Chapter41

Chapter41 - AE 221 Spring 2004 Structures II Chapter 4...

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AE 221 – Spring 2004 – Structures II Chapter 4 – Introduction to Buckling 1.. For an electronic chip design a conducting film (modulus E) of thickness t and width w is deposited on a much thicker silicon substrate. The deposit did not bond to the substrate over the conductor width w and for a length s (>>w) as shown. The coefficient of thermal expansion of the conductor is c a and that of the substrate is s ( s > c ). If the bonding takes place at a temperature T above the ambient (T o ), find the maximum allowable T so that the conductor does not fail upon cooling (assuming that any bending of the conductor results in fracture). Hint: The thermal uniaxial strain resulting from a temperature change of T D is T x D = e where is the coefficient of thermal expansion. 2. A pin ended beam of flexural rigidity EI and length L is supported by an elastic foundation of bulk modulus k per unit length. The support is such that, when the beam deflects by an amount v , a restoring force of magnitude kv is exerted by the foundation in a direction normal to the beam.
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Chapter41 - AE 221 Spring 2004 Structures II Chapter 4...

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