PROBLEM 2.6
The rigid beam is supported by a pin at A and by cables BD and CE. If the maximum allowable normal deformation in each cable is ϵmax = 0.002 mm/mm, determine the maximum vertical displacement of the load P.
00:00 Problem Interpretation
✅ Sketch the behavior of the beam due to the application of load P at its end. Draw a right triangle and show the offsets of the BD, CE and end cables in this triangle.
This scheme will be important for the next steps in solving the problem.
01:15 Case 1: Deformation in Cable BD Equals Allowable Deformation
✅ By considering that the rope BD reaches the maximum allowable normal strain (εmax), applying the normal strain formula, it is possible to find how much the rope BD has elongated.
In possession of this result, it is easy to determine the maximum displacement of the CE cable by similarity of triangles.
Note that when carrying out the check, we note that the normal deformation in cable CE EXCEEDS the maximum allowable normal deformation for each cable, therefore, we should not assume that the normal deformation in cable BD is equal to the given maximum normal deformation.
Go to case 2!
04:40 Case 2: Deformation in the CE Cable Equals Allowable Deformation
✅ When considering that the CE cable reaches the maximum allowable normal deformation (εmax),
applying the formula of normal deformation, it is possible to find the maximum displacement of the CE cable.
In possession of this result, it is easy to determine the maximum displacement of the BD cable by similarity of triangles.
Note that when carrying out the check, we notice that the normal deformation in cable BD DOES NOT EXCEED the allowable normal deformation for each cable, so using similarity of triangles it is easy to determine therefore the maximum vertical displacement of the end of the beam on which the load P Act.
📚 Source: Mechanics of Materials 7th Ed. (R.C. Hibbeler)
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