Flexural Analysis of Deep Aluminum Beam

Document Type : Regular Article

Authors

1 Associate Professor and Head, Civil Engineering Department, Maharashtra Institute of Technology, Aurangabad (M. S.), India

2 Civil Engineering Department, Shreeyash College of Engineering and Technology, Aurangabad, (M. S.), India

Abstract

Many parts of spacecraft, airplanes are made up of aluminum, due to its property of less density, which is deep in sections. For the analysis of deep parts of any structure, a shear deformation theory using the trigonometric sinusoidal function in displacement field in terms of thickness coordinate is developed to obtain the shear deformation effects. The shear stresses are obtained from the use of constitutive equations with outstanding accuracy, satisfying the zero shear stress at the both, top and bottom of beams. Also, the theory not requires the shear correction factor. By using the principle of virtual work, the governing differential equations and boundary conditions are obtained. A deep aluminum beam is assumed subjected to a cosine load for the analytical study to show the accuracy of the theory. The results are compared with other theories.

Highlights

Google Scholar

Keywords

Main Subjects

References

[1]     Timoshenko SP. LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. London, Edinburgh, Dublin Philos Mag J Sci 1921;41:744–6. doi:10.1080/14786442108636264.
[2]     Cowper GR. The Shear Coefficient in Timoshenko’s Beam Theory. J Appl Mech 1966;33:335. doi:10.1115/1.3625046.
[3]     K MA V. Vibration of Short Beams. AIAA J 1970;8:34–8.
[4]     Baluch MH, Azad AK, Khidir MA. Technical Theory of Beams with Normal Strain. J Eng Mech 1984;110:1233–7. doi:10.1061/(ASCE)0733-9399(1984)110:8(1233).
[5]     Bhimaraddi A, Chandrashekhara K. Observations on Higher‐Order Beam Theory. J Aerosp Eng 1993;6:408–13. doi:10.1061/(ASCE)0893-1321(1993)6:4(408).
[6]     Dahake AG, Ghugal YM. Flexure of Thick Simply Supported Beam Using Trigonometric Shear Deformation Theory. Int J Sci Res Publ 2012;2:1–7.
[7]     Ghugal YM, Dahake AG. Flexural analysis of deep beam subjected to parabolic load using refined shear deformation theory. Appl Comput Mech 2012;6:163–72.
[8]     Ghugal YM, Dahake AG. Flexure of thick beams using refined shear deformation theory. Int J Civ Struct Eng 2012;3:321–35.
[9]     Sawant MK, Dahake AG. A new hyperbolic shear deformation theory for analysis of thick beam. Int J Innov Res Sci Eng Technol 2014;3:9634–43.
[10]    Chavan VB, Dahake AG. Analysis of Thick Beam Bending Problem by Using a New Hyperbolic Shear Deformation Theory. Int J Eng Res Gen Sci 2014;2:209–15.
[11]    B. C V., G. DA. A Refined Shear Deformation Theory for Flexure of Thick Beam. Int J Pure Appl Res Eng Technol 2015;3:109–19.
[12]    Nimbalkar VN, Dahake AG. Displacement and Stresses for Thick Beam using New Hyperbolic Shear Deformation Theory. Int J Pure Appl Res Eng Technol 2015;4:120–30.
[13]    Jadhav VA, Dahake AG. Bending Analysis of Deep Beam Using Refined Shear Deformation Theory. Int J Eng Res 2016;5:526–31.
[14]    S. MS, M. SR, G. DA. A New Trigonometric Shear Deformation Theory for Thick Fixed Beam. Int J Eng Res 2016;5:532–6.
[15]    B. PP, G. DA. Finite Element Analysis Using 2D Plane Stress Elements for Thick Beam. J Aerosp Eng Technol 2016;6:1–8.
[16]    G. DA, S. MS, M. SR. Flexure of Fixed Thick Beam using Trigonometric Shear Deformation Theory. Proc. 6th Int. Congr. Comput. Mech. Simulation, Indian Inst. Technol. Powai Maharashtra, India, 2016, p. 1112–5.
[17]    A.G. Dahake D. H. Tupe GRG. COMPARISON OF VARIOUS DISPLACEMENT FIELDS FOR STATIC ANALYSIS OF THICK ISOTROPIC BEAMS. Struct. Eng. Conv. CSIR-SERC, Chennai, INDIA. 21-23, 2016, p. 468–72.
[18]    Properties of Aluminum 6061-T6, 6061-T651 n.d. http://www.aerospacemetals.com.

Files

Cited by

History

  • Receive Date: 23 August 2017
  • Revise Date: 27 August 2017
  • Accept Date: 28 August 2017

Share

How to cite

Statistics