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Mechanics of Materials Engr 350 - Lecture 9

Mechanics of Materials Engr 350 - Lecture 9 Axial Deformation 2 - Systems of Axially Deformed Members. “We cannot solve our problems with the same thinking we used when we created them.” -Albert Einstein. Deformations in a system of axially loaded bars.

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Mechanics of Materials Engr 350 - Lecture 9

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  1. Mechanics of Materials Engr 350 - Lecture 9 Axial Deformation 2 - Systems of Axially Deformed Members • “We cannot solve our problems with the same thinking we used when we created them.” • -Albert Einstein

  2. Deformations in a system of axially loaded bars • Consider deformations in more than one direction • Useful technique to analyze complex systems of homogeneous uniaxial bars loaded by forces at the end • We will assume some bars are perfectly rigid for now • 2 Types • Statically determinate (covered in Philpot 5.4) • Statically indeterminate (section 5.5) • What’s the difference?

  3. Statically Determinate Systems 1) Equilibrium equations 2) Find forces in members 3) Find deformations in members 4) Determine how structure as a whole deforms based on deformations in members - as necessary

  4. Statically indeterminate systems Solution procedure 1) Equilibrium Equations – Express in terms of unknown forces 2) Geometry of Deformation – Geometric relationship between various members (step unique to statically indeterminate system) 3) Force-Deformation Relationships – FLEA equation for each member 4) Compatibility Equation – Combine equations from Step 3 with Step 2, expressed in terms of unknown forces. Should have a closed set of equations after this step (equal number of knowns and unknowns) 5) Solve the Equations – by hand or via software

  5. Practice problem P5.15 • Write equilibrium equations • Equations from geometry of deformation • Force-deflection relationships • Create compatibility relationships: 2➞3

  6. Example: Philpot P5.24 • Write equilibrium equations • Equations from geometry of deformation • Force-deflection relationships • Create compatibility relationships: 2➞3 • Solve 1 & 4 simultaneously • 𝜎1= • 𝜎2= • Deflection at B: • Given: • E=200GPa • A=1475mm2 • Find: a) normal stress in the upper and lower pipes • b) the deflection of flange B

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