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Introduction:

Top assembly structure of the upper part named cross-arm structure on a concrete pole is described in this paper, where all of its specifications along with its designs are given here along with its mathematical calculation and virtual simulation. The main objective is to calculate the sustained load for the given structure and the weight capacity of that structure as well. To know about the failure point of the product.

Mainly the topics described here for calculation purpose of that structure are:

1. Moment of inertia due to vertical load
2. Bending moment
3. Deflection due to vertical load
4. Wind loading on the cross arm

2. Objective:

1. To discuss the main parameters required to design the said cross arm assembly along with its additional fittings.
2. To present the 3D model of the said product.
3. To obtain the virtual load test in software.
4. To obtain the characteristics of wind loading.

Note: The ice condensation on ACSR cable in Afghanistan is not discussed in here since it’s a rare case.

3. Technical specifications:

Sl no.	Parameter	Measurements
1	Cross arm length	2000 mm
2	Cross arm type	‘L’ section (70×70×7)
3	Cross arm weight
4	No of support on the pole	3
5	Coating	Hot deep galvanising
6	Nut bolts and accessories	4 nuts and bolts are attached on it

 

4. Mathematical calculation:

The load test and a simulation in software tools are given in this paper along with some of the mathematical calculation are given due to understanding the proper bending stress, diflection, shear stress without complexity.

The process is some kind of that first we calculated the mathematical load applied on the cross-arm in terms of its self-weight then the total load and the parameters are calculated and then by applying the load a virtual simulation is done.

5. Design criteria:

Let us consider the cross-arm as a short length bean having a cross sectional area of ‘L’ shaped. For that particular assembly, there the supports are provided at three positions of that structure, the first one is at the middle point of the structure and another two supports are provided at the left and the right side apart from the mid-point. The design of the structure is depending on the following points:

1. Magnitude and type of loading.
2. Duration of loading.
3. Material of the beam.
4. Shape of the bean cross-section.

Beams are designed according the given formulae.

5.1. Bending stress:

The maximum bending stress can be found by applying the properties of the said structure.

5.2. Deflection:

In addition, limitations are sometime placed on maximum deflection of the beam due to the effect of the dead load. The deflection can be calculated by the formulae,

5.3. Shear stress:

Likely allowable bending stress, allowable shear stress varies for different materials and can be obtained from a building code. Maximum shear force can be obtained from the shear force diagram.

6. Mathematical calculation:

From here we can calculate the parameters described above for the said product. There are three types of static loading can be observed on that cross-arm structure.

1. Pin type insulator weight along with 70/12 ACSR conductor weight.
2. Pin type insulator weight along with 120/20 ACSR conductor weight.
3. Pin type insulator weight along with 185/30 ACSR conductor weight.

Instead of three of this, another one weight can be add as a static load along with this, it is the dead weight of the suspension insulator.

Here the calculation is shown on the first one sample:

6.1. Bending stress:

6.2. Deflection:

6.2. Shear Stress:

Similarly, by applying the value of weight of the different sample of ACSR conductor (70/12,120/20, 185/30) we can find out the different parameters like bending stress, deflection and shear stress for the cross-arm. And we can check that the the structure is sustainable or not.

Along with the mathematical calculation of the cross-arm parameters (Bending stress, deflection, shear stress) we have produce some of the virtual simulation results which can give a sort of a proof about the acceptance of the product and its sustainability.

7. Virtual simulation:

The design and the virtual load testing of the said product have been done in Catia V5R20. The load applied as a vertical downward load on the cross-arm. The parameters described and tested are deformed mess, von mises stress and translational displacement. The loads are applied to that amount such as the load is maximum. Even the simulation has been done by applying higher value of load then the value of actual load on the cross-arm.

7.1. Software simulation result:

Fig (1): Boundary condition

 

Fig (2): Deformed mess

 

Fig (3): Von mises stress

 

Fig (4): Translational displacement

Note: In the rendered image on the two side of the cross-arm, two blocks are there just to show the position of distributed load application.

The simulation result contains here boundary conditions, Deformed mess, Von mises stress, Translational displacement. In this simulation the maximum deformation is 0.35mm which is very negligible compared to the structure measurement. And since the loads are applied to the structure are higher compared to the actual load so it can sustain the actual load without failure.

7.2. Software generated properties:

The software generated material properties is given here to ensure the quality of the material of the product.

Material	Steel
Young’s modulud	2e+011N_m2
Poisson’s ratio	0.266
Density	7860 kg_m3
Coefficiant of thermal expansion	1.17e-005_Kdeg
Yield strength	2.5e+008N_m2

 

8. Wind loading:

Since the cross sectional area of the product is not that much higher so drag against the wind flow is very few. Sometime the wind loading on the conductor also effects the loading capacity of the cross-arm, because at the time of wind flow the tension might be higher than the pre tension of the conductor. That is why the load application on the cross arm is taken very high compared to its healthy loading condition and on that condition also the cross-arm is in healthy condition. So undoubtedly the cross-arm can sustain the wind loading also. Along with it the wind loading calculation formulae is given here to check whether it can sustain or not.

Let, the wind speed is 110 km/ hr which is denoted as maximum wind speed  V_w.

Here the load is will be approximately 11.97 N obtained from the data getting from browse search. Here it is so obvious that, a load of 11.97 N will make a deformation on the cross-arm structure is very negligible.

9. Conclusion:

Here we have discussed about the various aspects of load testing on the cross-arm. Mainly the load testing is performed by considering the vertical load attached with the cross-arm like insulator, nuts and bolts, conductors.  At the time of virtual load testing of the product the conductor pre tension is taken  into consideration  so  that  the  perfect  sustainability  of  the  product  can  be  checked  properly.  And by performing the mathematical calculations and the virtual simulation it is clear to all of us that the product can sustain a load higher than the load of the component attaching with it practically.  On mathematical load testing the loads are applied on it there we can see the translational displacement is very small just tend to zero.  And at the time of virtual simulation conductor pre tensions are also taken into consideration then also the translational displacement is very negligible.

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