Wood Beam Analysis And Design - University Of Michigan
Architecture 324Structures IIWood Beam Analysisand Design ASD approachNDS criteriaWood Beam AnalysisWood Beam DesignUniversity of Michigan, TCAUPStructures IISlide 1 of 50Structures IISlide 2 of 50Allowable Stress DesignAllowable Stress Actual StressFb from the NDS SupplementUniversity of Michigan, TCAUP
Allowable Stress Design by NDSFlexureAllowable Flexure Stress Fb’Actual Flexure Stress fbFb from NDS Supplement tables determinedby species and gradefb Mc/I M/SS I/c bd2/6Fb’ Fb (usage factors)usage factors for flexure:CD Load Duration FactorCM Moisture FactorCt Temperature FactorCL Beam Stability FactorCF Size FactorCfu Flat UseCi Incising FactorCr Repetitive Member FactorUniversity of Michigan, TCAUPWood StructuresSlide 3 of 50Allowable Stress Design by NDSShearAllowable Shear Stress Fv’Actual Shear Stress fvFv from tables determined by speciesand gradefv VQ / I b 1.5 V/ACan use V at d from support asmaximumFv’ Fv (usage factors)usage factors for shear:CD Load Duration FactorCM Moisture FactorCt Temperature FactorCi Incising FactorUniversity of Michigan, TCAUPWood StructuresSlide 4 of 50
Allowable Stress Design by NDSCompressionAllowable Compression Stress Fc’Actual Compression Stress fcFc from NDS Supplement tables determinedby species and gradefc P/AFc’ Fc (usage factors)usage factors for flexure:CD Load Duration FactorCM Moisture FactorCt Temperature FactorCF Size FactorCi Incising FactorCP Column Stability FactorUniversity of Michigan, TCAUPWood StructuresSlide 5 of 50Adjustment FactorsSawn Lumber - 4University of Michigan, TCAUPStructures IISlide 6 of 50
Adjustment FactorsAllowable Flexure Stress Fb’Fb from tables determined by species and gradeFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )Usage factors for flexure:CD Load Duration FactorCt Temperature Factor2018 NDSUniversity of Michigan, TCAUPStructures IISlide 7 of 50Structures IISlide 8 of 50Adjustment FactorsAllowable Flexure Stress Fb’Fb from NDS tablesFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )Usage factors for flexure:CM Moisture FactorCF Size FactorUniversity of Michigan, TCAUP
Adjustment FactorsAllowable Flexure Stress Fb’Fb from NDS tablesFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )Usage factors for flexure:Cfu Flat UseCr Repetitive Member FactorUniversity of Michigan, TCAUPStructures IISlide 9 of 50Structures IISlide 10 of 50Adjustment FactorsAllowable Flexure Stress Fb’Fb from tables determined by species and gradeFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )Usage factors for flexure:Ci Incising FactorUniversity of Michigan, TCAUP
Adjustment FactorsAllowable Flexure Stress Fb’Fb from tables determined by species and gradeFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )Usage factors for flexure:CL Beam Stability Factor2012 NDSUniversity of Michigan, TCAUPStructures IISlide 11 of 50Structures IISlide 12 of 50CLCL 1.0for depth/width ratio in4.4.1 CL 1.0OtherwiseCL 1.0calculate factor usingsection 3.3.32x62x82x102x122x14University of Michigan, TCAUP
CL Beam Stability FactorIn the case bracing provisions of 4.4.1 cannot be met,CL is calculated using equation 3.3-6The maximum allowable slenderness, RB is 50University of Michigan, TCAUPStructures IISlide 13 of 50Adjustment Factors for ShearAllowable Flexure Stress Fv’Fv from tables determined by species and gradeFv’ Fv (usage factors)Usage factors for shear:CD Load Duration FactorCM Moisture FactorCt Temperature FactorCi Incising FactorUniversity of Michigan, TCAUPStructures IISlide 14 of 50
Analysis ProcedureGiven: loading, member size, material and span.Req’d: Safe or Unsafe1. Find Max Shear & Moment Simple case – equationsComplex case - diagrams2. Determine actual stresses fb M/Sfv 1.5 V/A3. Determine allowable stresses Fb and Fv (from NDS)Fb’ Fb (usage factors)Fv’ Fv (usage factors)4. Check that actual allowable fb F’bfv F’v5. Check deflection6. Check bearing (Fc Reaction/Abearing )University of Michigan, TCAUPfrom NDS 2012Structures IISlide 15 of 50Structures IISlide 16 of 50Analysis ExampleExampleGiven: loading, member size, materialand span.Req’d: Safe or Unsafe?University of Michigan, TCAUP
Analysis Example1.Find Max Shear & Moment Simple cases – equationsComplex cases - diagramsBy Diagrams:By equations:University of Michigan, TCAUPStructures IISlide 17 of 50Structures IISlide 18 of 50Analysis Example2.Determine actual stresses fb M/Sfv 1.5 V/AUniversity of Michigan, TCAUP
Species and GradeS-P-FNo.2Fb 875 psiFv 135 psiUniversity of Michigan, TCAUPStructures IISlide 19 of 50Structures IISlide 20 of 50Analysis Example3.Determine allowable stresses Fb 875 psiFv 135 psiDetermine factors:CD ?CM 1Ct 1CL 1CF ?Cfu 1Ci 1Cr 1University of Michigan, TCAUP
Analysis ExampleCD Load duration factorUse 1.6 (10 minutes)CF Size factor2x4use 1.5University of Michigan, TCAUPStructures IISlide 21 of 50Structures IISlide 22 of 50Analysis Example3.4.Determine allowable stresses Fb’ Fb (CD)(CF)Fb’ 875 (1.6)(1.5) 2100 psi Fv’ Fv (CD)Fv’ 135 (1.6) 216 psiCheck that actual allowable 5.6.fb F’bfv F’vCheck deflectionCheck bearing (Fc R/Ab )University of Michigan, TCAUP
Analysis ProcedureGiven: member size, material and span.Req’d: Max. Safe Load (capacity)1.Assume f F 2.Maximum actual allowable stressSolve stress equations for force 3.M Fb SV 0.66 Fv AUse maximum moment to find loads 4.Back calculate a load from momentAssumes moment controlsCheck Shear Use load found is step 3 to checkshear stress.If it fails (fv F’v), then find load basedon shear. 5.6.from NDS 2012Check deflectionCheck bearingUniversity of Michigan, TCAUPStructures IISlide 23 of 50Structures IISlide 24 of 50Analysis ExampleGiven: member size, material and span.Req’d: Max. Safe Load (capacity)1.Assume f F’ 2.Maximum actual allowable stressSolve stress equation for moment M F’b S (i.e. moment capacity)University of Michigan, TCAUP
Analysis Example (cont.)3.Use maximum forces to find loads 4.Check shear 4.5.Back calculate a maximum load frommoment capacityCheck shear for load capacity fromstep 3.Use P from moment to find VmaxCheck that fv Fv’Check deflection (serviceability)Check bearing (serviceability)University of Michigan, TCAUPStructures IISlide 25 of 50Structures IISlide 26 of 50Analysis ExampleGiven: loading, member size, material and span.Req’d: Safe or UnsafeUniversity of Michigan, TCAUP
Analysis ExampleFind Specific Gravity for Hem-Fir (from NDS)University of Michigan, TCAUPStructures IISlide 27 of 50Structures IISlide 28 of 50Analysis ExampleSection Properties:4 x 12 (3.5” x 11.25”)Area 39.38 in2Sx 73.83 in3University of Michigan, TCAUP
Analysis ExampleDetermine Loading Find Tributary area, AT6’ x 8’ 48 SF Determine member selfweight (w)University of Michigan, TCAUPStructures IISlide 29 of 50Structures IISlide 30 of 50Analysis ExampleSelfweight of member:Density at 0 m.c. 62.4 x G (dry)62.4 x 0.43 26.8 PCFTo include m.c. use NDS formula.w (PLF) D (PCF) x Area (IN2)/144University of Michigan, TCAUP
Analysis ExampleDetermine Beam Forcesby superposition equationsUniversity of Michigan, TCAUPorby diagramsStructures IISlide 31 of 50Structures IISlide 32 of 50Analysis ExampleDetermine actual stresses fb M/Sfv 1.5 V/AUniversity of Michigan, TCAUP
Analysis ExampleDetermine allowable stresses Fb and Fv (from NDS)University of Michigan, TCAUPStructures IISlide 33 of 50Structures IISlide 34 of 50Analysis Example3.Determine allowable stresses Fb 1400 psiFv 150 psiDetermine factors:CD CM Ct CL CF Cfu Ci Cr University of Michigan, TCAUP
Analysis ExampleDetermine allowable stressesM.C. 15%size: 4x12University of Michigan, TCAUPStructures IISlide 35 of 50Structures IISlide 36 of 50Adjustment FactorsAllowable Flexure Stress Fb’Fb from tables determined by species and gradeFb’ Fb (CD CM Ct CL CF Cfu Ci Cr )b/d 3.5 / 11.25 3.11 (case b)Assuming ends are braced, CL 1.02012 NDSUniversity of Michigan, TCAUP
Analysis Example3. Determine allowable stresses Fb’ Fb (usage factors)University of Michigan, TCAUPStructures IISlide 37 of 50Structures IISlide 38 of 50Analysis Example3. Determine allowable stresses Fv’ Fv (usage factors)University of Michigan, TCAUP
Analysis ExampleCheck that actual allowable fb F’bfv F’vCheck deflectionCheck bearing (Fc Reaction/Abearing )University of Michigan, TCAUPStructures IISlide 39 of 50Structures IISlide 40 of 50Design ProcedureGiven: load, wood, spanReq’d: member size1.Find Max Shear & Moment Simple case – equations Complex case - diagrams2.Determine allowable stresses3.Solve S M/Fb’4.Choose a section from Table 1B Revise DL and Fb’5.Check shear stress First for V max (easier) If that fails try V at d distancefrom support. If the section still fails, choose a newsection with A 1.5V/Fv’6.Check deflection7.Check bearingUniversity of Michigan, TCAUP
Design ExampleGiven: load, wood, spanReq’d: member size1.Find Max Shear & Moment Simple case – equations Complex case - diagramsUniversity of Michigan, TCAUPStructures IISlide 41 of 50Structures IISlide 42 of 50Design Example2.Determine allowable stresses(given in this example)F’b 1000 psiF’v 100 psi3.Solve S M/Fb’4.Choose a section from S table 5.Check shear stress 6.7.Revise DL and Fb’First for V max (easier)If that fails try V at d distance(remove load d from support)If the section still fails, choose anew section with A 1.5V/Fv’Check deflectionCheck bearingUniversity of Michigan, TCAUP
Design ExampleGiven: load, wood, spanReq’d: member sizeUniversity of Michigan, TCAUPStructures IISlide 43 of 50Structures IISlide 44 of 50Design ExampleDetermine allowable stresses Fb and Fv (from NDS)University of Michigan, TCAUP
Design ExampleDetermine allowable stressesUniversity of Michigan, TCAUPStructures IISlide 45 of 50Structures IISlide 46 of 50Design ExampleDetermine allowable stresses.Since the size is not known you have toskip CF (or make a guess).University of Michigan, TCAUP
Design ExampleDetermine Moment from LoadingFirst find the uniform beam load, w,from the floor loading.With the beam loading, calculatethe maximum moment.University of Michigan, TCAUPStructures IISlide 47 of 50Design ExampleEstimate the Required Section Modulus.Compare this required Sx to the actual Sxof available sections in NDS Table 1B.Remember CF will be multiplied whichmay make some pass which at first fail.University of Michigan, TCAUPStructures IISlide 48 of 50
Design ExampleChoose a section and test it (by analysiswith all factors including CF)University of Michigan, TCAUPStructures IISlide 49 of 50Design ExampleCheck DeflectionIn this case LL only against code limit of L/360University of Michigan, TCAUPStructures IISlide 50 of 50
University of Michigan, TCAUP Structures II Slide 39 of 50 Design Procedure Given: load, wood, span Req’d: member size 1. Find Max Shear & Moment Simple case – equations Complex case - diagrams 2. Determine allowable stresses 3. Solve S M/Fb’ 4.
BC1 Page 41 BEAM CLAMP BD1 Page 41 BEAM CLAMP BF1 Page 42 BEAM CLAMP BG1 Page 42 BEAM CLAMP BH1 Page 42 BEAM CLAMP BF2 Page 42 BEAM CLAMP BG2 Page 42 BEAM CLAMP BL FLANGE CLAMP Page 43 GRATE FIX Page 44 BEAM CLAMP GRATING CLIP Page 45 BEAM CLAMP FLOORFIX HT Page 46 FLOORFIX Page
standard duty lifting beam. i-beam design w/flame cut bail . page 9-10. hllb. load leveling beam. page 22-23. hdcrb. dual crane rotating beam. page 28. hsdlb. standard duty lifting beam. i-beam design w/pin bail . page 11. htplb. three point lifting beam. page 24. hbslb. basket sling lifting beam. page 12-14. hfplb. four .
3 Key Advantages of Wood-based Fuels 1.1 Wood energy is widely used and renewable 1.2 Sustainable wood production safeguards forest functions 1.3 Wood energy is available locally 1.4 Wood energy provides employment and income 1.5 Wood energy supports domestic economies 1.6 Wood energy is modern and leads to innovation 1.7 Wood energy can make a country independent of energy imports
wood (see Section "Role of wood moisture content on corrosion"). 3. Wood preservatives Wood preservatives are chemicals that are injected into the wood to help the wood resist attack by decay fungi, mold, and/or termites. Waterborne wood preservatives are commonly used when the wood may be in contact with humans or will be painted.
II. DEVELOPMENT OF BEAM STOCKER MACHINE The size, shape, and weight of the warp beam are generally too heavy to be handled without mechanical help. Basic information of warp beam Figure 1 Warp Beam Over all Beam dimensions Barrel Length 2500 mm Flange Diameter 1000 mm Maximum weight of the Beam (with yarn) 30,000 N
The Castellated Beam can also be detailed in single part drawings, assembly drawings and display accurate length and weight on BOM’s. Castellated beam with hexagonal/ octagonal /sinusoidal pattern Castellated beam Cellular beam Similar to the Castellated Beam the Cellular Beam, formed by welding two halves of the same beam profiled with a .
the high perveance ion beam efficiently to the lower beam line to be collimated and decelerated; 4. variable beam dimensions can be easily con-figured, and no additional beam line element is needed to extend an ion beam from 300 mm to 450 mm; 5. energy purity with low energy due to efficient neutral particle filtering by deflected beam collimation
BE03M-A 3X Optical Beam Expander, AR Coated: 400 - 650 nm 483.00 Lead Time BE03M-B 3X Optical Beam Expander, AR Coated: 650 - 1050 nm 483.00 Lead Time BE03M-C 3X Optical Beam Expander, AR Coated: 1050 - 1620 nm 483.00 3-5 Days. Hide 5X Optical Beam Expanders. 5X Optical Beam Expanders. Ite
