A cantilever is a beam that is fixed at one end and free at the other, like the jib of a tower crane extending out from the mast. When the crane lifts a load, the jib must carry the load without tipping, bending too much, or breaking. This matters in construction because cranes move heavy materials high above the ground, where stability and strength are critical.
Engineers use cantilever physics to predict forces before a crane is built or operated.
The suspended load creates a downward force at the free end of the jib, which produces a turning effect called torque or moment about the fixed mast. Inside the jib, the top members often experience tension while lower members experience compression, depending on the exact truss design and loading. The bending moment is largest near the fixed end, so the mast connection and inner jib sections must be especially strong.
Counterweights, truss geometry, and careful load limits help keep the crane balanced and safe.
Key Facts
- A cantilever beam is fixed at one end and free at the other.
- Torque or moment is calculated by M = Fd, where F is force and d is perpendicular distance from the pivot.
- For a point load at the free end of a cantilever, the maximum bending moment occurs at the fixed end.
- Weight force is W = mg, where m is mass and g is about 9.8 m/s^2 on Earth.
- A longer jib increases the moment from the same load because the distance d is larger.
- Static balance requires net force = 0 and net torque = 0.
Vocabulary
- Cantilever
- A beam or structure that is fixed at one end and extends outward with the other end unsupported.
- Jib
- The horizontal arm of a crane that extends from the mast and supports the moving trolley and load.
- Bending moment
- The internal turning effect in a beam caused by external forces acting at a distance.
- Tension
- A pulling stress that stretches a material or structural member.
- Compression
- A squeezing stress that shortens or presses together a material or structural member.
Common Mistakes to Avoid
- Using mass instead of weight in moment calculations is wrong because torque needs force, so convert mass to weight using W = mg.
- Forgetting the distance from the mast is wrong because the same load creates a larger moment when it is farther out on the jib.
- Assuming the bending moment is the same everywhere is wrong because it is largest near the fixed support and changes along the cantilever.
- Ignoring counterweights is wrong because a tower crane must balance torques from both the load side and the counter-jib side.
Practice Questions
- 1 A 500 kg load hangs from the end of a crane jib 20 m from the mast. Using g = 9.8 m/s^2, calculate the moment about the mast.
- 2 A crane lifts a 1200 kg load at a distance of 15 m from the mast. What counterweight force is needed 10 m on the opposite side to balance the torque?
- 3 Explain why engineers make the fixed end of a cantilever crane jib stronger than the free end, even though the load hangs at the free end.