Laravel多对多关系用户的转变

Question

I'm trying to get the users that are on today's shift. I have a many to many relationship between the User and Shift model with a pivot table called user_shifts.

My User model:

/**
 * Get the users shifts
 */
public function shift()
{
    return $this->belongsToMany('App\Shift', 'user_shifts', 'user_id', 'shift_id');
}

My Shift model

/**
 * The shift can have many users
 */
public function users()
{
    return $this->belongsToMany('App\User', 'user_shifts', 'shift_id', 'user_id')->withPivot('start_time', 'end_time');;
}

In my controller I thought I could do something like:

$shift = Shift::all()->where('date', date('Y-m-d'));

$users = User::all()->where('shift_id', $shift);

return $users;

But that is returning null. Any help would be appreciated!

If it matters my db schema is:

Schema::create('shifts', function (Blueprint $table) {
    $table->increments('id');
    $table->date('date');
    $table->boolean('weekend');
});

Schema::create('user_shifts', function (Blueprint $table) {
    $table->increments('id');
    $table->integer('shift_id');
    $table->integer('user_id');
    $table->time('start_time');
    $table->time('end_time');
});

Schema::create('users', function (Blueprint $table) {
    $table->increments('id');
    $table->string('fname');
    $table->string('lname');
    $table->string('email')->unique();
    $table->string('password', 60);
    $table->rememberToken();
    $table->timestamps();
});