CIVL3811 Chap.2 Long-Span Floors and Vibration
Long-Span Floors and Vibration
Long spans can make serviceability govern even when strength is adequate. This chapter compares joist and girder mode shapes, shows how compatible deflection contributions enter a frequency screen, and explains why mass, stiffness, damping, excitation and occupancy remain necessary for a comfort assessment.
The figure separates a shape where primary lines act as nodes from one where the primary girder moves, preventing unrelated deflections from being combined. Worked arithmetic prints every addition, square root and frequency result while preserving the mode label. The chapter then tests remedies rather than assuming that a heavier or deeper floor is automatically better.
Increased stiffness, added mass, shorter spans, different framing and more damping affect different parts of the response. Long-span options such as fabricated beams, haunches, trusses and service-integrated forms are also compared for fabrication, fire, headroom, erection and coordination consequences.
What this chapter covers
- 01
Joist mode
- 02
Girder mode
- 03
Frequency screening
- 04
Stiffness and mass
- 05
Damping and excitation
- 06
Long-span options
Worked example · free
Estimate the governing floor frequency
- +1Add compatible deflections for the joist mode.
- +1Substitute into the screening relationship.
- +1Repeat for the girder mode.
- +1Select the lower frequency.
- +1State why a comfort check still remains.
Key terms
- Natural frequency
- The rate of free vibration associated with a structural mode.
- Mode shape
- The deformed pattern in which a system vibrates.
- Damping
- The mechanisms that dissipate vibration energy over time.
- Effective mass
- The portion of system mass participating in a selected mode.
- Serviceability
- Performance under use, including comfort, deflection and vibration.
- Joist mode
- A floor vibration shape in which secondary members move while relatively stiff primary lines act approximately as nodes.
- Girder mode
- A global shape in which primary girders deflect between columns and the supported secondary system follows their movement.
- Resonance
- Amplified response that can occur when repeated forcing lies near a structural natural frequency.
- Acceleration response
- A serviceability measure connected to what occupants feel under dynamic excitation rather than static deflection alone.
- Frequency screen
- A simplified estimate used to identify a potentially governing mode before a fuller response and acceptance assessment.
Long-Span Floors and Vibration FAQ
Can a strong floor still vibrate poorly?
Yes. Ultimate strength and vibration serviceability test different behaviours, so both require explicit evaluation. Occupant comfort depends on mode shape, frequency, forcing, participating mass and damping, not simply member capacity.
Which floor-vibration mode governs the screening result?
Compare credible complete-floor modes and retain the lower calculated frequency for further assessment. Keep each component deflection with its assumed shape, because combining incompatible joist and girder contributions creates a meaningless number.
Does added mass always improve floor vibration?
Added mass does not automatically improve performance because many interventions change stiffness and mass together. Recalculate frequency and response for the modified system, then check the actual excitation and occupancy criterion before selecting the remedy.
Why keep the mode label beside a frequency?
The number is meaningful only for the assumed moving components and boundaries. Labelling joist or girder mode prevents a later reader from combining incompatible deflections or applying a local result to the entire floor.
What information completes a comfort assessment?
Occupancy, forcing frequency, walking path, participating mass, damping and an appropriate response or acceleration criterion are needed. The screening frequency locates a concern but does not itself demonstrate acceptable experience.
How can services affect long-span selection?
Deep fabricated beams or trusses may create useful service routes, while solid members and haunches can obstruct them. Openings, fire protection, fabrication tolerances and erection sequence must be coordinated with the structural benefit.
What makes a vibration remedy defensible?
Identify the governing mode and response variable first, then show how the proposal changes stiffness, mass, span or damping. State the construction consequence and calculate rather than assuming that deeper, heavier or stiffer is always better.
Why can a global girder mode be missed?
Checking secondary members alone treats primary lines as fixed and omits their movement. A flexible girder can add substantial deflection, lower the system frequency and become the controlling global shape even when each joist seems adequate.
How should a long-span option be concluded?
Name the system, explain how it meets span and service-zone constraints, and identify one critical verification. Include fabrication, erection stability, fire protection and vibration so structural efficiency does not hide a project burden.
Exam move
Draw the joist and girder modes without looking and mark nodes, moving supports and participating members. Under each sketch, list only the deflection contributions compatible with that shape. Rework the printed calculations by changing one deflection at a time, showing the sum, square root, substitution and hertz result. Then explain why the lower screened frequency does not itself decide comfort.
Create a remedy table with columns for stiffness, mass, damping, span, fabrication, services and fire; use it to compare a deeper girder, added slab thickness, a haunch and a truss. For each option, state the response variable it changes and one construction cost.
Finish with a figure-led answer that identifies excitation, mode, likely occupancy sensitivity and the further acceleration or response information needed before recommending a modification.
