Look at this sketch. Does the toilet exhaust steel duct penetrating the fire-rated shaft on the second floor but having no opening in the space require a combination fire-smoke damper? Yes, it does. Here is the code reference.


California Building Code 2010
Chapter 7: Fire and Smoke Protection Features

Section 716: Ducts and transfer openings

716.5.3 Shaft enclosures.
Shaft enclosures that are permitted to be penetrated by ducts and air transfer openings shall be produced with approved fire and smoke dampers installed in accordance with their listing.

Exceptions:
1. Fire dampers are not required at penetrations of shafts where:
1.1 Steel exhaust subducts are extended at least 22 inches (559 mm) vertically in exhaust shafts provided there is a continuous airflow upward to the outside; or
1.2 Penetrations are tested in accordance with ASTM E 119 or UL 263 as part of the fire-resistance-rated assembly; or
1.3 Ducts are used as part of an approved smoke control system designed and installed in accordance with Section 909 and where the fire damper will interfere with the operation of the smoke control system; or
1.4 The penetrations are in parking garage exhaust or supply shafts that are separated from other building shafts by not less that 2-hour fire-resistance-rated construction.
2. In Group B and R occupancies throughout with an automatic sprinkler system in accordance with Section 903.3.1.1, smoke dampers are not required at penetrations of shafts where:
2.1. Kitchen, clothes dryer, bathroom and toilet room exhaust openings are installed with steel exhaust subducts, having a minimum wall thickness of 0.0187-inch (0.4712 mm) (No. 26 gage);
2.2. The subducts are extended at least 22 inches (559 mm) vertically; and
2.3 An exhaust fan is installed at the upper terminus of the shaft that is powered continuously in accordance with the provisions of Section 909.11, so as to maintain a continuous upward airflow to the outside.

3. Smoke dampers are not required at penetration of exhaust or supply shafts in parking garages that are separated from other building shafts by not less than 2-hour fire-resistance-rated construction.
4. Smoke dampers are not required at penetrations of shafts where ducts are used as part of an approved smoke control system designed and installed in accordance with Section 909 and where the smoke damper will interfere with the operation of the smoke control system.
5. Fire dampers and combination fire/smoke dampers are not required in kitchen and clothes dryer exhaust system when installed in accordance with the California Mechanical Code.




Note that for fire damper requirements the installation shown in the sketch meets none of the exceptions under 716.5.3.1, and for smoke damper requirements the installation does not meet any of the exceptions under 716.5.3.2, 716.5.3.3, or 716.5.3.4.

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When are fire dampers required?
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Duct penetrations requiring fire and smoke dampers.
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I don’t need fire damper if the steel duct does not have any openings in the space?
Steel ducts can stop fire?
Steel ducts can stop smoke?
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If a duct penetrates a fire-rated shaft but does not have any openings in the space, does it need a fire damper?
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Do buildings with automatic fire sprinkler systems need fire dampers?