Name: jib crane reaction forces in frames
Uploaded: 2023-09-22T11:49:25.000Z
Duration: 1 min 24 s
Channel: JoVE

Consider a jib crane with an external load from the pulley.
If the dimensions of the crane members are known, what are the reaction forces at the pin joints, considering that the pulleys are frictionless?
The system is a frame structure, consisting of a two-force member BD and a multi-force member ABC.
Considering a free-body diagram and applying the force equilibrium conditions for the lower pulley section the tension in the cable can be obtained.
Considering point C, the tension in the vertical cable is directed downwards, while for horizontal cable, it is directed towards joint A.
In member DB, the force&#160; FBD can be expressed using a slope triangle.
The moment equilibrium condition at joint A gives the force along BD.
Applying the force equilibrium conditions, the horizontal and vertical reaction forces at joint A are calculated.
Now, considering the free-body diagram for member BD, the force equilibrium conditions can be applied at joint D to obtain the horizontal and vertical reaction forces at D.

frames: problem solving i

Consider a jib crane with an external load suspended from the pulley. The dimensions of the crane members are shown in the figure. A systematic analysis of the frame structure is required to determine the reaction forces at the pin joints, assuming that the pulleys are frictionless.
<img alt="Crane load analysis diagram; static equilibrium; force application; 20 kN load; beam system." src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1761830439000" data-alt="Figure 1">
The system has two main structural components: a two-force member BD and a multi-force member ABC. The two-force member BD refers to a straight element subjected only to forces at its two ends, B and D, with no additional forces acting along its length. These forces are equal in magnitude but opposite in direction, resulting in the member being either in pure tension or compression. On the other hand, the multi-force member ABC is subjected to more than two forces distributed along its length. These forces may include external loads, reaction forces at pin joints, and the force exerted by the cable. Due to multiple forces acting on member ABC, it experiences a more complex stress distribution compared to the simpler two-force member BD.
<img alt="Static equilibrium diagram with forces (ΣFx, ΣFy) on a pulley system lifting a weight." src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1761830439000" data-alt="Figure 2">
Considering the lower pulley section, the load weight balances the tension in the cables resulting in an upward tension of 10 kN for each cable. Now, considering the upper pulley section, the tension T in the vertical cable is directed downwards, while it points towards joint A for the horizontal cable. The tension in the vertical cable is also 10 kN as it is part of the same continuous cable system.
In member DB, the force FBD can be resolved into its horizontal and vertical components using a slope triangle. The moment equilibrium condition at joint A gives FBD as 50 kN.
The horizontal force equilibrium condition can be applied to joint A.
<img alt="Static equilibrium equation ΣF=0, involving forces and tensions, depicted in a scientific diagram." src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
Substituting the values of the length AB, AC, and radius of the pulley C, the force FBD is obtained as 50 kN.
The horizontal force equilibrium condition gives the reaction force at A as 40 kN.
<img alt="Static equilibrium equation ΣFy=0; diagram for force balance analysis in physics." src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
Similarly, using the vertical force equilibrium condition, the vertical reaction force at A is estimated as -20 kN.
<img alt="Static equilibrium equation ΣFx=0, illustrating balance of forces in a mechanical system." src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 3">
The force equilibrium conditions can be applied at joint D to obtain the horizontal and vertical reaction forces at D.
<img alt="Static equilibrium equation; ΣFx=0; formula for physics analysis." src="/files/ftp_upload/14291/14291_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 4">
<img alt="Static equilibrium equation, Fy-FDBy=0, used in force diagram and mechanics analysis." src="/files/ftp_upload/14291/14291_PT_Equation_5v2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 5">
The obtained results indicate that the horizontal and vertical reaction forces at point D are -30 kN and 40 kN, respectively.

Frames: Problem Solving I

Consider a jib crane with an external load suspended from the pulley. The dimensions of the crane members are shown in the figure. A systematic analysis ...

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jib crane reaction forces in frames

Jib crane reaction forces in frames are found by analyzing the pin joints, the cable tension, and the load carried by the pulley. The structure in this problem has an external load suspended from the pulley, and the member sizes are shown in the figure. Because the pulleys are frictionless, the force balance can be worked out step by step.

The frame has two main parts. Member BD is a two-force member, which means it is a straight part loaded only at its two ends, D and B. Those end forces are equal in size and opposite in direction, so the member is in either tension or compression. Member ABC is a multi-force member, so it carries more than two forces along its length. These forces include the pin reactions, the external load, and the cable force, which makes its stress state more complex.

The lower pulley section shows that the load weight is balanced by the cable tension. That gives an upward tension of 10 kN in each cable. In the upper pulley section, the tension T in the vertical cable points downward, while the horizontal cable tension points toward joint A. The vertical cable tension is also 10 kN because it is part of the same continuous cable system.

To solve member DB, the force FBD is split into horizontal and vertical parts with a slope triangle. A moment balance at joint A gives FBD as 50 kN. The horizontal force balance at A then uses the lengths AB and AC and the pulley radius at C to confirm this value. From that balance, the reaction at A is 40 kN in the horizontal direction, and the vertical reaction at A is -20 kN. The force balance at joint D gives the reaction forces there as -30 kN horizontally and 40 kN vertically.

Jib Crane Reaction Forces in Frames

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key terms and concepts

Analyze a jib crane frame with a frictionless pulley, two-force member BD, and multi-force member ABC to find reaction forces at joints A and D.

Jib Crane Reaction Forces in Frames | JoVE K12

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Jib Crane Reaction Forces in Frames

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