Skew plates are important elements of many structures. The two-dimensional structural action of plates results in lighter structures and therefore offer numerous economic advantages. Their application is extensive in fields of engineering such as: civil, mechanical, architecture, and aerospace. Openings of various shapes are made in the skew plates for practical reasons. Unfortunately, this results in strength degradations. Accordingly, there is a basic need to evaluate the structural behavior of these plates with some commonly used openings for a safe design. However, due to the mathematical difficulties in the analytical approaches and complex work involved in the various techniques, the extraction of solutions become challenging and cumbersome. Therefore, this basic work attempts to resolve this in a simplified and user-friendly manner using MSC (MacNeal-Schwendler Corporation) Nastran software. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. It was found that rectangular opening is the best. Since it is susceptible to less deflections, rotations and moments when compared to other openings.
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
A plate is a structural element that has a small thickness compared to the plane dimensions
[1]
Timoshenko, S and Krieger, S., (1959), “Theory of plates and Shells,” Second Edition, McGraw-Hill Inc., New York.
[1]
. The two-dimensional structural action of plates results in lighter structures and therefore offers economic advantages
[2]
Szilard. R., (1974), “Theory and Analysis of Plates -- classical numerical methods,” Prentice Hall, Inc. Englewood cliffs, New Jersey.
[2]
. Loaded plates are extensively used in all fields of engineering and therefore require analyses
[2]
Szilard. R., (1974), “Theory and Analysis of Plates -- classical numerical methods,” Prentice Hall, Inc. Englewood cliffs, New Jersey.
[2]
.
The tremendous potential of skew plates as an engineering structure has attracted attention of many researchers
[3]
Budiman, I., (2022), “Buckling Analysis of Skew Plates Subjected to Uniform Compression Loading,” International Journal of Civil Engineering and Infrastructure, Vol. 2, No. 1.
[4]
Chainarin, P., and Singhatanadgid, P., (2006), “Buckling Analysis of Composite Laminate Rectangular and Skew plates with Various Edge Support Conditions”, Mechanical Engineering Department, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand.
[5]
Kumar, A., et al, (2015), “Buckling Behaviour of Laminated Composite Skew Plates with Various Boundary Conditions Subjected to Linearly Varying in-plane Edge Loading,” International Journal of Mechanical Sciences, Vol. 100, pp. 136–144,
Das, D., et al, (2010), “Large Deflection Analysis of Skew Plates Under Uniformly Distributed Load for Mixed Boundary Conditions,” International Journal of Engineering, Science And Technology, Vol. 2, No. 4, pp. 100-112.
[7]
Srinivasa, C. V., et al, (2018), “Bending Behavior of Simply Supported Skew Plates,” International Journal of Scientific & Engineering Research, Volume 9, Issue 5, ISSN 2229-5518.
[8]
Singh, J., et al, (2022), “Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory,” Materials, Vol 15 (13),
Ukadgaonker, V. G, and Vyasraj, (2005), “Stress Analysis for an Orthotropic Plate with an Irregular Shaped Hole for Different in-plane Loading Conditions-Part 1,” Department of Mechanical Engineering, Indian Institute of Technology, Bombay.
[11]
Hassan, A., et al, (2023), “Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young’s Modulus,” Materials, Vol 16 (21),
Civalek, O, and Jalaei, M. H, (2020), “Shear Buckling Analysis of Functionally Graded (FG) Carbon Nanotube Reinforced Skew Plates with Different Boundary Conditions,” Aerospace Science and Technology, Vol 99,
Budiman, I., (2022), “Buckling Analysis of Skew Plates Subjected to Uniform Compression Loading,” International Journal of Civil Engineering and Infrastructure, Vol. 2, No. 1.
[3]
to study the buckling of skew plates subjected to uniform compressive load revealed thatcritical buckling load value depends on length to width ratios and skew angles. Increasing the ratio and anglecaused an increase in the value of critical buckling load. Another investigation to study
[4]
Chainarin, P., and Singhatanadgid, P., (2006), “Buckling Analysis of Composite Laminate Rectangular and Skew plates with Various Edge Support Conditions”, Mechanical Engineering Department, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand.
[4]
the effect of skew angle and transverse loading to the buckling behavior revealed that buckling load is proportional to the skew angle
[4
]. The buckling mode may change a little with the change in the skew angle. Under biaxial loading, the buckling load is increased with magnitude of transverse tensile load
[4]
Chainarin, P., and Singhatanadgid, P., (2006), “Buckling Analysis of Composite Laminate Rectangular and Skew plates with Various Edge Support Conditions”, Mechanical Engineering Department, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand.
[4]
. The buckling behavior of composite skew plate with varying skew angles, boundary conditions and linear loading has been investigated
[5]
Kumar, A., et al, (2015), “Buckling Behaviour of Laminated Composite Skew Plates with Various Boundary Conditions Subjected to Linearly Varying in-plane Edge Loading,” International Journal of Mechanical Sciences, Vol. 100, pp. 136–144,
. It was found that the buckling load increases with an increase in skew angle. A change in mode shape of the structure is also observed with an increase in angle. Deflection behavior of thin isotropic skew plates under uniformly distributed load for various boundary conditions under flexural loading was studied
[6]
Das, D., et al, (2010), “Large Deflection Analysis of Skew Plates Under Uniformly Distributed Load for Mixed Boundary Conditions,” International Journal of Engineering, Science And Technology, Vol. 2, No. 4, pp. 100-112.
[6]
. An analytical approach using the principle of minimum potential energy was carried. It was found that the analytically developed deflection plots can be used to study the effect of boundary conditions. Deflection studies
[7]
Srinivasa, C. V., et al, (2018), “Bending Behavior of Simply Supported Skew Plates,” International Journal of Scientific & Engineering Research, Volume 9, Issue 5, ISSN 2229-5518.
[7]
were carried out on skew plates subjected to uniformly distributed load/concentrated load for simply supported boundary conditions using MSC/NASTRAN. It was found that deflection decreases with skew angle. Static response of a graded material plate was studied
[8]
Singh, J., et al, (2022), “Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory,” Materials, Vol 15 (13),
using shear deformation theory. Important insights into central deflections and stresses were gained. Three-dimensional displacement and stress components in the functionally graded plates were studied
[9]
Zhang, P., et al, (2020), “Three Dimensional Mechanical Behaviors of In-Plane Functionally Graded Plates,” Composite Structures, Vol 241,
using a scaled finite element method along with an integration-based program. The accuracy of semi-analytical procedure was established by comparing with the classical plate theory. Plates with various shapes of openings under varying loads as non-shear, partial shear and pure shear conditions were studied
[10]
Ukadgaonker, V. G, and Vyasraj, (2005), “Stress Analysis for an Orthotropic Plate with an Irregular Shaped Hole for Different in-plane Loading Conditions-Part 1,” Department of Mechanical Engineering, Indian Institute of Technology, Bombay.
[10]
for stress concentrations. Finite element method was used for analysis. It was found that the plates had more stress concentrations around the holes for pure shear loads. Stress behavior of functional plates with a circular hole subjected to a uniaxial traction were studied
[11]
Hassan, A., et al, (2023), “Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young’s Modulus,” Materials, Vol 16 (21),
. It was found that stress decreased with an increase in stiffness ratio. Buckling behavior was studied
[12]
Civalek, O, and Jalaei, M. H, (2020), “Shear Buckling Analysis of Functionally Graded (FG) Carbon Nanotube Reinforced Skew Plates with Different Boundary Conditions,” Aerospace Science and Technology, Vol 99,
. Minimum potential energy along with Navier’s technique were used in the analysis. The solution yielded deflections and stresses.
2. Defining the Problem
The main goal of this work is to evaluate the structural behavior of skew plates with some commonly used openings for in a simplified and user-friendly manner. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. The structural behavior of the plates is evaluated in the context of deflections, rotations, and moments using MSC (MacNeal-Schwendler Corporation) Nastran software.
3. Loads and Dimensions of Skew Plates
Skew Plates with various shapes of openings were analyzed using MSC Nastran package by preparing input file for each type of plate and then executing the file to obtain results like deflections, rotations, and moments in the plates with openings. This section consists of solutions of skew plates with openings. As described earlier, five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal.
For all plates the loads taken were as follows:
a) Dead load (Self weight + floor finish load on plate)
b) Live load on plate
Dimensions of a typical skew plate used in the analysis are shown in Figure 1.
The loading conditions and other properties were kept constant for the analysis. However, only the dimensions of the openings were changed.
4. Computations and Comparisons
In this work we studied five cases. The cases with their respective images are shown below. The opening that is least susceptible to less deflections, rotations, and moments may be used for the field work. This evaluatory design is not for a specific component of structure and therefore no direct specifications are available in American codes. Accordingly, typical values are used.
4.1. Skew Plate with Circular Opening Clamped on All Edges
Thickness of plate = 0.492ft
Diameter of the circular opening = 14.76 ft
28- day compressive strength of concrete (f`’c) = 4000 psi;
Poisson’s ratio (μ) = 0.15; concrete modulus
(Ec) = 5000√(f`’c) = 5000√4000 =316227.7 psi
The minimum calculated loads were:
Dead load (Self weight + Floor finish load on plate) = thick ness of plate × unit weight of concrete = 0.492 ft * 0.150 kips/ft³ + 0.015kips = 0.0888 kips/ft²
Figure 16. Mxy Diagram of Skew Plate with Trapezoidal Opening.
4.6. Comparison of Results
The above cases provided us with valuable
information. Deflections, rotations, and moments of commonly used openings are shown in Table 1 for comparison purposes.
Table 1. Comparison of Results.
Opening
Deflection
Rotation
Moment
(in)
(rad)
(kip-ft)
Circular
0.0056
0.00235
3.85
Square
0.0059
0.00237
3.63
Rectangular
0.00548
0.00232
3.47
Triangular
0.0084
0.00357
6.46
Trapezoidal
0.00539
0.00242
4.44
The results show that in a context of an overall picture, rectangular opening is the best, when compared to other openings. This is because it is susceptible to less deflections, rotations, and moments. The second best is circular opening. Triangular opening generates the highest values of deflections, rotations, and moments.
5. Conclusions
The main goal of this basic work was to evaluate the structural behavior of skew plates with some commonly used openings for a safe design. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. The structural behavior of the plates is evaluated in the context of deflections, rotations, and moments using MSC Nastran software. The following limited main conclusion was obtained from this work:
In the context of an overall picture, rectangular opening is the best as it produces the least deflections, rotations, and moments.
Future Work
Further research is possible in this basic topic by applying different conditions, materials, and loading type. For example, effects of load on fiber reinforced plastics plates with openings.
Abbreviations
MSC
MacNeal-Schwendler Corporation
f`’c
28 Days Compressive Strength of Concrete
μ
Poisson’s Ratio
Ec
Concrete Modulus
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
Timoshenko, S and Krieger, S., (1959), “Theory of plates and Shells,” Second Edition, McGraw-Hill Inc., New York.
[2]
Szilard. R., (1974), “Theory and Analysis of Plates -- classical numerical methods,” Prentice Hall, Inc. Englewood cliffs, New Jersey.
[3]
Budiman, I., (2022), “Buckling Analysis of Skew Plates Subjected to Uniform Compression Loading,” International Journal of Civil Engineering and Infrastructure, Vol. 2, No. 1.
[4]
Chainarin, P., and Singhatanadgid, P., (2006), “Buckling Analysis of Composite Laminate Rectangular and Skew plates with Various Edge Support Conditions”, Mechanical Engineering Department, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand.
[5]
Kumar, A., et al, (2015), “Buckling Behaviour of Laminated Composite Skew Plates with Various Boundary Conditions Subjected to Linearly Varying in-plane Edge Loading,” International Journal of Mechanical Sciences, Vol. 100, pp. 136–144,
Das, D., et al, (2010), “Large Deflection Analysis of Skew Plates Under Uniformly Distributed Load for Mixed Boundary Conditions,” International Journal of Engineering, Science And Technology, Vol. 2, No. 4, pp. 100-112.
[7]
Srinivasa, C. V., et al, (2018), “Bending Behavior of Simply Supported Skew Plates,” International Journal of Scientific & Engineering Research, Volume 9, Issue 5, ISSN 2229-5518.
[8]
Singh, J., et al, (2022), “Static Analysis of Skew Functionally Graded Plate Using Novel Shear Deformation Theory,” Materials, Vol 15 (13),
Ukadgaonker, V. G, and Vyasraj, (2005), “Stress Analysis for an Orthotropic Plate with an Irregular Shaped Hole for Different in-plane Loading Conditions-Part 1,” Department of Mechanical Engineering, Indian Institute of Technology, Bombay.
[11]
Hassan, A., et al, (2023), “Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young’s Modulus,” Materials, Vol 16 (21),
Civalek, O, and Jalaei, M. H, (2020), “Shear Buckling Analysis of Functionally Graded (FG) Carbon Nanotube Reinforced Skew Plates with Different Boundary Conditions,” Aerospace Science and Technology, Vol 99,
Faruqi, M., Waseuddin, M., Bailey, B., Aguiniga, F. (2024). Basic Analysis of Skew Plates with Openings. Engineering and Applied Sciences, 9(3), 44-52. https://doi.org/10.11648/j.eas.20240903.13
Faruqi, M.; Waseuddin, M.; Bailey, B.; Aguiniga, F. Basic Analysis of Skew Plates with Openings. Eng. Appl. Sci.2024, 9(3), 44-52. doi: 10.11648/j.eas.20240903.13
Faruqi M, Waseuddin M, Bailey B, Aguiniga F. Basic Analysis of Skew Plates with Openings. Eng Appl Sci. 2024;9(3):44-52. doi: 10.11648/j.eas.20240903.13
@article{10.11648/j.eas.20240903.13,
author = {Mohammed Faruqi and Mohammed Waseuddin and Breanna Bailey and Francisco Aguiniga},
title = {Basic Analysis of Skew Plates with Openings
},
journal = {Engineering and Applied Sciences},
volume = {9},
number = {3},
pages = {44-52},
doi = {10.11648/j.eas.20240903.13},
url = {https://doi.org/10.11648/j.eas.20240903.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20240903.13},
abstract = {Skew plates are important elements of many structures. The two-dimensional structural action of plates results in lighter structures and therefore offer numerous economic advantages. Their application is extensive in fields of engineering such as: civil, mechanical, architecture, and aerospace. Openings of various shapes are made in the skew plates for practical reasons. Unfortunately, this results in strength degradations. Accordingly, there is a basic need to evaluate the structural behavior of these plates with some commonly used openings for a safe design. However, due to the mathematical difficulties in the analytical approaches and complex work involved in the various techniques, the extraction of solutions become challenging and cumbersome. Therefore, this basic work attempts to resolve this in a simplified and user-friendly manner using MSC (MacNeal-Schwendler Corporation) Nastran software. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. It was found that rectangular opening is the best. Since it is susceptible to less deflections, rotations and moments when compared to other openings.
},
year = {2024}
}
TY - JOUR
T1 - Basic Analysis of Skew Plates with Openings
AU - Mohammed Faruqi
AU - Mohammed Waseuddin
AU - Breanna Bailey
AU - Francisco Aguiniga
Y1 - 2024/06/19
PY - 2024
N1 - https://doi.org/10.11648/j.eas.20240903.13
DO - 10.11648/j.eas.20240903.13
T2 - Engineering and Applied Sciences
JF - Engineering and Applied Sciences
JO - Engineering and Applied Sciences
SP - 44
EP - 52
PB - Science Publishing Group
SN - 2575-1468
UR - https://doi.org/10.11648/j.eas.20240903.13
AB - Skew plates are important elements of many structures. The two-dimensional structural action of plates results in lighter structures and therefore offer numerous economic advantages. Their application is extensive in fields of engineering such as: civil, mechanical, architecture, and aerospace. Openings of various shapes are made in the skew plates for practical reasons. Unfortunately, this results in strength degradations. Accordingly, there is a basic need to evaluate the structural behavior of these plates with some commonly used openings for a safe design. However, due to the mathematical difficulties in the analytical approaches and complex work involved in the various techniques, the extraction of solutions become challenging and cumbersome. Therefore, this basic work attempts to resolve this in a simplified and user-friendly manner using MSC (MacNeal-Schwendler Corporation) Nastran software. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. It was found that rectangular opening is the best. Since it is susceptible to less deflections, rotations and moments when compared to other openings.
VL - 9
IS - 3
ER -
Faruqi, M., Waseuddin, M., Bailey, B., Aguiniga, F. (2024). Basic Analysis of Skew Plates with Openings. Engineering and Applied Sciences, 9(3), 44-52. https://doi.org/10.11648/j.eas.20240903.13
Faruqi, M.; Waseuddin, M.; Bailey, B.; Aguiniga, F. Basic Analysis of Skew Plates with Openings. Eng. Appl. Sci.2024, 9(3), 44-52. doi: 10.11648/j.eas.20240903.13
Faruqi M, Waseuddin M, Bailey B, Aguiniga F. Basic Analysis of Skew Plates with Openings. Eng Appl Sci. 2024;9(3):44-52. doi: 10.11648/j.eas.20240903.13
@article{10.11648/j.eas.20240903.13,
author = {Mohammed Faruqi and Mohammed Waseuddin and Breanna Bailey and Francisco Aguiniga},
title = {Basic Analysis of Skew Plates with Openings
},
journal = {Engineering and Applied Sciences},
volume = {9},
number = {3},
pages = {44-52},
doi = {10.11648/j.eas.20240903.13},
url = {https://doi.org/10.11648/j.eas.20240903.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20240903.13},
abstract = {Skew plates are important elements of many structures. The two-dimensional structural action of plates results in lighter structures and therefore offer numerous economic advantages. Their application is extensive in fields of engineering such as: civil, mechanical, architecture, and aerospace. Openings of various shapes are made in the skew plates for practical reasons. Unfortunately, this results in strength degradations. Accordingly, there is a basic need to evaluate the structural behavior of these plates with some commonly used openings for a safe design. However, due to the mathematical difficulties in the analytical approaches and complex work involved in the various techniques, the extraction of solutions become challenging and cumbersome. Therefore, this basic work attempts to resolve this in a simplified and user-friendly manner using MSC (MacNeal-Schwendler Corporation) Nastran software. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. It was found that rectangular opening is the best. Since it is susceptible to less deflections, rotations and moments when compared to other openings.
},
year = {2024}
}
TY - JOUR
T1 - Basic Analysis of Skew Plates with Openings
AU - Mohammed Faruqi
AU - Mohammed Waseuddin
AU - Breanna Bailey
AU - Francisco Aguiniga
Y1 - 2024/06/19
PY - 2024
N1 - https://doi.org/10.11648/j.eas.20240903.13
DO - 10.11648/j.eas.20240903.13
T2 - Engineering and Applied Sciences
JF - Engineering and Applied Sciences
JO - Engineering and Applied Sciences
SP - 44
EP - 52
PB - Science Publishing Group
SN - 2575-1468
UR - https://doi.org/10.11648/j.eas.20240903.13
AB - Skew plates are important elements of many structures. The two-dimensional structural action of plates results in lighter structures and therefore offer numerous economic advantages. Their application is extensive in fields of engineering such as: civil, mechanical, architecture, and aerospace. Openings of various shapes are made in the skew plates for practical reasons. Unfortunately, this results in strength degradations. Accordingly, there is a basic need to evaluate the structural behavior of these plates with some commonly used openings for a safe design. However, due to the mathematical difficulties in the analytical approaches and complex work involved in the various techniques, the extraction of solutions become challenging and cumbersome. Therefore, this basic work attempts to resolve this in a simplified and user-friendly manner using MSC (MacNeal-Schwendler Corporation) Nastran software. Five commonly used openings were used for the study, namely: circular, rectangular, square, triangular, and trapezoidal. It was found that rectangular opening is the best. Since it is susceptible to less deflections, rotations and moments when compared to other openings.
VL - 9
IS - 3
ER -
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