Concept of Conjugate beam - Introduction to Deflection of Beams - Structural analysis 1

TL;DR

This video discusses the difference between an actual beam and a conjugate beam, focusing on their end conditions, bending moments, shear forces, slope, deflection, and loading diagrams.

Transcript

hello students so here we are going to see uh in this particular class we are going to see a concept what is the difference between actual beam and conjugate beam and we will start with the cantilever beam okay how do we analyze that cantilever beam using conjugate beam method so previous classes we have discussed about simply supported beams okay ... Read More

Key Insights

• 😁 There are differences in deflection, slope, bending moments, shear forces, and loading diagrams between actual beams and conjugate beams.
• 😁 For simply supported end conditions, the deflection is zero in actual beams, while the bending moment is zero in conjugate beams.
• 😁 Converting a cantilever beam to a conjugate beam involves changing the fixed end to a free end and vice versa.
• 😁 The slope at any point in a cantilever beam can be calculated by dividing the shear force at the corresponding point in the conjugate beam.

Questions & Answers

Q: What is the primary difference between an actual beam and a conjugate beam for simply supported end conditions?

The deflection of an actual beam is zero, while the slope exists. In contrast, the bending moment is zero at the ends of a conjugate beam, but shear force exists.

Q: How do the slope and deflection differ for a cantilever beam when it becomes a conjugate beam?

For actual beam fixed ends, the slope and deflection are zero. However, for the conjugate beam, if it becomes a free end, the shear force and bending moment are zero.

Q: How is the bending moment diagram different between an actual beam and a conjugate beam?

The bending moment diagram for an actual beam is positive and saggy for a simply supported beam, while the bending moment by E/I diagram for a conjugate beam is positive and loading is in the downward direction.

Q: How can the slope and deflection of a cantilever beam with a point load at the free end be calculated using the conjugate beam method?

The slope at the free end can be calculated by dividing the shear force at the corresponding section of the conjugate beam. The deflection at the free end is determined by the bending moment at the corresponding section, divided by EI.

Summary & Key Takeaways

• The video begins by explaining the differences in deflection and slope between an actual beam and a conjugate beam for simply supported, free, and fixed end conditions.

• It then highlights how the system of loading differs between the two beams, with the actual beam using the given loading for bending moment calculations, while the conjugate beam uses a bending moment by the diagram as a load diagram.

• The video concludes with a demonstration of calculating the slope and deflection of a cantilever beam with a point load at the free end using the conjugate beam method.