Re: shade arbour
You called it a shade arbor. If it were me I wouldn't for 2 reasons. 1) you will be putting holes in the roof that can leak 2) you would be creating a dam for snow and water.
If you are talking about an extension roof. you would cut through the roof and nail the 2X's to the rafters or taper the ends to match the roof nail though the ends and the roof, add sheeting and install the roofing so it goes under the existing roofing.
Be sure you live your life, because you are a long time dead.-Scottish Proverb