Question: Why do subs, algsubs, and applyrule fail here?

I would like to replace in eqn1 the occurrence of

E__b*I__b*Eval(diff(phi__1(x__1), x__1 $ 3), x__1 = L__1)

using the relation defined in bc1.

I have already tried subs, algsubs, and applyrule, but none of them successfully performed the substitution. What would be the recommended or more robust way to carry out this replacement in Maple?
The details are as follows: question527.mw.

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