A cantilever beam is a structural member fixed at one end and unsupported at the other. Loads on the beam produce shear force and bending moment that are transferred to the fixed support. Cantilevers are used in balconies, canopies, sunshades, bridge decks and other projections. The formulas below describe ideal beam actions; an actual reinforced-concrete or steel cantilever requires design checks for strength, deflection, stability, anchorage and support fixity. For beam types and construction details, see our article on cantilever beam types and applications.
Basic Concept of Cantilever Beam
In the ideal cantilever model, the fixed support provides the vertical reaction and fixing moment needed for equilibrium. The free end has no support reaction; its bending moment is zero only when no external couple is applied at that end. Internal shear force and bending moment vary along the span according to the applied loading.
Key Characteristics
- Fixed at one end and free at the other
- Maximum bending moment occurs at the fixed support
- Maximum shear force occurs at the support
- Maximum deflection occurs at the free end
- Tension develops at the top face under downward loading
Structural Behavior of Cantilever Beam
When a downward load is applied, the upper portion of the beam near the fixed support experiences tensile stress, while the lower portion experiences compressive stress. In reinforced concrete cantilever beams, reinforcement is therefore placed at the top near the support. Deflection gradually increases toward the free end, and improper design may cause excessive cracking and serviceability problems.
Loading Conditions and Formulas
Cantilever beams may be subjected to point loads, uniformly distributed loads, or combined loads, and structural design depends on accurate moment and shear calculations.
1. Point Load at Free End
For a point load W acting downward at the free end of an ideal cantilever of length L:
Maximum shear at the fixed support: Vmax = W
Maximum bending moment at the fixed support: Mmax = W × L
Free-end deflection (linear-elastic prismatic beam): δmax = W L³ / (3 E I)
Here E is Young’s modulus and I is the second moment of area about the bending axis. These are elastic-analysis equations, not complete RCC or steel design checks.
2. Uniformly Distributed Load (UDL)
For a uniformly distributed load w over the full cantilever length L:
Maximum shear at the fixed support: Vmax = w × L
Maximum bending moment at the fixed support: Mmax = w L² / 2
Free-end deflection (linear-elastic prismatic beam): δmax = w L⁴ / (8 E I)
Here w is the load per unit length, E is Young’s modulus and I is the second moment of area. If the cantilever carries multiple or partial-span loads, calculate the effects using the appropriate load case and superposition where linear-elastic assumptions apply.
Cantilever Beam Design Considerations
Proper design ensures structural safety and long-term durability. The beam must resist maximum bending moment at the fixed support, and shear capacity must be checked carefully. Span-to-depth ratio should be maintained to control deflection. Adequate development length and anchorage of reinforcement are essential to achieve proper fixity. Crack control measures such as correct bar spacing and sufficient concrete cover must also be ensured.
Comparison: Cantilever Beam vs Simply Supported Beam
| Feature | Cantilever Beam | Simply Supported Beam |
|---|---|---|
| Support Condition | One end fixed | Both ends supported |
| Maximum Bending Moment Location | At fixed support | At mid-span |
| Maximum Deflection Location | At free end | At center |
| Reinforcement Placement (RCC) | Top near support | Bottom at mid-span |
| Structural Application | Projections and overhangs | Regular span systems |
Advantages of Cantilever Beam
Cantilever beams eliminate the need for support at the free end, offering architectural flexibility and open space beneath projections. They are efficient for balconies, sunshades, canopies, and bridge segments.
Limitations of Cantilever Beam
Cantilever beams experience high bending stress at the fixed support, requiring strong and rigid anchorage. Longer spans demand greater depth and stronger materials. Deflection control is critical to prevent structural and serviceability issues.
Applications of Cantilever Beam
Cantilever beams are commonly used in residential balconies, overhead slabs, canopies, flyovers, bridge construction, industrial platforms, and signboard supports. Their ability to extend outward without additional support makes them a fundamental component of structural engineering design.