- #1
garr6120
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Understanding Truss Mechanics: Why Use the Ratio 40/41 and Y Distance of 6.3?
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Discussion Overview
The discussion focuses on the mechanics of trusses, specifically addressing the calculation of forces in member AB. Participants explore the use of the ratio 40/41 and the significance of a y distance of 6.3 ft in their calculations, while also referencing a given distance of 9 ft. The conversation includes technical reasoning and calculations related to moments and angles in the context of truss analysis.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- Some participants express confusion regarding the use of the ratio 40/41 and the y distance of 6.3 ft, questioning why a ratio of 4/5 is not used instead.
- One participant asserts that the length of AD must be 41 ft based on the Pythagorean Theorem, leading to the conclusion that the tangent of the angle is 40/41.
- Another participant calculates the sum of moments around point G and arrives at a force of 9.33 kN for member AB, while noting that the expected answer is 8.20 kN, prompting questions about their approach.
- There is a discussion about the moment arm of AB being the perpendicular distance to point G, with differing interpretations of how to calculate this distance.
- One participant suggests that the sine, rather than the tangent, is relevant in their calculations, indicating a potential misunderstanding in earlier posts.
- Another participant questions the interpretation of the length in the x direction, suggesting it should be 12 ft instead of 40 ft, indicating uncertainty about the moment calculations.
- Participants explore multiple methods to calculate the moment arm and angles, indicating that there may be various valid approaches to the problem.
Areas of Agreement / Disagreement
Participants express differing views on the correct ratios and distances to use in their calculations, indicating that there is no consensus on the approach to solving the problem. Multiple competing interpretations of the mechanics involved remain unresolved.
Contextual Notes
Limitations in the discussion include unclear assumptions regarding the geometry of the truss, the definitions of distances used, and the specific calculations that lead to different conclusions about the forces in member AB.
- #2
Mapes
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You haven't shown any of the calculations, but it's immediately clear that the length of AD must by 41 ft because of the Pythagorean Theorem. Therefore, the tangent of the angle is 40/41. Presumably this is relevant.garr6120 said:
- #3
garr6120
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Mapes said:
Sorry I should of shown them my bad. I calculated: the sum of moments around G. which is equal to -1.8kips(14ft)-0.9kips(28ft+(9/15(Fab))(9ft)
solving for the Fab I get a force of 9.33kN however the answer is 8.20kN and they use a ratio of 40/41 times 6.3 ft. I was wondering how to approach this problem and what am I doing wrong. Isn't the moment of Fab 9ft above G?
- #4
Mapes
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Ah, got it. Good identification of the correct free-body diagram to use! But the moment arm of AB is the perpendicular distance to G. The way I'd calculate it is to say that the cosine of the far right angle is d / 28 ft (where d is the moment arm) and that the cosine is also 9 ft / 41 ft from the larger triangle. (Note that the first hypotenuse is on the bottom; the second is on the top.) This gives the same answer. There are probably a few ways to work it out; it would be good practice to try to find another way.garr6120 said:
EDIT: Sorry, earlier I should have written that the sine, not the tangent, is 40/41.
- #5
garr6120
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I have a question though I understand that AB is the perpendicular distance above G therefore you cannot find a moment using the length of AB in the x direction. However, I am still confused about the length in x being 40 from G shouldn't the length be 12ft. Am I thinking about Moments wrong?
- #6
Mapes
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I'm not sure what you mean when you say "the length in x being 40 from G". You may be referring to a calculation that I don't see. The moment arm of AB around point G is shown below. There are multiple ways to find this distance; the approach I took was to first find angle CDH, whose tangent is 9 ft / 40 ft. Then I used the fact that the sine of the angle is d / 28 ft, where d is the perpendicular distance from AB to G.
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