## Calculation of Section Slenderness for a Member Subject to Bending

## Calculation of Section Slenderness for a Member Subject to Bending

(OP)

Hi there, I am looking for some guidance in regards to the calculation of the section slenderness of a member subject to bending in accordance with AS4100-1998. My query is in how Table 5.2 is applied to bending of the section about both the major x-axis and minor y-axis. For the purposes of this discussion I will use a standard I section (Universal beam or column etc).

For Bending About the Major X-Axis:

For a standard I-section bent about the major x-axis, there are two different types of flat compression plate elements, these being the flange outstands and the web. I understand how to calculate the plate element slenderness of each of these components. My uncertainty is the stress distribution present in the plate element due to the section being bent about the x-axis (i.e. uniform compression, maximum compression at unsupported edge, zero stress or tension at supported edge etc). Is this stress distribution the stress distribution between the plate elements ends/supports? For example for the flange outstands is this the stress distribution from the supported edge to the free edge and for the web is this the stress distribution from the supported edge to the other supported edge? Assuming that this is the case, then for bending about the major x-axis, in accordance with Table 5.2 the flange outstands will be in uniform compression and the web will have compression at one edge, tension at the other. Is this correct? Calculating the section slenderness for a standard BHP Universal Beam bent about the x-axis using these assumptions gives results that correlate with those listed in the BHP catalogue.

For Bending About the Major Y-Axis:

This is where I run into problems. If I use the same assumptions as those used for bending of the section about the x-axis (i.e. the stress distribution is the stress distribution between the plate elements ends/supports) and try to calculate the section slenderness for a standard BHP Universal Beam bent about the y-axis I cannot achieve results that correlate to the BHP catalogue. Are both the flange outstands and web used to calculate the section slenderness when the section is bent about the y-axis? Are the plate element slenderness values for each element used for bending about the x-axis the same as for bending about the y-axis?

Any help on this matter would be greatly appreciated as I would like to fully understand how the section slenderness of a member subject to bending is determined so that I can apply the theory to non standard beam sections that do not have their effective section properties listed in a book or otherwise if I am required to do so. Thanking you for your time.

For Bending About the Major X-Axis:

For a standard I-section bent about the major x-axis, there are two different types of flat compression plate elements, these being the flange outstands and the web. I understand how to calculate the plate element slenderness of each of these components. My uncertainty is the stress distribution present in the plate element due to the section being bent about the x-axis (i.e. uniform compression, maximum compression at unsupported edge, zero stress or tension at supported edge etc). Is this stress distribution the stress distribution between the plate elements ends/supports? For example for the flange outstands is this the stress distribution from the supported edge to the free edge and for the web is this the stress distribution from the supported edge to the other supported edge? Assuming that this is the case, then for bending about the major x-axis, in accordance with Table 5.2 the flange outstands will be in uniform compression and the web will have compression at one edge, tension at the other. Is this correct? Calculating the section slenderness for a standard BHP Universal Beam bent about the x-axis using these assumptions gives results that correlate with those listed in the BHP catalogue.

For Bending About the Major Y-Axis:

This is where I run into problems. If I use the same assumptions as those used for bending of the section about the x-axis (i.e. the stress distribution is the stress distribution between the plate elements ends/supports) and try to calculate the section slenderness for a standard BHP Universal Beam bent about the y-axis I cannot achieve results that correlate to the BHP catalogue. Are both the flange outstands and web used to calculate the section slenderness when the section is bent about the y-axis? Are the plate element slenderness values for each element used for bending about the x-axis the same as for bending about the y-axis?

Any help on this matter would be greatly appreciated as I would like to fully understand how the section slenderness of a member subject to bending is determined so that I can apply the theory to non standard beam sections that do not have their effective section properties listed in a book or otherwise if I am required to do so. Thanking you for your time.

## RE: Calculation of Section Slenderness for a Member Subject to Bending

By way of example, consider a 310UB32.

Section properties

d = 298 mm

b

_{f}= 149 mmt

_{f}= 8.0 mmt

_{w}= 5.5 mm(b

_{f}- t_{w})/(2 x t_{f}) = 8.97 mmZ

_{x}= 424x10^{3}mm^{3}S

_{x}= 475x10^{3}mm^{3}Z

_{y}= 59.3x10^{3}mm^{3}S

_{y}= 91.8x10^{3}mm^{3}f

_{y}= 320 MPaFor bending about the x-axis:

λ

_{e}= 8.97 x √(320/250) = 10.2λ

_{ep}= 9λ

_{ey}= 16λ

_{ep}< λ_{e}< λ_{ey}, therefore section in non-compactZ

_{cx}= 475x10^{3}mm^{3}Z

_{ex}= 424x10^{3}+ [(16 - 10.2)/(16 - 9)] x (475x10^{3}- 424x10^{3}) = 467x10^{3}mm^{3}For bending about the y-axis:

λ

_{e}= 10.2λ

_{ep}= 9λ

_{ey}= 25λ

_{ep}< λ_{e}< λ_{ey}, therefore section in non-compactZ

_{cy}= 89.0x10^{3}mm^{3}Z

_{ey}= 59.3x10^{3}+ [(25 - 10.2)/(25 - 9)] x (89.0x10^{3}- 59.3x10^{3}) = 86.9x10^{3}mm^{3}Hope this example helps you.