A crane of mass 3000 kg supports a load of 10000 kg as shown in Figure P 12.41 . The crane is pi

step 1 Here, at point A, we have AY and AX. At point B, we only have Vpx, but no VBY. Now, at a distanc

A crane of mass 3000 kg supports a load of 10000 kg as shown...

A crane of mass 3000 $\mathrm{kg}$ supports a load of 10000 $\mathrm{kg}$ as shown in Figure $\mathrm{P} 12.41$ . The crane is pivoted with a frictionless pin at $A$ and rests against a smooth support at $B$ . Find the reaction forces at $A$ and $B .$

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Key Concepts

Reaction Forces at Supports

This concept involves calculating the forces exerted by supports or connections (like pins and rollers) on a structure. These forces are critical to maintain equilibrium, and understanding how to resolve their components, especially in systems with frictionless and smooth contacts, is essential for structural analysis.

Moment Equilibrium

Moment equilibrium involves ensuring that the sum of the moments (or torques) about any chosen pivot point is zero. This is crucial in determining unknown forces in structures, particularly when forces cause rotational effects, and helps to distribute loads appropriately across supports.

Static Equilibrium

This concept refers to a state in which a system or body is at rest, meaning that the sum of all forces and the sum of all moments (torques) acting on it are both zero. It is fundamental in analyzing structures because it ensures that there is no linear or rotational acceleration, and it allows for the determination of unknown reaction forces.

Free-Body Diagram

A free-body diagram is a simplified representation of a structure or object that shows all external forces and moments acting on it. By isolating the body and illustrating forces such as weight, reaction forces, and applied loads, it simplifies the process of applying the conditions of static equilibrium.

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