SUMIF function with mutiple SUM_RANGE values

[shep85]

I have created a program to track rebar for a project. I created a lookup function to refrence information regarding the rebar. i have multiple rebar types in each section, and now I am trying to sum the amount of each type of rebar for each stage of the project. I tried to do use a SUMIF function as a tool but can not seem to get it to work. Here is a section of how the sheet is set up,

I have each stage broken down into seperate sections as shown above, with all three stages on a seperate tab. The final tab I want to total all of the similar bars for each stage, the total h60 (E) bars for stage I for example. i am using =SUMIF('Stage I'!A:A,"=Totals!B5",'Stage I'!F6:F7) as my command. It works for a single SUM_RANGE value, but when I insert 'Stage I'!F6:F7,'Stage I'!F11:F14, etc in the SUM_RANGE value then I get a # VALUE! error. Can anyone help me sum the total number of bars for multiple sections?