[{"data":1,"prerenderedAt":211},["ShallowReactive",2],{"article:steel-beam-check:en":3},{"title":4,"seoTitle":5,"description":6,"label":7,"lead":8,"blocks":9},"How do you check a steel beam by hand to EN 1993-1-1?","Checking a steel beam by hand to EN 1993-1-1 · Struct4U","A simply supported IPE 300 checked by hand: design load, section class, bending, shear and deflection, each with its clause from EN 1990 and EN 1993-1-1.","EN 1990 · EN 1993-1-1 · §5.5 · §6.2.5 · §6.2.6","A simply supported steel beam is the first calculation most engineers learn, and still one of the most common. This worked example checks an IPE 300 in S235 over 6.00 m, step by step: the design load, the cross-section class, bending, shear and deflection.",[10,14,17,22,25,27,35,37,46,48,51,53,81,84,86,90,107,110,124,127,129,145,147,150,152,163,165,168,185,187,189,192,199,202,204],{"type":11,"id":12,"text":13},"h2","beam","The beam",{"type":15,"text":16},"p","A floor beam, simply supported over *L* = 6.00 m. The floor holds the compression flange laterally, so lateral-torsional buckling cannot occur. The loads per metre are a permanent load *g*_{k} = 5.0 kN\u002Fm, including self-weight, and a variable load *q*_{k} = 7.5 kN\u002Fm on a floor in category A (residential). The profile is an IPE 300 in S235.",{"type":18,"diagram":19,"caption":20,"clause":21},"figure","beam-diagrams","The beam with its design load, bending moment and shear force, and the deflection under the characteristic load. Bending governs.","EN 1993-1-1 §6.2",{"type":11,"id":23,"text":24},"load","Step 1: the design load",{"type":15,"text":26},"For the ultimate limit state EN 1990 combines the loads with partial factors. With the recommended values of equation (6.10):",{"type":28,"clause":29,"rows":30},"formula","EN 1990 (6.10)",[31],{"s":32,"f":33,"res":34},"*q*_{d}","= 1.35 *g*_{k} + 1.5 *q*_{k} = 1.35 · 5.0 + 1.5 · 7.5 = **18.0 kN\u002Fm**",true,{"type":15,"text":36},"The Dutch national annex, consequence class CC2, takes the less favourable of equations 6.10a and 6.10b instead. For a floor in category A, *ψ*_{0} = 0.4:",{"type":28,"clause":38,"rows":39},"NEN-EN 1990 NB, CC2",[40,43],{"s":41,"f":42},"(6.10a)","1.35 · 5.0 + 1.5 · 0.4 · 7.5 = 11.25 kN\u002Fm",{"s":44,"f":45,"res":34},"(6.10b)","1.2 · 5.0 + 1.5 · 7.5 = **17.25 kN\u002Fm**, governs",{"type":15,"text":47},"The example continues with 18.0 kN\u002Fm; the results with the Dutch annex follow at the end.",{"type":11,"id":49,"text":50},"material","Step 2: material and cross-section",{"type":15,"text":52},"S235 with a thickness of at most 40 mm has *f*_{y} = 235 N\u002Fmm² (Table 3.1), so *ε* = √(235 \u002F *f*_{y}) = 1.0. The partial factor *γ*_{M0} = 1.0, both as the recommended value and in the Dutch annex. *E* = 210 000 N\u002Fmm².",{"type":54,"caption":55,"head":56,"rows":59,"align":78,"compact":34},"table","IPE 300, hot-rolled (EN 10365)",[57,58],"Property","Value",[60,63,66,69,72,75],[61,62],"Depth *h*, width *b*","300 mm, 150 mm",[64,65],"Web *t*_{w}, flange *t*_{f}, root radius *r*","7.1 mm, 10.7 mm, 15 mm",[67,68],"Area *A*","53.81 cm^{2}",[70,71],"Second moment of area *I*_{y}","8356 cm^{4}",[73,74],"Plastic section modulus *W*_{pl,y}","628.4 cm^{3}",[76,77],"Shear area *A*_{v,z}","25.68 cm^{2}",[79,80],"l","r",{"type":11,"id":82,"text":83},"class","Step 3: the cross-section class",{"type":15,"text":85},"The class decides whether the plastic resistance may be used. Table 5.2 compares the width-to-thickness ratio *c*\u002F*t* of each compressed part with limits that depend on *ε*.",{"type":18,"diagram":87,"caption":88,"clause":89},"ipe-classification","The flange outstand and the web of an IPE 300, with the widths *c* that Table 5.2 compares with the thicknesses *t*.","EN 1993-1-1 Table 5.2",{"type":28,"clause":91,"rows":92},"EN 1993-1-1 §5.5, Table 5.2",[93,96,99,102,104],{"s":94,"f":95},"flange","*c* = (*b* − *t*_{w} − 2*r*) \u002F 2 = (150 − 7.1 − 30) \u002F 2 = 56.5 mm",{"s":97,"f":98},"","*c* \u002F *t*_{f} = 56.5 \u002F 10.7 = 5.28 ≤ 9*ε* = 9: class 1 (outstand in compression)",{"s":100,"f":101},"web","*c* = *h* − 2*t*_{f} − 2*r* = 300 − 21.4 − 30 = 248.6 mm",{"s":97,"f":103},"*c* \u002F *t*_{w} = 248.6 \u002F 7.1 = 35.0 ≤ 72*ε* = 72: class 1 (internal part in bending)",{"s":105,"f":106,"res":34},"section","**class 1**: the plastic resistance applies",{"type":11,"id":108,"text":109},"bending","Step 4: bending",{"type":28,"clause":111,"rows":112},"EN 1993-1-1 §6.2.5",[113,116,120],{"s":114,"f":115},"*M*_{Ed}","= *q*_{d} *L*^{2} \u002F 8 = 18.0 · 6.00^{2} \u002F 8 = 81.0 kNm",{"s":117,"f":118,"ref":119},"*M*_{c,Rd}","= *W*_{pl,y} *f*_{y} \u002F *γ*_{M0} = 628.4 · 10^{3} · 235 \u002F 1.0 = 147.7 kNm","(6.13)",{"s":121,"f":122,"ref":123,"res":34},"UC","= *M*_{Ed} \u002F *M*_{c,Rd} = 81.0 \u002F 147.7 = **0.55** ≤ 1.0","(6.12)",{"type":11,"id":125,"text":126},"shear","Step 5: shear",{"type":15,"text":128},"For a rolled I-section loaded parallel to the web, §6.2.6(3)a gives the shear area.",{"type":28,"clause":130,"rows":131},"EN 1993-1-1 §6.2.6",[132,135,138,142],{"s":133,"f":134},"*A*_{v}","= *A* − 2*b t*_{f} + (*t*_{w} + 2*r*) *t*_{f} = 5381 − 3210 + 397 = 2568 mm², at least *η h*_{w} *t*_{w} = 2374 mm²",{"s":136,"f":137},"*V*_{Ed}","= *q*_{d} *L* \u002F 2 = 18.0 · 6.00 \u002F 2 = 54.0 kN",{"s":139,"f":140,"ref":141},"*V*_{pl,Rd}","= *A*_{v} (*f*_{y} \u002F √3) \u002F *γ*_{M0} = 2568 · (235 \u002F √3) \u002F 1.0 = 348.4 kN","(6.18)",{"s":121,"f":143,"ref":144,"res":34},"= 54.0 \u002F 348.4 = **0.16** ≤ 1.0","(6.17)",{"type":15,"text":146},"Two more conditions. The web needs no shear buckling check, because *h*_{w} \u002F *t*_{w} = 278.6 \u002F 7.1 = 39.2 ≤ 72*ε* \u002F *η* = 60 (§6.2.6(6), with *η* = 1.2 from EN 1993-1-5; *η* = 1.0 is allowed as a conservative value). And the shear force does not reduce the bending resistance, because *V*_{Ed} = 54.0 kN ≤ 0.5 *V*_{pl,Rd} = 174.2 kN (§6.2.8); at midspan, where the moment is largest, the shear force is zero anyway.",{"type":11,"id":148,"text":149},"deflection","Step 6: deflection",{"type":15,"text":151},"Deflection is a serviceability check, with the characteristic loads and without partial factors.",{"type":28,"clause":153,"rows":154},"EN 1990 Annex A1.4",[155,158,161],{"s":156,"f":157},"*δ*","= 5 (*g*_{k} + *q*_{k}) *L*^{4} \u002F (384 *E I*_{y}) = 5 · 12.5 · 6000^{4} \u002F (384 · 210 000 · 8356 · 10^{4}) = 12.0 mm",{"s":159,"f":160},"*δ*_{lim}","= *L* \u002F 250 = 24.0 mm (example limit)",{"s":121,"f":162,"res":34},"= 12.0 \u002F 24.0 = **0.50**",{"type":15,"text":164},"EN 1990 leaves the deflection limits to the national annex and the client, so *L*\u002F250 is only an example here.",{"type":11,"id":166,"text":167},"result","The result",{"type":54,"head":169,"rows":173,"align":184,"compact":34},[170,171,172],"Check","Clause","Unity check",[174,177,180],[175,111,176],"Bending","**0.55**",[178,130,179],"Shear","0.16",[181,182,183],"Deflection, *L*\u002F250","EN 1990 A1.4","0.50",[79,79,80],{"type":15,"text":186},"Bending governs, with a unity check of 0.55: the IPE 300 is far from fully used. With the Dutch annex the design load is 17.25 kN\u002Fm, *M*_{Ed} = 77.6 kNm and the bending check 0.53; shear becomes 0.15.",{"type":15,"text":188},"An IPE 270, also class 1 (*W*_{pl,y} = 484.0 cm^{3}, *I*_{y} = 5790 cm^{4}), gives a bending check of 81.0 \u002F 113.7 = 0.71 and a deflection of 17.3 mm, 0.72 of *L*\u002F250.",{"type":11,"id":190,"text":191},"left-out","What this example leaves out",{"type":193,"items":194},"list",[195,196,197,198],"**Lateral-torsional buckling** (§6.3.2). Without lateral restraint of the compression flange, the buckling resistance moment *M*_{b,Rd} = *χ*_{LT} *W*_{y} *f*_{y} \u002F *γ*_{M1} (6.55) takes the place of the cross-section resistance.","**Supports and concentrated loads.** The web has to carry the reactions without crippling (EN 1993-1-5 §6).","**Vibration of the floor**, a separate serviceability criterion.","**Fire resistance** (EN 1993-1-2).",{"type":11,"id":200,"text":201},"software","The same check in XBeam2D",{"type":15,"text":203},"[XBeam2D](product:xbeam2d) does this calculation for beams on any number of supports, in steel, concrete and timber, and checks steel members including lateral-torsional buckling. The report shows each check the way this article does: the clause, the formula, the values that went in and the unity check. A reviewer can follow it, and you can recheck any number by hand.",{"type":205,"items":206},"sources",[207,208,209,210],"EN 1990:2002+A1:2005, Basis of structural design: equation (6.10) and Annex A1 (in the Netherlands NEN-EN 1990+A1+A1\u002FC2:2011 with its national annex: 6.10a and 6.10b, consequence classes).","EN 1993-1-1:2005, Eurocode 3, Part 1-1: Table 3.1, §5.5, Table 5.2, §6.2.5, §6.2.6, §6.2.8, §6.3.2.","EN 1993-1-5:2006, Plated structural elements: §5 (shear buckling) and §6 (resistance to transverse forces).","Profile data: hot-rolled IPE sections to EN 10365.",1792702121213]