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Cable Mass Calculation for Ceiling Suspension

Design a MATLAB script to calculate the minimum mass of a cable required to support an object hanging from a ceiling, given the object's mass, initial cable length, maximum deflection, cable density, and cable yield stress.

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Cable Mass Calculation for Ceiling Suspension

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  1. ceiling l0 mobj T = mobjg ca05 review - problem solving Problem Statement #1: A cable of length l0 is needed to suspend an object of mass mobj from the ceiling. The load, T = mobjg, is the force that the mass exerts on the cable. The deflection (elongation) of the cable under the load must be less than lmax. Ignoring the mass of the cable (mcable, which adds to the load), what cable mass is required to just support the load without permanent deformation? step 1: draw a sketch!!! needs l0 mobj lmax Engr 0012 (04-1) LecNotes 06-01

  2. strain need equation for volume elastic (Young’s) modulus stress material property look it up add to needs list A0 l0 step 2: review relevant engineering stress-strain problem: S = Ee permanent deformation when S > Sy looking for mass of cable Engr 0012 (04-1) LecNotes 06-02

  3. can calculate T = mobjg need value use Sy add to needs list already on needs list need equation step 2: review relevant engineering needs list l0 mobj lmax  Sy Engr 0012 (04-1) LecNotes 06-03

  4. step 3: restate problem Design a MATLAB script to find the minimum mass of a cable required to support an object hanging from a ceiling given the mass of the object, initial length of the cable, maximum deflection, cable density, and cable yield stress. step 4: algorithm 1. Ask user for mass of the object, initial length of the cable, maximum deflection, cable density, and cable yield stress. 2. Compute mass of cable. 3. Report mass of cable. Engr 0012 (04-1) LecNotes 06-04

  5. step 5: expand step 2 of algorithm 2. Compute mass of cable. a. Compute tension. b. Compute cable diameter. c. Compute cable volume. d. Compute cable mass. Engr 0012 (04-1) LecNotes 06-05

  6. ca05 review - problem solving Problem Statement #2: My boss at the Internal Revenue Service (IRS) has asked me to develop a program that will determine how much taxes are due based upon a taxpayer’s annual salary. The tax due is based upon a provided table. step 1: draw a sketch!!! needs list salary Can’t - not applicable. step 2: review relevant information Need to find where salary falls in table. Compute tax due as base + % time amount in excess of minimum in range Engr 0012 (04-1) LecNotes 06-06

  7. step 3: restate problem Design a MATLAB script to find the tax due based upon a taxpayer’s salary. step 4: algorithm 1. Ask user for salary. 2. Compute tax due. 3. Report tax due. step 5: expand step 2 of algorithm 2. Compute tax due. a. Use salary and if/elseif/else structure to find appropriate row in table b. Compute appropriate excess. c. Compute appropriate tax due. Engr 0012 (04-1) LecNotes 06-07

  8. decision making - design issues Whenever you need to make a decision, make a decision table Raining Take umbrella Take hat Cloudy Sunny Take sunblock and hat A decision table is a simple listing of conditions and actions that result if the condition is met. Engr 0012 (04-1) LecNotes 06-08

  9. Mutually exclusive conditions Conditions have no overlap, i.e., only one of the conditions can be true Nonexclusive conditions Conditions can overlap, i.e., one or more of the conditions can be true at same time Example decision making - design issues Two types of decision conditions Nonexclusive - Why? Engr 0012 (04-1) LecNotes 06-09

  10. Example decision making - design issues Nonexclusive - Why? score of 84 satisfies conditions 2, 3, and 4 Important because we will use an if/elseif command structure to find proper condition and action Engr 0012 (04-1) LecNotes 06-10

  11. first conditon from table first conditon actions from table perform these actions if none of the conditons are met if/else if/else command structure if (condition 1) perform condition 1 actions elseif (condition 2) perform condition 2 actions elseif (condition 3) perform condition 3 actions else perform “default” actions end default is frequently omitted Engr 0012 (04-1) LecNotes 06-11

  12. Example decision making - MATLAB syntax if (score < 60) grade = ‘F’; elseif (score >= 60) grade = ‘D’; elseif (score >= 70) grade = ‘C’; elseif (score >= 80) grade = ‘B’; elseif (score >= 90) grade = ‘A’; end MATLAB moves through structure looking for first condition that is satisfied. MATLAB then executes the “action statements” under the condition. When the last “action statement” is finished, MATLAB goes to the end. Engr 0012 (04-1) LecNotes 06-12

  13. note use of default rather than condition decision making - nonexclusive conditions nonexclusive conditions are a problem - can either rearrange table to make sure order of execution is appropriate if (score >= 90) grade = ‘A’; elseif (score >= 80) grade = ‘B’; elseif (score >= 70) grade = ‘C’; elseif (score >= 60) grade = ‘D’; else grade = ‘F’; end Engr 0012 (04-1) LecNotes 06-13

  14. decision making - nonexclusive conditions nonexclusive conditions are a problem - can either rearrange table to make sure order of execution is appropriate or make conditions mutually exclusive if (score < 60) grade = ‘F’; elseif (score >= 60 & score < 70) grade = ‘D’; elseif (score >= 70 & score < 80) grade = ‘C’; elseif (score >= 80 & score < 90) grade = ‘B’; else grade = ‘A’; end Order of execution of mutually exclusive conditions not important because only one condition can be true Engr 0012 (04-1) LecNotes 06-14

  15. comparison (relational) operators greater than > less than < greater than or equal >= less than or equal <= is the same as == is not the same as ~= logical (set) operators and & or | not ~ decision making operators Engr 0012 (04-1) LecNotes 06-15

  16. example function using decision making grade_earned.m how do you know it is working properly? test it!!! Engr 0012 (04-1) LecNotes 06-16

  17. programming assignment 03 due Wed 17 Sep class activity 06 : ca06_e12(04-1).pdf Engr 0012 (04-1) LecNotes 06-17

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