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6.14: Frames: Problem Solving II

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Mechanical Engineering

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Frames: Problem Solving II

6.14: Frames: Problem Solving II

Consider a hydraulic hoist supporting a load of 1 kN. Assuming a simplified schematic representation of this frame structure, the force acting on BD and BF members can be determined.

Figure 1

The member dimensions and the weight of the load are known parameters. This structure can be considered a frame with BF and BD acting as two-force members, while EFG and EDC are multi-force members.

A free-body diagram for the member EFG is considered. The inclined force FBF can be resolved into the vertical and horizontal components. The moment equilibrium condition is applied to joint E.

Equation 1

The force FBF is calculated to be 1.546 kN. Then, the horizontal force equilibrium condition is applied at joint E.

Equation 2

Substituting the value of the horizontal component of FBF into the equilibrium equation, the horizontal reaction force at E is calculated as 0.375 kN. Similarly, the vertical force equilibrium condition is applied.

Equation 3

The calculated vertical reaction force at joint E is 0.500 kN.

Now, a free-body diagram for the member EDC is considered. The horizontal and vertical components of FBD can be expressed using a slope triangle. The moment equilibrium condition at point C is applied.

Equation 4

The force FBD is calculated as 1.677 kN.

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Relevant Keywords: Hydraulic Hoist Frame Structure Two-force Members Multi-force Members Free-body Diagram Force Equilibrium Moment Equilibrium Force Components Reaction Forces

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