The trips and segments elements are arrays of objects, not a single object.
So you need to reference the array element [0] which part of the structure.
$trips = $routings[0]->trips;
$segments = $trips[0]->segments;
Note, that there appear to be two trips, you'll also need $trips[1]->segments if you want all the segments.
More likely, you'll be wanting to use foreach() loops to read them, rather than directly referencing the array keys.
Something like this?
foreach($routings as $routing) {
$trips = $routing->trips;
.... do something here with $trips? ....
foreach($trips as $trip) {
$segments = $trip->segments;
.... do something here with $segments? ....
}
}