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Cable Support: Anchor Position Optimization for Pin-and-Cable Supported Beam

Analyze cable tension and anchor position to optimize beam support. Use MATLAB for calculations and sensitivity analysis. Determine maximum possible anchor position and find solutions both analytically and graphically.

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Cable Support: Anchor Position Optimization for Pin-and-Cable Supported Beam

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  1. Engineering 25 Problems2.24 Solutions Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. P2.24 Cable Support • Consider a Pin-and-Cable Supported Beam • The Cable Anchor Pt-D is VARIABLE For the Constant Parameters shown 5m 400N≈ 90 lbs 3m

  3. P2.24 Cable Support • Since the VERTICAL Anchor-Pt for Lc is also Variable, the Horizontal Anchor-pt, D, can be MOVED • Using the Methods of ENGR36 We find the Cable-Tension function, T(D)

  4. P2.24  Problem • a. Use Element-by-Element operations and the MATLAB min command to • Find the Anchor-Position, D, The MINIMIZES T • Calc this minimum Value of T • b. Check T vs. D Sensitivity by plotting T vs. D. • By How Much can D change if T is allowed to rise to 1.1*Tmin (110% of Tmin)

  5. ¿¿Class Question?? • Given • What is the MAXIMUM POSSIBLE Value of D (regardless of T)? 5m 400N≈ 90 lbs 3m

  6. ¿¿Class Question?? • HOW Many Values of D Satisfy the given Criteria: • What is D when T is allowed to rise to 1.1*Tmin (110% of Tmin) 5m 400N≈ 90 lbs 3m

  7. 2.24 Game Plan • Part a) Solve analytically using min as instructed • Part b) Solve • Approximately using the Graph • Anallytically using the find command

  8. 2.24 Graphical Soln • The T vs D graph (fully labeled) 2.12m, 1333N ≈1.62 ≈2.54

  9. 2.24 Analytical Soln

  10. Overall Sensitivity • Any D between 1m-2.8m yields relatively low Tension

  11. MATLAB Code-a

  12. MATLAB Code-b

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