Rigid vs Flexible Bracing Systems for HVAC Equipment

Fundamental Bracing Classification

Seismic bracing systems for HVAC equipment fall into two distinct categories based on their lateral stiffness characteristics: rigid bracing and flexible bracing. The classification depends on the natural frequency of the equipment-brace system relative to the supporting structure’s fundamental frequency.

Rigid bracing systems exhibit high lateral stiffness, creating a strong mechanical coupling between equipment and structure. These systems force equipment to follow structural motion with minimal relative displacement.

Flexible bracing systems incorporate compliance through isolation elements or yielding members, allowing controlled relative motion between equipment and structure while maintaining seismic restraint.

Stiffness and Deflection Relationships

Lateral Stiffness Calculation

The lateral stiffness of a bracing system is defined as:

$$k = \frac{F}{\delta}$$

where:

• $k$ = lateral stiffness (lb/in or N/mm)
• $F$ = applied lateral force (lb or N)
• $\delta$ = lateral deflection (in or mm)

For a diagonal brace at angle $\theta$ from horizontal:

$$k_{lateral} = \frac{EA}{L} \cos^2\theta$$

where:

• $E$ = elastic modulus of brace material (psi or MPa)
• $A$ = cross-sectional area (in² or mm²)
• $L$ = brace length (in or mm)
• $\theta$ = brace angle from horizontal (degrees)

Deflection Under Seismic Load

The lateral deflection of equipment under seismic force is:

$$\delta = \frac{F_p}{k_{total}}$$

where:

$$F_p = 0.4 a_p S_{DS} W_p \left(\frac{1 + 2\frac{z}{h}}{R_p}\right)$$

per ASCE 7-22 Section 13.3.1, and:

• $a_p$ = component amplification factor
• $S_{DS}$ = design spectral response acceleration
• $W_p$ = component operating weight (lb or N)
• $z$ = height of attachment point above grade
• $h$ = structure height
• $R_p$ = component response modification factor

Natural Frequency Considerations

Equipment-Brace System Frequency

The natural frequency of the combined equipment-brace system is:

$$f_n = \frac{1}{2\pi}\sqrt{\frac{k_{total}}{m}}$$

where:

• $f_n$ = natural frequency (Hz)
• $k_{total}$ = combined lateral stiffness (lb/in or N/mm)
• $m$ = equipment mass (lb-s²/in or kg)

For English units: $m = \frac{W_p}{386.4}$ where $W_p$ is in pounds.

Classification Criteria

Per ASCE 7-22 and ASHRAE HVAC Applications, systems are classified as:

Comparison of System Applications

Rigid Bracing Systems

Design characteristics:

• Deflection typically < 0.25 inches under design seismic load
• Brace angles typically 30° to 60° from horizontal
• Steel members with L/r < 200 for compression
• Connection capacity governs design

Flexible Bracing Systems

Design characteristics:

• Deflection typically 0.5 to 4.0 inches under design seismic load
• Incorporates elastomeric elements or yielding members
• Must verify restoring force capability
• Requires clearance for operational and seismic displacement

Dynamic Amplification Effects

When equipment natural frequency approaches the structure’s fundamental frequency, dynamic amplification occurs. The amplification factor is:

$$\beta = \frac{1}{\sqrt{\left(1 - \left(\frac{f_n}{f_s}\right)^2\right)^2 + \left(2\xi\frac{f_n}{f_s}\right)^2}}$$

where:

• $f_s$ = structure fundamental frequency (Hz)
• $\xi$ = damping ratio (typically 0.02 to 0.05 for HVAC equipment)

Maximum amplification occurs when $f_n \approx f_s$, potentially doubling or tripling seismic forces on equipment.

Design Selection Criteria

Choose Rigid Bracing When:

1. Equipment is not vibration-isolated
2. Equipment weight < 1,000 lb and lateral forces are manageable
3. Equipment operates at low speeds with minimal vibration
4. Simple, cost-effective installation is prioritized
5. Building has stiff lateral system ($f_s > 4$ Hz)

Choose Flexible Bracing When:

1. Equipment is vibration-isolated for operational reasons
2. Equipment has high center of gravity requiring controlled motion
3. Building has flexible lateral system ($f_s < 2$ Hz)
4. Equipment is in seismically isolated structure
5. Reducing transmitted forces to structure is critical

Code Requirements and Verification

Per ASCE 7-22 Chapter 13:

Rigid systems must satisfy:

• $F_p$ calculated per Section 13.3.1
• Connections designed for 1.4 $F_p$ per Section 13.4
• Bracing members checked for combined axial and bending

Flexible systems must additionally verify:

• Adequate clearance for design displacement plus 2.5 times operational movement
• Restoring force adequate to return equipment to neutral position
• Isolator stability under combined vertical and lateral loads
• Snubbing mechanism prevents excessive displacement

Installation Considerations

Rigid bracing installation:

• Verify structural attachment capacity before installation
• Maintain brace angles within 30° to 60° from horizontal
• Ensure tight connections with minimal play
• Document as-built brace geometry for record drawings

Flexible bracing installation:

• Verify clearances in all directions before final positioning
• Confirm isolator alignment and uniform compression
• Test restoring force by manual displacement verification
• Install limit stops or snubbers at design displacement plus margin

Conclusion

Selection between rigid and flexible bracing depends on equipment characteristics, operational requirements, structural properties, and seismic design parameters. Rigid systems offer simplicity and direct load paths for non-isolated equipment, while flexible systems maintain vibration isolation effectiveness and accommodate larger structural displacements. Proper classification using natural frequency criteria and dynamic analysis ensures code-compliant, effective seismic restraint that protects both equipment and building occupants.