Single-Girder vs Double-Girder Dynamic Behavior
While vertical vibration governs bending response under gravity loading, horizontal vibration is closely related to trolley movement and bridge frame stiffness.
In overhead cranes, horizontal natural frequency plays an important role in dynamic stability, especially when the trolley is positioned at mid-span.
Horizontal Natural Frequency
For horizontal vibration with the trolley located at the center of the span, the natural frequency is expressed as:
fz = 1 2π √ K2 M3
Where:
- K2 – horizontal stiffness of the girder system
- M3 – equivalent vibrating mass for horizontal motion
K2 = 192 E Iy L3
Where:
- E – modulus of elasticity
- Iy – moment of inertia about the vertical axis
- L – span
As with vertical vibration, stiffness decreases rapidly with increasing span due to the cubic dependence on L.
Equivalent Mass for Horizontal Vibration
The equivalent mass for horizontal vibration differs from the vertical case and is typically expressed as:
M3 = 0.383 Gq + MV n
Where:
- Gq – girder mass
- MV – trolley mass
- n – number of girders
The coefficient 0.383 represents the modal mass participation for the first horizontal bending mode.
Again, not all structural mass contributes equally to vibration.
Recommended Frequency Limits
Recommended minimum horizontal frequencies are:
- Single-girder cranes: fz ≥ 3 Hz
- Double-girder cranes: fz ≥ 2 Hz
The lower permissible frequency for double-girder cranes is justified by their higher overall bridge frame rigidity.
A two-girder system forms a more stable structural frame, reducing sensitivity to lateral oscillations.
Why Configuration Matters
The difference between single and double-girder cranes is not merely structural weight.
A double-girder crane:
- Has improved torsional rigidity
- Provides better load distribution
- Reduces lateral flexibility
As a result, acceptable dynamic performance can be achieved at slightly lower horizontal natural frequencies.
In contrast, single-girder cranes are more sensitive to horizontal flexibility and therefore require higher minimum frequency values to maintain stable operation.
Conclusion
Horizontal vibration behavior depends strongly on structural configuration and span. Because stiffness scales with EI/L3 , increasing span significantly reduces horizontal natural frequency unless inertia is increased.
Single-girder cranes require higher minimum frequencies due to lower frame rigidity, whereas double-girder systems can tolerate slightly lower values while maintaining acceptable dynamic performance.
Proper evaluation of horizontal natural frequency is therefore essential for ensuring operational stability and structural reliability in overhead crane design.