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To calculate the deflection of a jib crane , we need to consider the structural behavior of the cantilever beam that forms the jib. The deflection depends on factors such as the load, material properties, length of the jib, and its cross-sectional geometry.

The jib crane is typically modeled as a cantilever beam subjected to a point load or uniformly distributed load at the free end. Below is the step-by-step process for calculating the deflection:

1. Known Parameters

• Load ($F$): The weight of the load applied at the free end of the jib.
• Length of the jib ($L$): The horizontal distance from the fixed support to the free end.
• Material Properties:
  • Young’s modulus ($E$) of the material (e.g., steel: $200\text{GPa}$).
• Cross-sectional properties:
  • Moment of inertia ($I$) of the jib’s cross-section.
• Load type: Point load at the free end or uniformly distributed load.

2. Assumptions

• The jib is a straight, horizontal cantilever beam.
• The load is either a point load at the free end or a uniformly distributed load along the length.
• The material is linearly elastic and follows Hooke’s law.

3. Deflection Formulas

Case 1: Point Load at the Free End

For a cantilever beam with a point load ($F$) at the free end:

Where:

• $\delta$ = Maximum deflection at the free end.
• $F$ = Point load at the free end.
• $L$ = Length of the jib.
• $E$ = Young’s modulus of the material.
• $I$ = Moment of inertia of the cross-section.

Case 2: Uniformly Distributed Load

For a cantilever beam with a uniformly distributed load ($w$) along its length:

Where:

• $w$ = Uniformly distributed load per unit length ($w=F/L$, if total load is known).