4.1 General
In BS 59501: 2000 effective section properties are required for design of members with Class 3 semicompact and Class 4 slender crosssections. Effective section properties are given for sections subject to compression, bending and also combined axial compression and bending. Effective section properties depend on the grade of steel used; effective properties for grades S275 and S355 are given next to each other or on facing pages.
4.2 Effective section properties of members subject to compression (except angles)
The compression resistance of class 4 slender sections is calculated using the effective cross‑sectional area A_{eff} instead of the gross area A, according to BS 59501^{[1]}, Clause 4.7.4(b). The section classification depends on the width/thickness ratios of the webs and the flanges. The tables list sections that can be Class 4 slender and the character W or F indicates whether the section is slender due to the web or the flange. The effective area of the section is given for all slender sections and is calculated as follows:
For UB, UC and Joists with the web controlling the classification
A_{eff} = A – t(d – 40tε)
For circular hollow sections
A_{eff} = A [ (80/(D/t)) (275/p_{y}) ]^{0.5}
For hotfinished square and rectangular hollow sections with web controlling
A_{eff} = A – 2t( (D3t) – 40tε)
For hotfinished square and rectangular hollow sections with web and flange controlling
A_{eff} = A – 2t( (D3t) + (B3t) – 80tε)
For coldformed square and rectangular hollow sections with web controlling
A_{eff} = A – 2t( (D5t) – 35tε)
For coldformed square and rectangular hollow sections with web and flange controlling
A_{eff} = A – 2t( (D5t) + (B5t) – 70tε)
where:
ε 
= (275/p_{y})^{0.5} 
A 
is the gross cross‑sectional area 
d 
is the depth between fillets 
p_{y} 
is the design strength 
D, B and t are as defined in Section 3.3.2. 

The ratio of effective area to gross area (A_{ef }/A) is also given in the table to provide a guide as to how much of the section is effective.
4.3 Effective section properties of members subject to compression (angles)
The crosssection classification is given along with the design strength and the reduced design strength. The reduced design strength is used for angles instead of the effective area because otherwise the effect of the additional moments induced by the shift of the centroid of the effective section would need to be considered (BS 59501, Clause 3.6.3).
Only members which are class 4 slender in S275 or S355 are listed. The reduced design strength for class 4 slender sections is calculated as follows:
p_{yr} = Minimum { p_{y }(15ε /(d/t))^{2} , p_{y }(15ε /(b/t))^{2} , p_{y}(24ε /((b+d)/t))^{2} }
where:
ε 
= (275/p_{y})^{0.5} 
d 
is the length of the long leg 
b 
is the length of the short leg 
p_{y} 
is the design strength 
t 
is the leg thickness. 
4.4 Effective section properties of members subject to pure bending
The section classification depends on the width/thickness ratios of the webs and the flanges. The tables give sections that are Class 3 semicompact or Class 4 slender in S275 or S355 and the character W or F indicates whether the web or the flange controls the section classification.
For Class 3 semicompact sections the effective plastic modulus S_{eff} is given, which is calculated as in BS 59501, Clauses 3.5.6.2, 3.5.6.3 and 3.5.6.4.
For Class 4 slender sections the effective elastic modulus Z_{eff} and the effective second moment of area I_{eff} are given and are calculated as follows:
For hotfinished square and rectangular hollow sections with flange controlling
I_{xeff }=
Z_{xeff} =
I_{xeff} /
y_{xeff}
where:
y_{xeff} 
= 
A_{eff} 
= A – (B  40tε  3t)t 
I_{x} 
is the second moment of area about the x axis 
I_{y} 
is the second moment of area about the y axis 
A 
is the gross cross‑sectional area and D, B, t, ε are as defined in Section 4.3. 
For coldformed square and rectangular hollow sections with flange controlling
I_{xeff} =
Z_{xeff} =
I_{xeff} /
y_{xeff}
where:
y_{xeff} 
= 
A_{eff} 
= A – (B  35tε  5t)t 
I_{x} 
is the second moment of area about the x axis 
I_{y} 
is the second moment of area about the y axis 
A 
is the gross cross‑sectional area and D, B, t, ε are as defined in Section 4.3. 
Other section types do not become Class 4 slender when subject to bending only, for the range of sections covered by this website.
Also given in the tables is β_{w}, which is defined as:
S_{x}/S_{x} 
For Class 1 plastic and Class 2 compact sections 
S_{xeff}/S_{x} 
For Class 3 semicompact sections 
Z_{xeff}/S_{x} 
For Class 4 slender sections 
4.5 Effective section properties of members subject to axial compression and bending
The crosssection classification is dependent on the level of axial load. Therefore, the classification and effective plastic modulus is given for a range of axial loads, expressed as a proportion of the squash load, P_{z}. The tables give sections which can be Class 3 semicompact or Class 4 slender in S275 or S355 and the character W or F indicates whether the section classification is controlled by the web or the flange.
The effective plastic modulus is calculated in accordance with BS 59501, Clauses 3.5.6.2, 3.5.6.3 and 3.5.6.4. It should be noted that the limits used from Tables 11 and 12 are the "Web – Generally" limits.