6.13
Marcos: Resolución de problemas I
Considera una grúa horca con una carga externa suspendida del polipasto. Las dimensiones de los componentes de la grúa se muestran en la figura. Se re…
Considere una grúa giratoria con una carga externa de la polea.
Si se conocen las dimensiones de los miembros de la grúa, ¿cuáles son las fuerzas de reacción en las uniones de los pasadores, teniendo en cuenta que las poleas no tienen fricción?
El sistema es una estructura de marco, que consta de un miembro BD de dos fuerzas y un miembro ABC de múltiples fuerzas.
Considerando un diagrama de cuerpo libre y aplicando las condiciones de equilibrio de fuerzas para la sección inferior de la polea, se puede obtener la tensión en el cable.
Teniendo en cuenta el punto C, la tensión en el cable vertical se dirige hacia abajo, mientras que para el cable horizontal, se dirige hacia la junta A.
En el miembro DB, la fuerza FBD se puede expresar mediante un triángulo de pendiente.
La condición de equilibrio de momento en la unión A da la fuerza a lo largo de BD.
Aplicando las condiciones de equilibrio de fuerzas, se calculan las fuerzas de reacción horizontal y vertical en la junta A.
Ahora, considerando el diagrama de cuerpo libre para el miembro BD, las condiciones de equilibrio de fuerzas se pueden aplicar en la unión D para obtener las fuerzas de reacción horizontal y vertical en D.
Q1: What is the difference between a two-force member and a multi-force member in frame analysis?
A two-force member is a straight element subjected only to forces at its two ends, with forces equal in magnitude but opposite in direction, causing pure tension or compression. A multi-force member experiences more than two forces distributed along its length, including external loads, reaction forces at pin joints, and cable forces, resulting in complex stress distribution.
Q2: How do you determine cable tension in a jib crane pulley system?
For a frictionless pulley system, the load weight balances the tension in the cables. In the lower pulley section, each cable carries an upward tension equal to half the total load. For the upper pulley, the vertical cable tension remains the same as the lower section since it is part of the continuous cable system.
Q3: What equilibrium conditions are applied to find reaction forces at pin joints?
Force equilibrium conditions require that the sum of horizontal and vertical forces equals zero at each joint. Moment equilibrium conditions require that the sum of moments about a point equals zero. These conditions are applied systematically to free-body diagrams of each structural member to solve for unknown reaction forces.
Q4: How is the force in member BD resolved in a jib crane frame analysis?
The force FBD in member BD is resolved into horizontal and vertical components using a slope triangle, which relates the member's geometry to its force components. The moment equilibrium condition at joint A yields the magnitude of FBD. Substituting known dimensions and pulley radius values determines FBD as 50 kN in this example.
Q5: What are the typical reaction force values at pin joints in a loaded jib crane?
Reaction forces depend on load magnitude and structural geometry. In this jib crane example, the horizontal reaction force at joint A is 40 kN, while the vertical reaction force is -20 kN. At joint D, the horizontal reaction is -30 kN and the vertical reaction is 40 kN, determined by applying force equilibrium conditions.
Q6: Why is analyzing the lower pulley section important before analyzing the upper pulley?
The lower pulley section directly supports the external load, establishing the cable tension value. This tension value propagates through the continuous cable system to the upper pulley section. Determining lower pulley tension first provides known force values needed to solve for reaction forces at pin joints in the frame structure.
Q7: How does the free-body diagram method apply to frame problem solving?
Free-body diagrams isolate each structural member and show all forces acting on it, including external loads, cable tensions, and reaction forces at pin joints. Applying force and moment equilibrium conditions to these diagrams systematically yields unknown reaction forces. This method using method of joints problem solving principles allows solving complex frame structures step by step.