1.2 - Variation of σ in the cross-section
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Practice Questions
Test your understanding with targeted questions
What is the formula for calculating σ in the context of non-uniform bending?
💡 Hint: Think about how bending moments relate to stress.
What does τ represent in mechanical systems?
💡 Hint: Consider forces acting parallel to a cross-section.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary factor that causes variation in σ across the beam's cross-section?
💡 Hint: Think about which forces cause bending.
True or False: The shear stress τ is assumed to be a function of both y and z in the analysis.
💡 Hint: Reflect on the simplifications made in calculations.
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Challenge Problems
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A steel beam with a rectangular cross-section experiences a non-uniform load giving rise to varying bending moments. Analyze the stress distribution and calculate σ at three key points of the beam.
💡 Hint: Break down the stress at each location with the formula provided.
For an I-beam under loading, derive the shear stress distribution analytically and graphically depict how τ varies from the neutral axis to the edges.
💡 Hint: Pay attention to how I-beams have distinct width regions and adjust calculations accordingly.
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