Equilibrium of a Suspended Clothesline
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Transcript of Equilibrium of a Suspended Clothesline
Simply Mechanics (STATICS): An Application Case StudyEQUILIBRIUM OF A SUSPENDED CLOTHESLINE
ByPEREZ, NIKKA JANINE L.
PEREZ, YHAJ NICOLE THADDEUS T.Dept. of Civil Engineering
De La Salle University – Manila10 December 2012
INTRODUCTION:A clothesline is a rope or wire on which washed clothes are hung to dry. It is usually
stretched between two points (e.g. two rods), whether outside or indoors, above the level of the ground. Figure 1 shows examples of clotheslines of different types.
Figure 1. Examples of clotheslines
The principles in engineering mechanics about force systems in equilibrium can be demonstrated by analyzing the equilibrium of a suspended clothesline. Consider the actual clothesline shown in Figure 2.
Figure 2. A suspended clothesline.
The suspended clothesline is an example of a parallel force system. A parallel force system is a type of force system where in all forces are oriented along one axis. In this case, all forces acting on the steel pipe are vertical since only gravity loads due to the weights of the hanging objects act. The suspended clothesline is actually a parallel force system in space or three dimensional (3D). However, it can be reduced into a two dimensional system (2D).
Figure 3. The clothesline as a parallel force system
EQUILIBRIUM ANALYSIS:Haven’t you wondered how much force each material (as for our example of a
suspended clothesline, it is a metal or specifically, an angle bar) supports to keep the clothesline in equilibrium? Let’s apply the principles of engineering mechanics to answer this query.
Figure 4. A Parallel Force System
The length of the horizontal clothesline itself (steel pipe) is 123.5 cm. Figure 5 shows pictures of the clothesline showing its actual length, which is about 123.5 cm.
Figure 5. The length, L, of the clothesline itself (steel pipe)
Figure 6. 5 identical hangers were used as shown.
Figure 7. 5 shirts of the same sizes were also used as shown.
The shirts were drenched and the hangers were put to each of the shirts. The masses and weights of each are as follow:
Hanger with shirt Mass (kg) Weight (N)M x 9.81 m/s2
1 0.5 4.912 0.36 3.533 0.41 4.024 0.45 4.415 0.5 4.91
The free body diagram of the suspended clothesline with the hangers with shirts on it is shown below in Figure 8. The hangers with shirts are represented in the free body diagram (FBD) as W and the tensile forces in the angel bars are represented by T. Neglect the weight of the steel pipe and assume to be rigid in the analysis.
Figure 8. Free Body Diagram
To compute the force acting on T1, the equilibrium equation of summation of forces with respect to the vertical axis is applied.
Since there are two unknowns in the equation, the equilibrium equation of summation of moments about point A is applied to cancel T1 to have only one unknown, which is T2.
Since T2 is already known, it can now be substituted to the equilibrium equation of summation of forces with respect to the vertical axis to get T1.
So, the forces acting at the two angle bars are as follow.
CONCLUSION:The arrangement of the clothes (wet and dry) that are hung on the clothesline will
affect the magnitude of the forces acting on the steel. In the design of the clothesline, the following factors should be considered:
a. Mass of each hanging objectb. Whether the clothes hung are wet or dryc. Location of the clothesline — if it is screwed to the wall, or two sticks pinned on
the ground that is connected by a wire, etc.
The location of the angle bar on the steel pipe depends on the weights supported by the steel pipe. If the weights are hanged symmetrically, then the angle bar is placed at the mid span of the steel pipe to satisfy equilibrium. However, for unsymmetrical loading where the weight at the left is not equal to the weight at the right, the location can be obtained by applying the equation of equilibrium for moments.
RECOMMENDATION FOR FURTHER STUDY:
The case study can still be improved by discussing related scenario or other parameters such as:
1. If the clothesline used are made of metal wires or ropes, how much weight for the hanging clothes (wet and dry) can be used to avoid sagging of the wires.
2. Design of the clothesline — like it can be stretched between two sticks above the level of the ground instead of having it pinned on the wall.
3. Analysis and design of different types of a clothesline in 3D and/or 2D.4. Analysis of clothesline that can be frequently located in back gardens, or on
balconies.5. Analysis of longer clotheslines which often have props holding up sections in the
middle due to the weight of the clothing.6. Analysis of supports or pin reactions, and force of the members. Here, the
student has to make further experiments or research.