D3.E.3 Design Equations
D3.E.3.1 Tensile Strength
The allowable tensile strength, as calculated in STAAD as per BS5950-5, section 7 is described below.
The tensile strength, Pt of the member should be determined from clause 7.2.1
Pt = Aepy
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D3.E.3.2 Combined bending and tension
As per clause 7.3 of BS 5950-5:1998 members subjected to both axial tension and bending should be proportioned such that the following relationships are satisfied at the ultimate limit state
Ft/Pt + Mz/Mcz + My/Mcy ≤ 1
Mz/Mcz ≤ 1
and
My/Mcy ≤ 1
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D3.E.3.3 Compressive Strength
The allowable Compressive strength, as calculated in STAAD as per BS5950-5, section 6 is described below
For sections symmetrical about both principal axes or closed cross-sections which are not subjected to torsional flexural buckling, the buckling resistance under axial load, Pc, may be obtained from the following equation as per clause 6.2.3 of the subject code
For sections symmetrical about a single axis and which are not subject to torsional flexural buckling, the buckling resistance under axial load, Pc, may be obtained from the following equation as per clause 6.2.4 of the subject code
Where the meanings of the symbols used are indicated in the subject clauses.
D3.E.3.4 Torsional flexural buckling
Design of the members which have at least one axis of symmetry, and which are subject to torsional flexural buckling should be done according to the stipulations of the clause 6.3.2 using factored slenderness ratio αLE/r in place of actual slenderness ratio while reading Table 10 for the value of Compressive strength(pc).
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Where the meanings of the symbols used are indicated in the subject clause.
D3.E.3.5 Combined bending and compression
Members subjected to both axial compression and bending should be checked for local capacity and overall buckling
Local capacity check as per clause 6.4.2 of the subject code
Fc/Pcs + Mz/Mcz + My/Mcy ≤ 1
D3.E.3.6 Overall buckling check as per clause 6.4.3 of the subject code
For beams not subjected to lateral buckling, the following relationship should be satisfied
For beams subjected to lateral buckling, the following relationship should be satisfied:
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Mcz, Mcy, and Mb are calculated from clause numbers 5.2.2 and 5.6 in the manner described herein below.
For restrained beams, the applied moment based on factored loads should not be greater then the bending moment resistance of the section, Mc
Mcz = Szz x po
Mcy = Syyx po
Where
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For unrestrained beams the applied moment based on factored loads should not be greater than the smaller of the bending moment resistance of the section , Mc , and the buckling resistance moment of the beam, Mb
Then buckling resistance moment, Mb, may be calculated as follows
φB = [My + (1 + η)ME]/2 |
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Please refer clause numbers 5.2.2 and 5.6 of the subject code for a detailed discussion regarding the parameters used in the above mentioned equations.
The maximum shear stress should not be greater then 0.7 ´ py as per clause 5.4.2
The average shear stress should not exceed the lesser of the shear yield strength, pv or the shear buckling strength, qcr as stipulated in clause 5.4.3 of the subject code.
The parameters are calculated as follows:
pv = 0.6·py |
qcr = (1000·t/D)2 N/mm2 |
Pv = A·min(pv, qcr) |
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For beam webs subjected to both bending and shear stresses the member should be designed to satisfy the following relationship as per the stipulations of clause 5.5.2 of the subject code
(Fv/Pv)2 + (M/Mc)2 ≤ 1
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