Analytical formulation for Beam or Beam

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The discussion focuses on seeking analytical formulations for beams or bars under tensile loading, specifically addressing stress, deflection, and crack propagation. The inquiry acknowledges the complexity of the topic, suggesting that it encompasses material from at least two university-level courses. Participants recommend utilizing online resources for comprehensive information, indicating that the Physics Forums may not be the ideal platform for such detailed inquiries. Suggested articles include those on Euler-Bernoulli beam theory and fracture mechanics. Overall, the conversation emphasizes the need for thorough research and study to understand these mechanical concepts.
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I want to know the analytical formulation for a beam or bar without crack and with crack subjected to tensile loading through mechanics approach.
 
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That's a little broad. What specific analytical formulations are you looking for? Stress? Deflection? Crack propagation?
 
Thank you for replying i want Derivations for all i.e Stress,Deflection,Crack propagation
 

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