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Stress Analysis of a Tower Using the Method of Joints

This analysis explores the stress distribution in a tower structure using the method of joints. By focusing on joints A, B, and C, we derive equations for the forces acting on each joint, taking into account both X and Y directional forces. A free body diagram visualizes these forces, and we consider yield strength to evaluate the maximum force the tower can withstand. We calculate the stress based on the cross-sectional area of balsa wood, acknowledging factors that may cause discrepancies in our predictions, such as craftsmanship imperfections and unaccounted forces.

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Stress Analysis of a Tower Using the Method of Joints

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  1. Stress Analysis of a Tower

  2. F0 The Method of Joints A B C Joint B F0 E F D FAB FCB +Y +X G H I FDB FFB FEB A Free Body Diagram K L J M N O FR

  3. Joint B X Forces F0 +FAB -FCB +FDBX -FFBX = 0 FAB FCB Y Forces FDB FDBY -F0 +FEB +FDBY +FFBY FDB FFB FDBX FEB +Y = 0 +X

  4. F0 15 Joints A B C 15 FX equations 15 FY equations E F D 30 Variables G H I A “system of equations” K L J Solution would required computer software M N O FR

  5. And now….A simplified approach

  6. Yield Strength The amount of stress a material can withstand before it begins to deform Values can differ for tension or compression Use the internet to find a value for the yield strength of balsa wood in compression

  7. Cross Sectional Area Depth = 3mm Width = 4mm 12mm2 Area = 4mm * 3mm = ?

  8. Maximum Force P = F / A Stress = Pressure = Force / Area Stress = Yield Strength Yield Strength * Area = Max Force

  9. Total Force Our ‘max force’ only accounts for a single truss Must count all the trusses at a given height to get total force 1 2 3 4 5 1 2 3 Sided Tower 3 Total Force = Max Force * ? 5 * 3

  10. Reasons our predictions may be off We only accounted for forces in the Y direction Considered trusses to only experience compression Calculations did not account for imperfect craftsmanship

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