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To Eurocode BS EN 1993-1-1/NA:2008

Design summary

Resistance / LimitApplied / ActualUtilisation
Shear61.3 kN10.7 kN18 %OK
Bending moment6.71 kNm2.69 kNm40 %OK
Buckling5.12 kNm2.69 kNm52 %OK
Total deflection5 mm1.5 mm29 %OK
Deflection due to variable actions2.8 mm0.6 mm21 %OK

Section details

Type Parallel flange I section
Section IPE AA 80
Steel grade S355
Width b = 46 mm
Depth h = 78 mm
Web thickness tw = 3.2 mm
Flange thickness tf = 4.2 mm
Root radius r = 5 mm
Mass per metre w = 4.9 kg/m

Span and restraints

Effective span L = 1,000 mm
Buckling length Lcr = 1,000 mm

Deflection limits

Variable action deflection limit ΔQ = L / 360 = 2.78 mm
Total deflection limit ΔG+Q = L / 200 = 5 mm

Safety factors

Partial factor for permanent actions γG = 1.35
Partial factor for variable actions γQ = 1.5

Loading details

Self weight
Permanent action  SW = w × 9.81 / 1000 = 0.0481 kN/m
Load 1: UDL - Sloping roof, 0° to 30°
Permanent action  G1 = 1.15 kN/m² × 8 m = 9.2 kN/m
Variable action  Q1 = 0.75 kN/m² × 8 m = 6 kN/m

Reactions

Permanent (unfactored) Variable (unfactored) Total (unfactored) Total (factored)
Left reaction 4.62 kN 3 kN 7.62 kN 10.7 kN
Right reaction 4.62 kN 3 kN 7.62 kN 10.7 kN

Design shear force

Design shear forceVEd = 10.7 kN
Design shear resistanceVc,Rd = 61.3 kN
UtilisationVEd / Vc,Rd = 18 %OK

Design bending moment

Design bending moment, major axisMEd = 2.69 kNm
Design resistance for bendingMc,Rd = 6.71 kNm
Bending utilisationMEd / Mc,Rd = 40 %OK
Design resistance for bucklingMb,Rd = 5.12 kNm
Buckling utilisationMEd / Mb,Rd = 52 %OK

Deflection

Variable action deflection limitΔQ = 2.8 mm
Variable action deflectionδQ = 0.6 mmOK
Total deflection limitΔG+Q = 5 mm
Total deflectionδG+Q = 1.5 mmOK

Section properties

Elastic modulus - major axis, yy Wel = 16.4 cm3
Plastic modulus - major axis, yy Wpl = 18.9 cm3
Second moment of area - major axis, yy Iy = 64.1 cm4
Second moment of area - minor axis, zz Iz = 6.85 cm4
Warping constant Iw = 0.00009 dm6
Torsional constant IT = 0.38 cm4
Area of section A = 630 mm2

Factors and design values of material coefficients (EN 1993-1-1:2005 and National Annex)

Young's modulus of elasticityE = 210,000 N/mm²cl.3.2.6
Poisson's ratio in elastic stagev = 0.3 cl.3.2.6
Shear modulusGs = 81,000 N/mm²cl.3.2.6
Partial factor for resistance of cross-sectionsγM0 = 1 cl.6.1(1)B / BS-EN NA
Partial factor for resistance to instabilityγM1 = 1 cl.6.1(1)B / BS-EN NA
Factor for shear areaη = 1 EN 1993-1-5:2006 cl.5.1(2) / BS-EN NA
Limiting non dimensional slenderness ratioλLT,0 = 0.4 cl.6.3.2.3(1) / BS-EN NA
Beta factor for buckling reduction factor calculationβ = 0.75 cl.6.3.2.3(1) / BS-EN NA

Yield strength

Nominal yield strength for S355 grade and nominal section thickness 4.20 mmfy = 355 N/mm²Arcelor Mittal orange book

Section classification (EN 1993-1-1:2005 cl.5.5)

Epsilonε = 0.814EN 1993-1-1:2005 Table 5.2
Flange ratio for local bucklingcf / tf = 3.9
Flange ratio limit for class 19 ε = 7.32Table 5.2 (sheet 2 of 3)
Flange classClassf = 1
Web ratio for local bucklingcw / tw = 18.6
Web ratio limit for class 172 ε = 58.6Table 5.2 (sheet 1 of 3)
Web classClassw = 1
Section classClass = 1

Shear resistance (EN 1993-1-1:2005 cl.6.2.6)

Height of webhw = 69.6 mm
Shear area for I and H sectionsAv = 299 mm²cl.6.2.6 (3)
Design shear resistanceVpl,Rd = 61.3 kNeq (6.18)

Shear buckling (EN 1993-1-5:2006 cl.5)

The shear buckling resistance for webs should be verified according to Section 5 of EN 1993-1-5 if (hw / tw) > (72 ε / η)
Web ratio for shear bucklinghw / tw = 21.7 EN 1993-1-5:2006 cl.5.1 (2)
Shear buckling limit72 ε / η = 58.6 EN 1993-1-5:2006 cl.5.1 (2)
(hw / tw) <= (72 ε / η) therefore shear buckling calculation not required

Bending resistance (EN 1993-1-1:2005 cl.6.2.5)

The shear force (11 kN) is less than half of the plastic shear resistance (61 kN / 2 = 31 kN), therefore its effect on moment resistance may be neglected.
Class 1 section, therefore use plastic modulusWpl = 18,900 mm³
Design bending resistanceMc,Rd = 6.71 kNmeq (6.13)

Design buckling resistance (EN 1993-1-1:2005 cl.6.3.2)

C1 factorC1 = 1
Shear modulus of elasticityGs = 81,000 N/mm²cl.3.2.6 (1)
Buckling lengthLcr = 1,000 mm
Critical buckling momentMCR = 8.38 kNmNCCI SN003b-EN-EU
Class 1 section, therefore use plastic modulusWpl = 18,900 mm³cl.6.3.2.1(3)
Non-dimensional slenderness ratioλLT = 0.895cl.6.3.2.2 (1)
Depth to width ratio for buckling curveh / b = 1.7
Buckling curve for h / b ratioBuckling curve = bTable 6.5 / BS-EN NA
Imperfection factor for buckling curve bαLT = 0.34Table 6.3 / BS-EN NA
Intermediate factor for reduction factor calculationφLT = 0.884cl.6.3.2.3 (1)
Buckling reduction factorχLT = 0.763eq (6.57)
Correction factor for moment distributionkc = 1Table 6.6
Moment distribution modification factorf = 1cl.6.3.2.3 (2)
Modified buckling reduction factorχLT,mod = 0.763eq (6.58)
Design buckling resistanceMb,Rd = 5.12 kNmeq (6.55)

Notes

C1 value conservatively taken as 1.0

Ends of beam are to be laterally restrained. Ends of beams can be laterally restrained using one of the following methods;

1) End of beam built into masonry wall.
2) End of beam fixed to a masonry wall.
3) End of beam fixed to a column or a beam.

The designer is to ensure that the proposed detail adequately ensures that the end of the beam is laterally restrained.

No allowance has been made for destabilising loads which are outside the scope of these calculations (Destabilising loads would not normally occur in a traditional masonry structure)

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