Calculation and Verification of ZPZ Values in IS 800:2007

Abstract

Plastic Section Modulus of a section is the first moment of the cross sectional area about an axis which divides the sectional area into two equal halves. In this paper an attempt has been made to calculate and verify the Zpz values of tapered flange I and C Sections. I-Section has been divided into a total of 13 component areas and C-Section into 7 component areas. The area of each component is calculated and the position of centroid of each component area is identified and used in the calculation of the Plastic Section Modulus of the cross section about Z-Z axis. Eleven I-sections and One C-section Zpz values are found to differ from the values given in the IS 800 : 2007[2] by more than 100 mm3, i.e., 0.1 cm3 and are reported here. These verifications gain significance due to the fact that, in case of four I-sections, the difference is found to be more than 10000 mm3, i.e., 10cm3.

Introduction

I. INTRODUCTION

IS 800:2007[2] gives the values of Plastic Sectional Modulii, Zpz, of I and C-Sections about z-z axis, in Annexure H, pages 138 to 140. The values given are in cm3. The values of Zpz are used in the determination of Moment of Resistance of Plastic and Compact sections as per IS 800: 2007[2]  and hence play an important role in the design of beams by Limit State Method. For Semi-Compact sections Elastic Section Modulus Ze is to be used as per the Code, which is the ratio of Moment of Inertia of the section, I, and the distance of extreme fibre from the neutral axis.

Plastic Section Modulus of a section is the first moment of the cross sectional area about an axis which divides the sectional area into two equal halves. It is usually called ‘Equal Area Axis’. For symmetrical sections the identification of such axis is very simple – the axes of symmetry represent the Equal Area Axis. But in case of unsymmetrical sections it is necessary to first identify the Equal Area Axis, before proceeding to the calculations of Plastic Section Modulus. In unsymmetrical sections Neutral Axis (Centroidal Axis) and Equal Area Axis do not coincide.

In the present case the I-section has two axes

of symmetry and the Z-Z axis is located at half the depth of the section, while the Y-Y axis is located through the centerline of the web. In case of C-section, the Z-Z axis is the only axis of symmetry and is located at half the depth of the section, while the Equal Area Axis in ‘Y’ direction is to be worked out considering the geometry of the web, flange, fillet and rounded end of flange. For the calculation of Zpz,  the Z-Z axis is only necessary to be identified.

The Plastic Sectional Modulii, Zpz, values for I and C sections have been calculated with higher accuracy, in mm3, and presented here. A few values are found to differ from the values given in the IS 800:2007[2]  and have been reported here.

II. METHOD OF CALCULATION

Typical calculations of Zpz for one I-Section – ISLB 400 @ 558.2 N/m and one C-Section ISMC 300 @ 351.2 N/m have been given hereunder. I-Section has been divided into a total of 13 component areas and C-Section into 7 component areas. The area of each component is calculated and the position of centroid of each component area is identified and used in the calculation of the Plastic Section Modulus of the cross section about Z-Z axis.

A. Plastic Section Modulus, Zpz, of ISLB 400 @ 558.2 N/m:

For ISLB 400@ 558.2 N/m the various geometrical parameters, as per SP: 6(1)-1964,[1] are as follows:

h = 400 mm ;   b = 165 mm ;   tf = 12.5 mm ;   tw = 8 mm ;   (D)θ = 98o ;   r1 = 16 mm ;   r2 = 8 mm ;

In the Figure 1 :

Z-Z represents the horizontal neutral axis

Z’-Z’ represents the horizontal Equal Area Axis – Z-Z and Z’-Z’ axes coincide.

Y-Y represents the vertical neutral axis

Y’-Y’ represents the vertical Equal Area Axis – Y-Y and Y’-Y’ axes coincide.

IV. DISCUSSION

A difference of more than 100 mm3, i.e., 0.1 cm3 in the value of Zpz has been considered for reporting. These values affect the first decimal place of Zpz value given by the IS:800-2007.[2] Even though differences from 10 to 99 affect the second decimal place, they have been neglected for reporting. It has been found that Eleven I- Sections and One C-Section come under the category selected for reporting. Particularly four I-Sections, viz., ISHB400@77.4kg/m, ISMB450@72.4kg/m, ISWB400@66.7kg/m and ISMB100@11.5kg/m have difference of more than 10000 mm3 (10 cm3) in the Zpz values. The highest difference observed being 29992.59 mm3 (29.9926 cm3) for ISWB400@66.7kg/m. Some of the differences found, appear to be printing errors.

Conclusion

The Zpz values are very important in the design of beams and other structural elements like beam-columns which are subjected to bending moments, especially when the sections chosen are plastic or compact sections, by classification according to IS:800-2007.[2] Correct selection of sections during the process of structural designing requires correct values of Zpz. Hence the results obtained are of importance in structural designs. These values will also affect built up beams, gantry girders, etc. if the sections with large differences in Zpz values mentioned above, are used in the designs. However, a further scrutiny of the methodology and calculations, presented here, is always helpful, if differences found herein are to be finally accepted.

References

[1] SP: 6(1)-1964, Handbook for Structural Engineers, Bureau of Indian Standard (Reaffirmed in 1998). [2] IS 800-2007 Genral Construction In Steel--Code of Practice (Third Revision), Bureau of Indian Standards [3] IS 808-1989 (Reaffirmed 1999), Edition 4.1 (1992-07), Indian Standard Dimensions for Hot Rolled Steel Beam, Column, Channel and Angle Sections, (Third Revision) Bureau of Indian Standards [4] Onesteel Manufacturing (Australia), Hot Rolled and Structural Steel Products, (Seventh Edition) [5] K.V. Pramod and Gururaj A. Kulkarni, Verification of Areas of IS Rolled Steel Sections, International Journal of Research in Engineering and Technology, Volume 02, Issue: 09, pp. 339-342 (2013), eISSN: 2319-1163 | pISSN: 2321-7308 [6] K.V. Pramod and Gururaj A. Kulkarni, Verification Of Areas Of Indian Standard I- Sections With Multiple Unit Weights. International Journal of Research in Engineering and Technology, Volume 02, Issue: 10, pp. 230-234 (2013), eISSN: 2319-1163 | pISSN: 2321-7308 [7] S.S. Bhavikatti and K.V. Pramod, Steel Tables with Plastic Modulus of I.S. Sections, IK International Publishing House Pvt. Ltd., New Delhi, India (2013). [8] K.V. Pramod, Steel Data Handbook, IK International Publishing House Pvt. Ltd., New Delhi, India (2015).

Copyright

Copyright © 2022 K. V. Pramod, Dr. B. R. Patagundi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.