This document discusses the conjugate beam method for determining influence line diagrams (ILDs) for indeterminate beams. It outlines the steps as removing restraints, applying unit loads, determining reactions using conjugate beams, plotting bending moments and deflections to obtain the ILDs for moment, shear, reactions, and displacement at various points along the beam.

1. ILD for indeterminate beams

4. ILD for simply supported beam

6. ILD for continuous beam
• =
𝑀𝐷 𝑖𝑛 𝑐𝑜𝑛𝑗𝑢𝑔𝑎𝑡𝑒 𝑏𝑒𝑎𝑚
𝑀𝐴 𝑖𝑛 𝑐𝑜𝑛𝑗𝑢𝑔𝑎𝑡𝑒 𝑏𝑒𝑎𝑚

7. Conjugate beam method

8. Analysis steps
• Aim is to plot the ILD for indeterminate beam at given interval (1m, 2m…..)
• Remove the restraint and apply unit load at the point where ILD is asked
• Determine the support reactions due to unit load (Ra, Rb)
• Use Conjugate beam method
• Draw BM in the original beam due to unit load
• Make a conjugate beam (observing the support conditions)
• Draw M/EI diagram and apply M/EI diagram as load in conjugated beam
• Determine support reaction (Ra’, Rb’)
• Determine BM in conjugate beam at each interval due to loads (M/EI)
• Deflection in original beam = BM in conjugate beam
• For ILD, divide all the moments in the conjugate beam by Moment at considered ordinate

12. ILD for reaction at A

14. M/EI diagram
BMD

16. ILD for RB

17. ILD for Moment

22. ILD for Moment B

25. ILD for shear force

30. ILD for shear at D