAL 3 Dr. Henry LUK SCE5321 Theory of Structures 2 2 Tutorial Example 1 Determine joint 1 displacements and support reactions. 3 y 4m 1 300 kN 3m E = 200 GPa 30o 2 A = 500 mm2 x 1 4 k = 15000 kN/m 2 8m 3 Solution to Tutorial Example
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    Tutorial 3 (1)

  • 8 pages Tutorial 10 (rev)
    • Tutorial 10 (rev)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 10 PLASTICITY SCE5321 Theory of Structures 2 Dr. Henry Luk TUTORIAL EXAMPLE 1 Determine the collapse load W using upper bound theorem. 2W 5m W 2.5m 2.5m 2 TUTORIAL EXAMPLE 2 Determine the collapse load W using upper bound theorem. 2W 2m W 2m 2m 3
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    Tutorial 10 (rev)

  • 3 pages Tutorial 4 Example
    • Tutorial 4 Example
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Example 3 kN/m Determine the unknown displacements and reactions at nodal points. E = 200 GPa A = 6(103) mm2 I = 200(106) mm4 12 m 20 m Solution 2 Fixed-end forces in member 2 5 3 6 2 1 4 3 1 0 3 20 / 2 30 kN 2 3 20 / 12 100 kNm qo2 0 30 kN 100 kNm 1
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    Tutorial 4 Example

  • 11 pages SCE5321 Mid-term - Sol
    • SCE5321 Mid-term - Sol
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Question 1 (35 marks) A pin-jointed truss composed of three truss elements is shown in Figure 1. The structure is now subjected to a vertical downward force of 800 kN at joint 2. Support movement of 15 mm toward the positive x-direction at joint 1 is obse
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    SCE5321 Mid-term - Sol

  • 11 pages Assignment 3 - Sol
    • Assignment 3 - Sol
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Solution to Question 1 (1) Stiffness and mass matrices are given as 8 4 0 4 K 10 4 8 4 0 4 4 5 0 0 M 10 0 5 0 0 0 5 3 (2) Characteristic equation det[K 2M] 0 or det[K M] 0 The solutions are 1 1.259 ; 2 3.527 ; 3 5.097 To obtain the mode shape 1 = [11
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    Assignment 3 - Sol

  • 10 pages Assignment 2 - Sol
    • Assignment 2 - Sol
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Solution to Question 1: 1) Natural period, Structural stiffness Mass of structure TD Tn 1.6 s P 17.5 103 1750000 N/m 1750 kN/m 1102 m Tn 2 k T m n 2 k 113480 kg 113.5 tons 4 k 2) Natural frequency n 3) Damping ratio Damping coefficient 2 3.93 rad/s Tn
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    Assignment 2 - Sol

  • 4 pages Assignment 2
    • Assignment 2
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Faculty of Science and Technology Civil Engineering SCE5321 Theory of Structures 2 Assignment 2 Due date: 10th Nov 2016 1. 2. Please answer ALL questions with detail procedures. You may use other software (Excel, Matlab, C+, etc) to present your solutions
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    Assignment 2

  • 3 pages Assignment 1
    • Assignment 1
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Faculty of Science and Technology Civil Engineering SCE5321 Theory of Structures 2 Assignment 1 Due date: 6th Oct 2016 1. 2. Please answer ALL questions with detail procedures. You may use computer programme (e.g. Excel or Matlab) to handle the complex ma
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    Assignment 1

  • 2 pages Assignment 3
    • Assignment 3
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Faculty of Science and Technology Civil Engineering SCE5321 Theory of Structures 2 Assignment 3 Due date: 5th Dec 2015 1. 2. Please answer ALL questions with detail procedures. You may use other software (Excel, Matlab, C+, etc) to present your solutions.
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    Assignment 3

  • 59 pages 1. Introduction to Steel Design
    • 1. Introduction to Steel Design
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Steel Structures Dr. Henry LUK Contents Steel Structures Structural Steel Manufacturing process Steel properties Basic Design of Steel Members 2 Limit state design Design strength Steel sections Local plate buckling Section classification Steel Structures
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    1. Introduction to Steel Design

  • 29 pages Matrix Analysis
    • Matrix Analysis
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • APPENDIX Matrix Analysis Dr. Henry LUK 1 SCE5321 Theory of Structures 2 Basic Definitions and Types of Matrices 2 Basic Definitions A matrix is a rectangular arrangement of number having m rows and n columns. The numbers, which are called elements, are
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    Matrix Analysis

  • 113 pages Construction_of_bridges
    • Construction_of_bridges
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Construction of Bridges Information prepared by Raymond Wong Division of Building Science and Technology, City University of Hong Kong January 2012 e-mail of Raymond Wong [email protected] Materials suitable for the Construction of Long-span Bridges 1
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    Construction_of_bridges

  • 10 pages Tutorial 5 (rev)
    • Tutorial 5 (rev)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 5 Dr. Henry Luk SCE5321 Theory of Structures 2 u(t) Equation of Motion For SDOF system, m k mu cu ku p (t ) Rigid beam: kcol k1 = 1 + 2 k2 k1 c 12 EI 3 h kcol Flexible beam: p(t) 3EI 3 h k2 1 = 1 1 + 1 2 2 Free Vibration EOM: mu cu ku 0 Initi
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    Tutorial 5 (rev)

  • 10 pages Tutorial 8
    • Tutorial 8
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 8 Dr. Henry Luk SCE5321 Theory of Structures 2 Tutorial Example 1 Determine the mode shapes and natural frequencies for the following shear building. 1.0 1.5 2.0 600 Assuming all quantities are in standard unit 1200 1800 2 Solution to Tutorial Ex
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    Tutorial 8

  • 70 pages Topic 6 - SDOF Harmonic Excitation and Force Vibration
    • Topic 6 - SDOF Harmonic Excitation and Force Vibration
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Topic 6 Harmonic Excitation and Force Vibration Dr. Henry Luk SCE5321 Theory of Structures 2 Force Excitations Equation of motion + + = () () , The solution for u(t) depends on the form of external excitation p(t) Harmonic excitation = sin Impulse fo
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    Topic 6 - SDOF Harmonic Excitation and Force Vibration

  • 64 pages Topic 2 - Beam Element
    • Topic 2 - Beam Element
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • TOPIC 2 STIFFNESS METHODS BEAM ANALYSIS USING THE STIFFNESS METHOD SCE5321 Theory of Structures 2 Dr. Henry LUK 2 PRELIMINARY REMARKS 3 Member and Node Identification In general, each element must be free from load; and have a prismatic cross section.
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    Topic 2 - Beam Element

  • 39 pages Topic 13 - Plasticity for Statically Indeterminate Structures
    • Topic 13 - Plasticity for Statically Indeterminate Structures
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • TOPIC 13 PLASTICITY Collapse analysis of continuous beams and frames SCE5321 Theory of Structures 2 Dr. Henry Luk ULTIMATE STRENGTH OF COMPLEX AND CONTINUOUS BEAMS 2 CONTINUOUS BEAMS In order to examine all possible collapse modes for continuous beams and
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    Topic 13 - Plasticity for Statically Indeterminate Structures

  • 30 pages Topic 5 - SDOF Free Vibration (1)
    • Topic 5 - SDOF Free Vibration (1)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Topic 5 SDOF Free Vibration Dr. Henry Luk SCE5321 Theory of Structures 2 Free Vibration 2 Free Vibration An elastic structure disturbed from its static equilibrium condition by the application and removal of forces will oscillate about its position of st
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    Topic 5 - SDOF Free Vibration (1)

  • 31 pages Tutorial 2
    • Tutorial 2
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • STIFFNESS METHODS TUTORIAL 2 Dr. Henry LUK SCE5321 Theory of Structures 2 2 Overall Procedure Define notation Determine fixedend forces and boundary conditions Q0 Du Solve for unknown displacements Qu k Construct structure stiffness matrix K Dk Q k Determ
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    Tutorial 2

  • 21 pages Tutorial 1 (1)
    • Tutorial 1 (1)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • STIFFNESS METHODS TUTORIAL 1 Dr. Henry LUK SCE5321 Theory of Structures 2 2 Tutorial Example 1 Determine the displacements at node A and member forces. A 500 kN y E = 200 GPa 1 2 4m AAB = 6000 mm2 AAC = 8000 mm2 B x 6m C 3m 3 Solution to Tutorial Example
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    Tutorial 1 (1)

  • 29 pages Topic 4 - SDOF System and EOM (1)
    • Topic 4 - SDOF System and EOM (1)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Topic 4 SDOF system and Equation of Motion Dr. Henry Luk SCE5321 Theory of Structures 2 Equation of Motion and SDOF Systems 2 Introduction I The previous chapters dealt with structures subjected to static forces producing displacements that do not vary w
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    Topic 4 - SDOF System and EOM (1)

  • 9 pages Tutorial 3 Examples
    • Tutorial 3 Examples
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • SCE5321 Theory of Structure 2 Tutorial 3 Beam element Example 1 Determine the deflection at the roller support and the reactions. Take EI as a constant. P 2m 2m Solution Code number diagram: 3 1 1 2 5 2 4 6 Member stiffness matrices: Element 1 1.5 1.5 1.5
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    Tutorial 3 Examples

  • 26 pages Topic 12 - Plasticity for Beams
    • Topic 12 - Plasticity for Beams
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • TOPIC 12 PLASTICITY Collapse analysis of beams SCE5321 Theory of Structures 2 Dr. Henry Luk PLASTIC BEHAVIOUR OF SIMPLE BEAMS 2 COLLAPSE ANALYSIS OF SIMPLE BEAMS In a statically determinate beam or frame, a single plastic hinge forms where bending moment
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    Topic 12 - Plasticity for Beams

  • 12 pages Tutorial 4 (rev) (1)
    • Tutorial 4 (rev) (1)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • STIFFNESS METHODS TUTORIAL 4 Dr. Henry LUK SCE5321 Theory of Structures 2 2 E 200 GPa Tutorial Example 1 A 5000 mm 2 I 200 106 mm 4 Determine displacements and reactions. P = 500 kN 2m 2 3 2 P = 1000 kN y 1 M = 1000 kNm 5m 3 2.5 m 1 x 4m 4 3 Solution to E
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    Tutorial 4 (rev) (1)

  • 20 pages Tutorial 11 (rev)
    • Tutorial 11 (rev)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 11 PLASTICITY SCE5321 Theory of Structures 2 Dr. Henry Luk TUTORIAL EXAMPLE 1 Determine the collapse load P using upper bound theorem. 6L 2P 2L 3P 2L 2 SOLUTION TO TUTORIAL EXAMPLE 1 Mechanism 1 6L 3P(2 L ) M p ( 2 ) 2P 2L 3P P1 2M p 3L 2L 3 Mec
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    Tutorial 11 (rev)

  • 11 pages Tutorial 9 (rev)
    • Tutorial 9 (rev)
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Tutorial 9 Dr. Henry Luk SCE5321 Theory of Structures 2 Tutorial Example 1 Decoupled the equation of motion. Determine the displacement response of the MDOF system at steady state. 1.0 100 sin(5) 1.5 2.0 600 1200 Damping ratio = 5% for all modes 1800 2 So
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    Tutorial 9 (rev)

  • 47 pages Numerical methods
    • Numerical methods
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Numerical Evaluation of Dynamic Response Chapter 5 November 9, 2016 CC Chang / HKUST Time-Domain Analysis given mx i cx i kx i pi mx i 1 cx i 1 kx i 1 pi 1 seek Displacement x mx (t) cx (t) kx(t) p(t) Loading p n e v i g pi p1 p pi+1 2 Time stepping k e x
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    Numerical methods

  • 61 pages Topic 1 - Truss Element Part 1
    • Topic 1 - Truss Element Part 1
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • TOPIC 1 STIFFNESS METHODS TRUSS ANALYSIS USING THE STIFFNESS METHOD PART 1 SCE5321 Theory of Structures 2 Dr. Henry LUK 2 REVIEWS ON STRUCTURAL ANALYSIS 3 Structural Analysis Structural analysis is the procedures to determine internal forces and deformat
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    Topic 1 - Truss Element Part 1

  • 31 pages Topic 10 - MDOF Modal Superposition Part 2
    • Topic 10 - MDOF Modal Superposition Part 2
    • Technological and Higher Education Institute of Hong Kong
    • Theory of Structures 2
    • CN SCE5321 - Fall 2016
    • Topic 10 Modal Superposition Part 2 Dr. Henry Luk SCE5321 Theory of Structures 2 Modal Superposition 2 Modal Superposition Equation of motion of undamped MDOF system under free vibration + + = Initial conditions: (0) and (0) Any set of N independent vec
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    Topic 10 - MDOF Modal Superposition Part 2

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