CAN/CSA-S157-05/S157.1-05 April 2007
7 Net area, effective section, and effective strength .1 General
Both the drilling of holes and welding reduce the strength of a member. To accommodate this change, deductions shall be made from the gross cross-section to give a net or effective section. Strength reduction due to local buckling shall be represented by a reduction in the effective thickness or in the effective strength. (See Clauses 7.2 to 7.5.)
7.2 Gross area
The gross area of a member shall be determined by summing the products of the thickness and the gross width of each element as measured perpendicular to the axis of the member.
7.3 Net area
The net cross-sectional area of members in tension shall be the gross area less the sum of the hole diameters multiplied by the thickness (Σdot) in line across the section. For a chain of holes extending in any diagonal or zigzag line across a tension member (see Figure C1 in the Commentary), the net width of the part shall be obtained by deducting from the gross width the sum of the diameters of all the holes in the chain and adding, for each gauge space in the chain, a quantity given by
13
(Replaces p. 13, February 2005)
Licensed for/Autorisé à Reid Costley, Cascade Engineering Group, Sold by/vendu par CSA on/le 10/27/2009. Single user license only. Storage, distribution or use on network prohibited./Permis d'utilisateur simple seulement. Le stockage, la distribution ou l'utilisation sur le réseau est interdit.
S157-05 © Canadian Standards Association
s2/4g where
s = spacing of successive holes in the direction of the force g = transverse spacing of the two holes
do = hole diameter t = thickness
The least net width so obtained shall be used in calculating the net area. The staggered rupture line controls when s2 is less than 2gdo. The distance between holes shall not be less than 2.5d, where d is the fastener diameter.
Clause 9.7.2 gives effective net areas for eccentrically loaded tension members.
7.4 Effective section 7.4.1 General
Both welding and local buckling cause a reduction in the overall strength, which is accounted for by using an effective section to establish the bending resistance of a member. The geometric properties of the effective section shall be computed using the effective thicknesses of the elements according to Clauses 7.4.2 and 7.4.3.
The section modulus of the effective section shall be multiplied by the yield strength of the base metal to give the limiting moment (characteristic resistance).
7.4.2 Effective thickness at welds 7.4.2.1 Plastic section modulus
Where only parts of the cross-section are influenced by welding, as with longitudinal welds, the effective thickness, tm , of the metal in the heat-affected zone (see Clause 11.3.6), shall be determined as follows:
tm = t (Fwy /Fy) ≤ t
The section modulus of the effective section shall be multiplied by the yield strength of the base metal to give the limiting moment (characteristic resistance).
7.4.2.2 Elastic section modulus
The effective thickness, tm , used in calculating the elastic section modulus to determine the moment at first yield in the base metal shall be given by
tm = t (Fwy /Fy)(c/y) ≤ t where
t = original thickness
Fwy = yield strength in the heat-affected zone Fy = yield strength of the base metal
c = distance from the neutral axis of the gross cross-section to the extreme fibre y = distance from the neutral axis of the gross section to the centre of the weld
If local buckling occurs in a welded element, the influence of the weld may be neglected and the reduced thickness attributed to local buckling shall be used.
7.4.2.3 Deflections
The gross cross-section of welded members shall be used for the calculation of deflections.
Δ
© Canadian Standards Association Strength design in aluminum
April 2007
7.4.3 Effective thickness after local buckling of flat elements 7.4.3.1 Flat elements with both long edges supported
For a flat element supported at both longitudinal edges, subjected in some part to compressive stress which causes local buckling, the effective thickness, tm , of the entire element at the ultimate limit state shall be taken as
tm = t ( )1/2 where
t = element thickness
= normalized buckling stress for plates, from Clause 9.3.3, using a normalized slenderness, from Clause 9.3.1, with Fo = Fy , and the slenderness, λ, given by
λ = mb/t where
m = a factor from Clause 8.2 appropriate to the stress distribution and boundary conditions b = element width
7.4.3.2 Angles and flanges
Angle sections, and outstanding elements supported along one long edge only, shall not be considered to possess postbuckling strength, and torsional or local buckling shall be deemed to lead to collapse.
7.4.4 Deflection under service loads
Local buckling due to unfactored service loads is not extensive and the gross section properties shall be used when calculating deflections.
7.5 Effective strength and overall buckling 7.5.1 General
Where welding, or local buckling with postbuckling strength, influences the flexural buckling of columns or lateral buckling of beams, the capacity shall be established by using the effective strength, Fm , given in Clauses 7.5.2 and 7.5.3.
This effective strength represents the limiting stress, Fo , described in Clause 9.3.2, for use in Clause 9.4.1 to determine the mean stress to cause overall buckling.
7.5.2 Influence of welding
For members containing longitudinal welds, the effective strength, Fm , shall be given by Fm = Fy – (Fy – Fwy)Aw /A
where
Fy = yield strength of the base metal
Fwy = yield strength of the heat-affected zone Aw = cross-sectional area of the heat-affected zone A = gross cross-sectional area
This value of the effective strength, Fm , shall be used as the limiting stress, Fo , in Clauses 9.3.2(g) and 9.4.1, in conjunction with the gross cross-sectional area, when determining the resistance to overall buckling (see also Clause 9.4.2.2). Note that the location of the HAZ is not a factor (see Clause 11.3.6).
7.5.3 Influence of local buckling
For flat elements supported on both long edges, subjected to a compressive stress that causes local buckling, the effective strength, Fm , of the element shall be given by
Fm = 1/2 Fy
(Replaces p. 15, February 2005)
Licensed for/Autorisé à Reid Costley, Cascade Engineering Group, Sold by/vendu par CSA on/le 10/27/2009. Single user license only. Storage, distribution or use on network prohibited./Permis d'utilisateur simple seulement. Le stockage, la distribution ou l'utilisation sur le réseau est interdit.
S157-05 © Canadian Standards Association
where
= normalized buckling stress for plates, obtained from Clause 9.3.3, corresponding to a normalized slenderness, , obtained from Clause 9.3.1, using Fo = Fy and the slenderness given by
λ = mb/t where
m = a factor from Clause 8.2 appropriate to the stress distribution and boundary conditions b = element width
t = element thickness Fy = yield strength
This value of the effective strength, Fm , shall be used as the limiting stress, Fo , in Clause 9.4.1, in conjunction with the gross cross-sectional area, to determine the resistance to overall buckling.