Champion Series: Plastic Analysis and Collapse Load of Beams

Introduction

• Lecturer: Satiji Sahu
• Focus: Plastic analysis, specifically on collapse load of beams in steel structures.
• Experience: 10 years in ESC domain, B.Tech & M.Tech from IIT Kharagpur, selected into several PSUs through GATE.

Announcements

• Upcoming sessions for HPCL, BHEL, and TSPSC exams.
• Scholarship test on October 1st.

Collapse Load of Beams

• Key Concept: Finding the load at which a beam collapses by forming a plastic hinge.

Plastic Hinges

• Possible Locations:
  • Fixed ends
  • Below point loads
  • Where cross-section changes
  • Points of zero shear force

Analysis Methodology

• External Work Done = Internal Work Done
• Example: Simply supported beam with load
  • External work done = (W_u \times \delta)
  • Internal work done uses plastic moment capacity ((M_p)) and rotations.

Formula Derivations

• Simply Supported Beam:

  • (W_u = \frac{M_p , L}{ab})
  • For load at center: (4 \frac{M_p}{L})

• Fixed Beam:

  • (W_u = 2 \frac{M_p , L}{ab})
  • For load at center: (8 \frac{M_p}{L})

• Propped Cantilever Beam:

  • (W_u = \frac{M_p , (L + b)}{ab})
  • For load at center: (6 \frac{M_p}{L})

Examples and Problems

• Set of problems solving for collapse load using derived formulas.
• Various scenarios including changes in cross-section and different load positions.

Special Case: Cross Section Changes

• Example: Fixed beam with cross-sectional change in the middle.
  • Analyze using internal and external work done.
  • Different hinge formations lead to different mechanisms.
• Mechanism Analysis:
  • Consider multiple possible mechanisms for hinge formation and calculate collapse load for each.

Conclusion

• Understanding Key Concepts: Formulas derived are crucial for solving standard and variable problems.
• Practice: Regular practice of derived formulas and understanding mechanisms helps in solving competitive exam problems efficiently.

Upcoming Sessions

• Tomorrow at 11 AM: Geotech session focusing on HPCL, BHEL, and TSPSC exam patterns.
• Join scholarship test on 1st October for potential discounts on courses.