Question

Can I find the reaction forces by only analyzing the slope without taking in consideration the defection y?

Answer 1

For statically determinate beams and trusses you find the reactions by simply using equilibrium equations and

For statically indeterminate structural members the slope is considered as extra known redundant force to find out reactions.For example at fixed ends the slope is zero ,we use this to apply and calculate reactions.

In some cases deflection are considered for finding reactions,such as for propped cantilever the deflection at propped end is zero,we use this to find reactions.

So,you can find reactions using slope without considering deflection at some cases