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Computers in Civil Engineering CEE3100 Spring 2002

Computers in Civil Engineering CEE3100 Spring 2002. Lecture #2. Outline. Examples of civil engineering problems that require application of numerical methods: Flow in open channels Truss analysis Sailboat mast design Computation of work. Example 1. Flow In Open Channels

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Computers in Civil Engineering CEE3100 Spring 2002

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  1. Computers in Civil EngineeringCEE3100 Spring 2002 Lecture #2

  2. Outline • Examples of civil engineering problems that require application of numerical methods: • Flow in open channels • Truss analysis • Sailboat mast design • Computation of work

  3. Example 1 • Flow In Open Channels • Roots of Equations

  4. T(y)=surface width y A(y)=area P(y) = wetted perimeter Uniform Flow

  5. Colebrook-White Formula for Uniform Flow

  6. Problem Formulation Find the depth y of uniform flow for a given flow rate Q and channel geometry. In other words: given Q and channel geometry, solve: f(y) = 0 Problem: Explicit solution does not exist! Solution:Numerically find root of equation (could you do it with Excel??)

  7. Example 2 • Structural Analysis • Systems of Linear Equations

  8. 1000 kg F1 90° F3 H2 60° 30° F2 V2 V3 Truss Analysis

  9. Force Equilibrium Analysis

  10. Problem Formulation Find the forces F1, F2, F3, and reactions, V1, V2, H2, associated with a statically determinant truss. In other words: solve the system of six linear equations with six unknowns. Solution: Solve System Using Gaussian Elimination or Gauss-Jordan Method

  11. (Could you solve the problem using exact methods learned in Statics??)

  12. Example 3 • Sailboat Mast Design • Curve Fitting

  13. Wind Force

  14. Definitions force in mast stress= cross-sectional area of mast extension or shortening strain= total length Hooke’s law: stress = K * strain Length Change DL = strain * length

  15. Strain Stress Experimental Stress-Strain Data

  16. Problem Formulation Based on the experimental data, estimate the change in lengthDLof the mast due to stress caused by wind force. Problem:Data points do not lie on a smooth, known curve Solution: Assume some relationship and fit a curve using least squares error criterion

  17. Strain Stress Curve Fitting Quadratic (2nd order) curve Linear (1st order) curve

  18. Example 4 • Computation of Work • Numerical Integration

  19. F(x) F(x) (x) (x) x Variable Force and Direction

  20. F(x) x (x) Experimental Data x

  21. Problem Formulation Based on the experimental data of variable force and angle, estimate the total work performed to pull a block a given distance x, i.e. calculate: Problem:F(x) and q(x) are not analytical Solution: Numerical Integration

  22. Reading AssignmentChapra and Canale: Chapter 1

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