Run an Algorithm: Difference between revisions
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The term ''running an algorithm'' | The term ''running an algorithm''is used here to mean doing a set of calculations: | ||
{{#drawio:algorithm_intro|type=png}} | {{#drawio:algorithm_intro|type=png}} | ||
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==== Apply vertical equilibrium: ==== | ==== Apply vertical equilibrium: ==== | ||
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==== Apply horizontal equilbrium: ==== | ==== Apply horizontal equilbrium: ==== | ||
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* <math>F_{BD}=-3+F_{BC}</math> | * <math>F_{BD}=-3+F_{BC}</math> | ||
* <math>F_{BD}=-3-3=6kN</math> | * <math>F_{BD}=-3-3=6kN</math> | ||
|} | |} | ||
==== The steps in the algorithm are: ==== | |||
# Draw the free body diagram for the joint. The input variables are: | |||
#* The 9 kN force in member AB that has been previously calculated | |||
#* The 3 kN load on the joint | |||
#* The geometry of the joint in terms of the angles between the members | |||
# The output variables are: <math>F_{BD}</math> and <math>F_{BC}</math> | |||
# Resolve the forces into the <math>x</math> and <math>y</math> directions. | |||
# Write the equation of equilibrium for the <math>x</math> or the <math>y</math> direction. | |||
# Use the rules of algebra to find an expression for one of the output variables (A) in terms of the other output variable (B). | |||
# Write the equation of equilibrium for the other direction. | |||
# Substitute the expression for variable A and solve for the value of variable B | |||
# Back-substitute to get the value of variable A. | |||
==== How do you practise so as to be able to do that? ==== | |||
* You could start by working with examples, exercises, definitions and explanations until you have an understanding of the process. Practise using the algorithm. | |||
* Keep asking questions such as ‘What does that mean?’ ‘How do I do that?’ | |||
* Then work on your memory. Memory should follow understanding. | |||
* Write down the variables and make sure that you know how to assign values to them. | |||
* Write out the algorithm. Make sure that you can do that from memory and that you know how to perform the steps. | |||
* Do not leave anything to the last minute. Few people can cram for understanding; both memorising facts and developing understanding need repetition. | |||
* That is the process that I used as a student. It got me good marks. | |||
Latest revision as of 08:02, 21 May 2021
The term running an algorithmis used here to mean doing a set of calculations:
What do you need to know to run an algorithm in an examination?
- You need to understand the meanings of all variables to an extent that you are able to assign correct values to them.
- You need to be able to write down the steps in the algorithm.
- You need to be able to run the algorithm.
For example, here's a 'run' of the algorithm for solving for the forces at joint B in the Nodal Analysis key example:
| Isolate Joint B | |
|---|---|
 |
|
Apply vertical equilibrium:
Substitute for: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\textstyle \sin{30} = 0.5}
Rearrange to find an expression for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F_{BD}}
|
Apply horizontal equilbrium:
Divide each term by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \cos{30}} :
Substitute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F_{BD} =-3 + F_{BC}} :
Solve for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F_{BD}} :
|
The steps in the algorithm are:
- Draw the free body diagram for the joint. The input variables are:
- The 9 kN force in member AB that has been previously calculated
- The 3 kN load on the joint
- The geometry of the joint in terms of the angles between the members
- The output variables are: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F_{BD}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F_{BC}}
- Resolve the forces into the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y} directions.
- Write the equation of equilibrium for the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x} or the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y} direction.
- Use the rules of algebra to find an expression for one of the output variables (A) in terms of the other output variable (B).
- Write the equation of equilibrium for the other direction.
- Substitute the expression for variable A and solve for the value of variable B
- Back-substitute to get the value of variable A.
How do you practise so as to be able to do that?
- You could start by working with examples, exercises, definitions and explanations until you have an understanding of the process. Practise using the algorithm.
- Keep asking questions such as ‘What does that mean?’ ‘How do I do that?’
- Then work on your memory. Memory should follow understanding.
- Write down the variables and make sure that you know how to assign values to them.
- Write out the algorithm. Make sure that you can do that from memory and that you know how to perform the steps.
- Do not leave anything to the last minute. Few people can cram for understanding; both memorising facts and developing understanding need repetition.
- That is the process that I used as a student. It got me good marks.